Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.
The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:
- Immediately to the left;
- Immediate to the right;
- Second to the left; or
- Second to the right.
The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.
<img src="https://balti.aftergrad.in/questions/DQelrQtQGhURYSi" width="500px"/>
Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.
The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:
- Immediately to the left;
- Immediate to the right;
- Second to the left; or
- Second to the right.
The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.
<img src="https://balti.aftergrad.in/questions/DQelrQtQGhURYSi" width="500px"/>
Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.
The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:
- Immediately to the left;
- Immediate to the right;
- Second to the left; or
- Second to the right.
The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.
<img src="https://balti.aftergrad.in/questions/DQelrQtQGhURYSi" width="500px"/>
For which of the following pass types can the total number of occurrences be uniquely determined?
Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.
The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:
- Immediately to the left;
- Immediate to the right;
- Second to the left; or
- Second to the right.
The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.
<img src="https://balti.aftergrad.in/questions/DQelrQtQGhURYSi" width="500px"/>
For which of the following children is it possible to determine how many times they received the Buck?
Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.
In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.
The following additional facts are known.
1. Ustad Samiran never trained more than one of these students in the same year.
2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.
In which of the following years were Ananya and Bhaskar Gurubhai?
Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.
In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.
The following additional facts are known.
1. Ustad Samiran never trained more than one of these students in the same year.
2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.
In which year did Charu begin her training under Pandit Meghnath?
Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.
In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.
The following additional facts are known.
1. Ustad Samiran never trained more than one of these students in the same year.
2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.
In which of the following years were Bhaskar and Devendra Gurubhai?
Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.
In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.
The following additional facts are known.
1. Ustad Samiran never trained more than one of these students in the same year.
2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.
Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.
In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.
The following additional facts are known.
1. Ustad Samiran never trained more than one of these students in the same year.
2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.
In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?
A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known.
1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
What is the number of the chair initially occupied by Bashir?
A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known.
1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
Who sits on the chair numbered 4 at the end of Turn 3?
A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known.
1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
Which of the chairs are occupied at the end of Turn 6?
A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known.
1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below. $$\newline$$ <img src="https://balti.aftergrad.in/questions/Fi8IYM3FtUnADAb" width="400px"/> $$\newline$$ <ol><li>Numbers in any row appear in an increasing order from left to right. $$\newline$$ </li><li>Numbers in any column appear in a decreasing order from top to bottom. $$\newline$$ </li><li>1 is placed either in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 2 nor 3 is placed in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 7 nor 8 is placed in the same row or in the same column as 9. $$\newline$$ </li><li>4 and 6 are placed in the same row.</li></ol>
What is the row number which has the least sum of numbers placed in that row?
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below. $$\newline$$ <img src="https://balti.aftergrad.in/questions/Fi8IYM3FtUnADAb" width="400px"/> $$\newline$$ <ol><li>Numbers in any row appear in an increasing order from left to right. $$\newline$$ </li><li>Numbers in any column appear in a decreasing order from top to bottom. $$\newline$$ </li><li>1 is placed either in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 2 nor 3 is placed in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 7 nor 8 is placed in the same row or in the same column as 9. $$\newline$$ </li><li>4 and 6 are placed in the same row.</li></ol>
Which of the following statements MUST be true?<br><br>I. 10 is placed in a slot in Row 1.<br>II. 1 is placed in a slot in Row 4.
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below. $$\newline$$ <img src="https://balti.aftergrad.in/questions/Fi8IYM3FtUnADAb" width="400px"/> $$\newline$$ <ol><li>Numbers in any row appear in an increasing order from left to right. $$\newline$$ </li><li>Numbers in any column appear in a decreasing order from top to bottom. $$\newline$$ </li><li>1 is placed either in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 2 nor 3 is placed in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 7 nor 8 is placed in the same row or in the same column as 9. $$\newline$$ </li><li>4 and 6 are placed in the same row.</li></ol>
Which of the following statements MUST be true? $$\newline$$ I. $2$ is placed in a slot in Column $2$. $$\newline$$ II. $3$ is placed in a slot in Column $3$.
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below. $$\newline$$ <img src="https://balti.aftergrad.in/questions/Fi8IYM3FtUnADAb" width="400px"/> $$\newline$$ <ol><li>Numbers in any row appear in an increasing order from left to right. $$\newline$$ </li><li>Numbers in any column appear in a decreasing order from top to bottom. $$\newline$$ </li><li>1 is placed either in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 2 nor 3 is placed in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 7 nor 8 is placed in the same row or in the same column as 9. $$\newline$$ </li><li>4 and 6 are placed in the same row.</li></ol>
For how many slots in the grid, placement of numbers CANNOT be determined with certainty?
The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below. $$\newline$$ <img src="https://balti.aftergrad.in/questions/Fi8IYM3FtUnADAb" width="400px"/> $$\newline$$ <ol><li>Numbers in any row appear in an increasing order from left to right. $$\newline$$ </li><li>Numbers in any column appear in a decreasing order from top to bottom. $$\newline$$ </li><li>1 is placed either in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 2 nor 3 is placed in the same row or in the same column as 10. $$\newline$$ </li><li>Neither 7 nor 8 is placed in the same row or in the same column as 9. $$\newline$$ </li><li>4 and 6 are placed in the same row.</li></ol>
What is the sum of the numbers placed in Column 4?
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest. $$\newline$$ The following additional information is known. $$\newline$$ <ol> $\newline$ <li>Xena trained more players than Yuki.</li> $$\newline$$ <li>Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.</li> $$\newline$$ <li>Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.</li> $$\newline$$ <li>The average of the ratings of all the players was 4.</li> $$\newline$$ <li>Player-2 got the highest rating.</li> $$\newline$$ <li>The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.</li> $$\newline$$ <li>Player-4's rating was double of Player-8's and less than Player-5's.</li> $\newline$ </ol>
What best can be concluded about the number of players coached by Zara?
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest. $$\newline$$ The following additional information is known. $$\newline$$ <ol> $\newline$ <li>Xena trained more players than Yuki.</li> $$\newline$$ <li>Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.</li> $$\newline$$ <li>Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.</li> $$\newline$$ <li>The average of the ratings of all the players was 4.</li> $$\newline$$ <li>Player-2 got the highest rating.</li> $$\newline$$ <li>The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.</li> $$\newline$$ <li>Player-4's rating was double of Player-8's and less than Player-5's.</li> $\newline$ </ol>
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest. $$\newline$$ The following additional information is known. $$\newline$$ <ol> $\newline$ <li>Xena trained more players than Yuki.</li> $$\newline$$ <li>Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.</li> $$\newline$$ <li>Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.</li> $$\newline$$ <li>The average of the ratings of all the players was 4.</li> $$\newline$$ <li>Player-2 got the highest rating.</li> $$\newline$$ <li>The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.</li> $$\newline$$ <li>Player-4's rating was double of Player-8's and less than Player-5's.</li> $\newline$ </ol>
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest. $$\newline$$ The following additional information is known. $$\newline$$ <ol> $\newline$ <li>Xena trained more players than Yuki.</li> $$\newline$$ <li>Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.</li> $$\newline$$ <li>Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.</li> $$\newline$$ <li>The average of the ratings of all the players was 4.</li> $$\newline$$ <li>Player-2 got the highest rating.</li> $$\newline$$ <li>The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.</li> $$\newline$$ <li>Player-4's rating was double of Player-8's and less than Player-5's.</li> $\newline$ </ol>
For how many players the ratings can be determined with certainty?
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest. $$\newline$$ The following additional information is known. $$\newline$$ <ol> $\newline$ <li>Xena trained more players than Yuki.</li> $$\newline$$ <li>Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.</li> $$\newline$$ <li>Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.</li> $$\newline$$ <li>The average of the ratings of all the players was 4.</li> $$\newline$$ <li>Player-2 got the highest rating.</li> $$\newline$$ <li>The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.</li> $$\newline$$ <li>Player-4's rating was double of Player-8's and less than Player-5's.</li> $\newline$ </ol>
An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant. $$\newline$$ <p>The following information is also known:</p> $$\newline$$ <ol> $\newline$ <li>Every dealer sold at least two window ACs.</li> $$\newline$$ <li>D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.</li> $$\newline$$ <li>A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.</li> $$\newline$$ <li>The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.</li> $$\newline$$ <li>D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.</li> $\newline$ </ol>
An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant. $$\newline$$ <p>The following information is also known:</p> $$\newline$$ <ol> $\newline$ <li>Every dealer sold at least two window ACs.</li> $$\newline$$ <li>D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.</li> $$\newline$$ <li>A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.</li> $$\newline$$ <li>The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.</li> $$\newline$$ <li>D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.</li> $\newline$ </ol>
What percentage of ACs sold were of Non-Inverter type?
An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant. $$\newline$$ <p>The following information is also known:</p> $$\newline$$ <ol> $\newline$ <li>Every dealer sold at least two window ACs.</li> $$\newline$$ <li>D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.</li> $$\newline$$ <li>A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.</li> $$\newline$$ <li>The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.</li> $$\newline$$ <li>D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.</li> $\newline$ </ol>
What was the total number of ACs sold by D2 and D4?.
An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant. $$\newline$$ <p>The following information is also known:</p> $$\newline$$ <ol> $\newline$ <li>Every dealer sold at least two window ACs.</li> $$\newline$$ <li>D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.</li> $$\newline$$ <li>A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.</li> $$\newline$$ <li>The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.</li> $$\newline$$ <li>D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.</li> $\newline$ </ol>
Which of the following statements is necessarily false? $\newline$ A) D1 and D3 together sold more ACs as compared to D2 and D4 together. $\newline$ B) D4 sold more Split ACs as compared to D3. $\newline$ C) D2 sold the highest number of ACs. $\newline$ D) D1 and D3 sold an equal number of Split ACs.
An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant. $$\newline$$ <p>The following information is also known:</p> $$\newline$$ <ol> $\newline$ <li>Every dealer sold at least two window ACs.</li> $$\newline$$ <li>D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.</li> $$\newline$$ <li>A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.</li> $$\newline$$ <li>The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.</li> $$\newline$$ <li>D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.</li> $$\newline$$ <li>D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.</li> $\newline$ </ol>
If D3 and D4 sold an equal number of ACs, then what was the number of Non-Inverter ACs sold by D2?
Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.
| Firm | First year of existence | Last year of existence | Total amount raised (Rs. crores) |
|------|-------------------------|------------------------|-----------------------------------|
| Alfloo | 2009 | 2016 | 21 |
| Bzygoo | 2012 | 2015 | |
| Czechy | 2013 | | 9 |
| Drjbna | 2011 | 2015 | 10 |
| Elavalaki | 2010 | | 13 |
For which firm(s) can the amounts raised by them be concluded with certainty in each year?
Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.
| Firm | First year of existence | Last year of existence | Total amount raised (Rs. crores) |
|------|-------------------------|------------------------|-----------------------------------|
| Alfloo | 2009 | 2016 | 21 |
| Bzygoo | 2012 | 2015 | |
| Czechy | 2013 | | 9 |
| Drjbna | 2011 | 2015 | 10 |
| Elavalaki | 2010 | | 13 |
What best can be concluded about the total amount of money raised in 2015?
Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.
| Firm | First year of existence | Last year of existence | Total amount raised (Rs. crores) |
|------|-------------------------|------------------------|-----------------------------------|
| Alfloo | 2009 | 2016 | 21 |
| Bzygoo | 2012 | 2015 | |
| Czechy | 2013 | | 9 |
| Drjbna | 2011 | 2015 | 10 |
| Elavalaki | 2010 | | 13 |
What is the largest possible total amount of money (in Rs. crores) that could have been raised in $2013$?
Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.
| Firm | First year of existence | Last year of existence | Total amount raised (Rs. crores) |
|------|-------------------------|------------------------|-----------------------------------|
| Alfloo | 2009 | 2016 | 21 |
| Bzygoo | 2012 | 2015 | |
| Czechy | 2013 | | 9 |
| Drjbna | 2011 | 2015 | 10 |
| Elavalaki | 2010 | | 13 |
If Elavalaki raised Rs. 3 crores in 2013, then what is the smallest possible total amount of money (in Rs. crores) that could have been raised by all the companies in 2012?
Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.
| Firm | First year of existence | Last year of existence | Total amount raised (Rs. crores) |
|------|-------------------------|------------------------|-----------------------------------|
| Alfloo | 2009 | 2016 | 21 |
| Bzygoo | 2012 | 2015 | |
| Czechy | 2013 | | 9 |
| Drjbna | 2011 | 2015 | 10 |
| Elavalaki | 2010 | | 13 |
If the total amount of money raised in $2014$ is Rs. $12$ crores, then which of the following is not possible?
Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9, both inclusive. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants' scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Table 1: 2-day averages for Days 2<br>through 5</th><th></th><th></th><th></th><th></th></tr><tr><th></th><th>Day 2</th><th>Day 3</th><th>Day 4</th><th>Day 5</th></tr></thead><tbody><tr><td></td><td>15</td><td>15.5</td><td>16</td><td>17</td></tr></tbody></table><br> $$\newline$$ Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Table 2: Ranks of participants on each day</th><th></th><th></th><th></th><th></th><th></th></tr><tr><th></th><th>Day 1</th><th>Day 2</th><th>Day 3</th><th>Day 4</th><th>Day 5</th></tr></thead><tbody><tr><td>Akhil</td><td>1</td><td>2</td><td>2</td><td>3</td><td>3</td></tr><tr><td>Bimal</td><td>2</td><td>3</td><td>2</td><td>1</td><td>1</td></tr><tr><td>Chatur</td><td>3</td><td>1</td><td>1</td><td>2</td><td>2</td></tr></tbody></table><br> $$\newline$$ The following information is also known.<br><ol> $$\newline$$ <li>Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil's score on Day 4.</li> $$\newline$$ <li>The total score on Day 3 is the same as the total score on Day 4.</li> $$\newline$$ <li>Bimal's scores are the same on Day 1 and Day 3.</li></ol>
What is the minimum possible total score of Bimal?
Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9, both inclusive. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants' scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Table 1: 2-day averages for Days 2<br>through 5</th><th></th><th></th><th></th><th></th></tr><tr><th></th><th>Day 2</th><th>Day 3</th><th>Day 4</th><th>Day 5</th></tr></thead><tbody><tr><td></td><td>15</td><td>15.5</td><td>16</td><td>17</td></tr></tbody></table><br> $$\newline$$ Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Table 2: Ranks of participants on each day</th><th></th><th></th><th></th><th></th><th></th></tr><tr><th></th><th>Day 1</th><th>Day 2</th><th>Day 3</th><th>Day 4</th><th>Day 5</th></tr></thead><tbody><tr><td>Akhil</td><td>1</td><td>2</td><td>2</td><td>3</td><td>3</td></tr><tr><td>Bimal</td><td>2</td><td>3</td><td>2</td><td>1</td><td>1</td></tr><tr><td>Chatur</td><td>3</td><td>1</td><td>1</td><td>2</td><td>2</td></tr></tbody></table><br> $$\newline$$ The following information is also known.<br><ol> $$\newline$$ <li>Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil's score on Day 4.</li> $$\newline$$ <li>The total score on Day 3 is the same as the total score on Day 4.</li> $$\newline$$ <li>Bimal's scores are the same on Day 1 and Day 3.</li></ol>
If the total score of Bimal is a multiple of 3, what is the score of Akhil on Day 2?
Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. $$\newline$$ Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. $$\newline$$ Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below. $$\newline$$ <ol> $\newline$ <li>There cannot be more than two candidates from a single department.</li> $$\newline$$ <li>A candidate cannot vote for himself/herself.</li> $$\newline$$ <li>Faculty members cannot vote for a candidate from their own department.</li> $\newline$ </ol> $$\newline$$ After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Which two candidates can belong to the same department?
Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. $$\newline$$ Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. $$\newline$$ Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below. $$\newline$$ <ol> $\newline$ <li>There cannot be more than two candidates from a single department.</li> $$\newline$$ <li>A candidate cannot vote for himself/herself.</li> $$\newline$$ <li>Faculty members cannot vote for a candidate from their own department.</li> $\newline$ </ol> $$\newline$$ After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Which of the following can be the number of votes that Prof. Qureshi received from a single department?
Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. $$\newline$$ Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. $$\newline$$ Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below. $$\newline$$ <ol> $\newline$ <li>There cannot be more than two candidates from a single department.</li> $$\newline$$ <li>A candidate cannot vote for himself/herself.</li> $$\newline$$ <li>Faculty members cannot vote for a candidate from their own department.</li> $\newline$ </ol> $$\newline$$ After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
If Prof. Samuel belongs to B&H, which of the following statements is/are true? $$\newline$$ Statement A: Prof. Pakrasi belongs to M&S. $\newline$ Statement B: Prof. Ramaswamy belongs to O&Q.
Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. $$\newline$$ Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. $$\newline$$ Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below. $$\newline$$ <ol> $\newline$ <li>There cannot be more than two candidates from a single department.</li> $$\newline$$ <li>A candidate cannot vote for himself/herself.</li> $$\newline$$ <li>Faculty members cannot vote for a candidate from their own department.</li> $\newline$ </ol> $$\newline$$ After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
What best can be concluded about the candidate from $\mathrm{O} \& \mathrm{Q}$ ?
Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively. $$\newline$$ Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q. $$\newline$$ Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below. $$\newline$$ <ol> $\newline$ <li>There cannot be more than two candidates from a single department.</li> $$\newline$$ <li>A candidate cannot vote for himself/herself.</li> $$\newline$$ <li>Faculty members cannot vote for a candidate from their own department.</li> $\newline$ </ol> $$\newline$$ After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Which of the following statements is/are true? $$\newline$$ Statement A: Non-candidates from M&S voted for Prof. Qureshi. $\newline$ Statement B: Non-candidates from F&A voted for Prof. Qureshi.
There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0, 1, 2 or 3. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There was at least one new case in every neighbourhood on Day 1.</li> $$\newline$$ <li>On each of the five days, there were more new cases in Kitmisto than in Pesmisto.</li> $$\newline$$ <li>The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.</li> $$\newline$$ <li>The maximum number of new cases in a day in Pesmisto was 2, and this happened only once during the five-day period.</li> $$\newline$$ <li>Kitmisto is the only place to have 3 new cases on Day 2.</li> $$\newline$$ <li>The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were 12, 12, 5 and 14 respectively.</li> $$\newline$$ </ol>
What BEST can be concluded about the total number of new cases in the Levmisto on Day 2?
There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0, 1, 2 or 3. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There was at least one new case in every neighbourhood on Day 1.</li> $$\newline$$ <li>On each of the five days, there were more new cases in Kitmisto than in Pesmisto.</li> $$\newline$$ <li>The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.</li> $$\newline$$ <li>The maximum number of new cases in a day in Pesmisto was 2, and this happened only once during the five-day period.</li> $$\newline$$ <li>Kitmisto is the only place to have 3 new cases on Day 2.</li> $$\newline$$ <li>The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were 12, 12, 5 and 14 respectively.</li> $$\newline$$ </ol>
What BEST can be concluded about the number of new cases in Levmisto on Day 3?
There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0, 1, 2 or 3. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There was at least one new case in every neighbourhood on Day 1.</li> $$\newline$$ <li>On each of the five days, there were more new cases in Kitmisto than in Pesmisto.</li> $$\newline$$ <li>The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.</li> $$\newline$$ <li>The maximum number of new cases in a day in Pesmisto was 2, and this happened only once during the five-day period.</li> $$\newline$$ <li>Kitmisto is the only place to have 3 new cases on Day 2.</li> $$\newline$$ <li>The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were 12, 12, 5 and 14 respectively.</li> $$\newline$$ </ol>
There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0, 1, 2 or 3. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There was at least one new case in every neighbourhood on Day 1.</li> $$\newline$$ <li>On each of the five days, there were more new cases in Kitmisto than in Pesmisto.</li> $$\newline$$ <li>The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.</li> $$\newline$$ <li>The maximum number of new cases in a day in Pesmisto was 2, and this happened only once during the five-day period.</li> $$\newline$$ <li>Kitmisto is the only place to have 3 new cases on Day 2.</li> $$\newline$$ <li>The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were 12, 12, 5 and 14 respectively.</li> $$\newline$$ </ol>
Which of the two statements below is/are necessarily false? $$\newline$$ Statement A: There were 2 new cases in Tyhrmisto on Day 3. $$\newline$$ Statement B: There were no new cases in Pesmisto on Day 2.
There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0, 1, 2 or 3. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There was at least one new case in every neighbourhood on Day 1.</li> $$\newline$$ <li>On each of the five days, there were more new cases in Kitmisto than in Pesmisto.</li> $$\newline$$ <li>The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.</li> $$\newline$$ <li>The maximum number of new cases in a day in Pesmisto was 2, and this happened only once during the five-day period.</li> $$\newline$$ <li>Kitmisto is the only place to have 3 new cases on Day 2.</li> $$\newline$$ <li>The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were 12, 12, 5 and 14 respectively.</li> $$\newline$$ </ol>
On how many days did Levmisto and Tyhrmisto have the same number of new cases?
The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals. $$\newline$$ The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players. $$\newline$$ <ol> $\newline$ <li>Only one goal was scored in every even numbered match.</li> $$\newline$$ <li>Harita scored more goals than Bimla.</li> $$\newline$$ <li>The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.</li> $$\newline$$ <li>Bimla scored a goal in Match 1 and one each in three other consecutive matches.</li> $$\newline$$ <li>An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.</li> $$\newline$$ <li>The match in which the highest number of goals was scored was unique and it was not Match 5.</li> $\newline$ </ol>
The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals. $$\newline$$ The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players. $$\newline$$ <ol> $\newline$ <li>Only one goal was scored in every even numbered match.</li> $$\newline$$ <li>Harita scored more goals than Bimla.</li> $$\newline$$ <li>The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.</li> $$\newline$$ <li>Bimla scored a goal in Match 1 and one each in three other consecutive matches.</li> $$\newline$$ <li>An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.</li> $$\newline$$ <li>The match in which the highest number of goals was scored was unique and it was not Match 5.</li> $\newline$ </ol>
Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?
The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals. $$\newline$$ The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players. $$\newline$$ <ol> $\newline$ <li>Only one goal was scored in every even numbered match.</li> $$\newline$$ <li>Harita scored more goals than Bimla.</li> $$\newline$$ <li>The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.</li> $$\newline$$ <li>Bimla scored a goal in Match 1 and one each in three other consecutive matches.</li> $$\newline$$ <li>An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.</li> $$\newline$$ <li>The match in which the highest number of goals was scored was unique and it was not Match 5.</li> $\newline$ </ol>
Which of the following statement(s) is/are true? $$\newline$$ Statement-1: Amla and Sarita never scored goals in the same match. $$\newline$$ Statement-2: Harita and Sarita never scored goals in the same match.
The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals. $$\newline$$ The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players. $$\newline$$ <ol> $\newline$ <li>Only one goal was scored in every even numbered match.</li> $$\newline$$ <li>Harita scored more goals than Bimla.</li> $$\newline$$ <li>The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.</li> $$\newline$$ <li>Bimla scored a goal in Match 1 and one each in three other consecutive matches.</li> $$\newline$$ <li>An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.</li> $$\newline$$ <li>The match in which the highest number of goals was scored was unique and it was not Match 5.</li> $\newline$ </ol>
Which of the following statement(s) is/are false? $$\newline$$ Statement-1: In every match at least one player scored a goal. $$\newline$$ Statement-2: No two players scored goals in the same number of matches.
The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals. $$\newline$$ The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players. $$\newline$$ <ol> $\newline$ <li>Only one goal was scored in every even numbered match.</li> $$\newline$$ <li>Harita scored more goals than Bimla.</li> $$\newline$$ <li>The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.</li> $$\newline$$ <li>Bimla scored a goal in Match 1 and one each in three other consecutive matches.</li> $$\newline$$ <li>An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.</li> $$\newline$$ <li>The match in which the highest number of goals was scored was unique and it was not Match 5.</li> $\newline$ </ol>
If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true? $$\newline$$ Statement-1: Amla scored goals in consecutive matches. $$\newline$$ Statement-2: Sarita scored goals in consecutive matches.
Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only. $$\newline$$ Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000. $$\newline$$ Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000. $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.</li> $$\newline$$ <li>Rasheeda received the highest number of tokens that anyone received, but she did not receive one from Esther.</li> $$\newline$$ <li>Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.</li> $\newline$ </ol>
Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only. $$\newline$$ Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000. $$\newline$$ Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000. $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.</li> $$\newline$$ <li>Rasheeda received the highest number of tokens that anyone received, but she did not receive one from Esther.</li> $$\newline$$ <li>Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.</li> $\newline$ </ol>
Who among the following definitely received a token from Bithi but not from Dhanavi
Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only. $$\newline$$ Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000. $$\newline$$ Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000. $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.</li> $$\newline$$ <li>Rasheeda received the highest number of tokens that anyone received, but she did not receive one from Esther.</li> $$\newline$$ <li>Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.</li> $\newline$ </ol>
Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only. $$\newline$$ Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000. $$\newline$$ Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000. $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.</li> $$\newline$$ <li>Rasheeda received the highest number of tokens that anyone received, but she did not receive one from Esther.</li> $$\newline$$ <li>Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.</li> $\newline$ </ol>
Adhara, Bithi, Chhaya, Dhanavi, Esther, and Fathima are the interviewers in a process that awards funding for new initiatives. Every interviewer individually interviews each of the candidates individually and awards a token only if she recommends funding. A token has a face value of 2, 3, 5, 7, 11, or 13. Each interviewer awards tokens of a single face value only. $$\newline$$ Once all six interviews are over for a candidate, the candidate receives a funding that is Rs.1000 times the product of the face values of all the tokens. For example, if a candidate has tokens with face values 2, 5, and 7, then they get a funding of Rs.1000 × (2 × 5 × 7) = Rs.70,000. $$\newline$$ Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000. $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>Fathima awarded tokens to everyone except Qahira, while Adhara awarded tokens to no one except Pragnyaa.</li> $$\newline$$ <li>Rasheeda received the highest number of tokens that anyone received, but she did not receive one from Esther.</li> $$\newline$$ <li>Bithi awarded a token to Smera but not to Qahira, while Dhanavi awarded a token to Qahira but not to Smera.</li> $\newline$ </ol>
Which of the following could be the amount of funding that Tantra received? $$\newline$$ (a) Rs. $66,000$ $$\newline$$ (b) Rs. $165,000$
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer. $$\newline$$ Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.</li> $$\newline$$ <li>Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.</li> $$\newline$$ <li>70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.</li> $$\newline$$ <li>No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.</li> $$\newline$$ <li>The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.</li> $\newline$ </ol>
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer. $$\newline$$ Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.</li> $$\newline$$ <li>Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.</li> $$\newline$$ <li>70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.</li> $$\newline$$ <li>No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.</li> $$\newline$$ <li>The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.</li> $\newline$ </ol>
Which of the following can be determined from the given information? $$\newline$$ I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers. $$\newline$$ II. The number of female dancers who are interested in attending a 1-day event.
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer. $$\newline$$ Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.</li> $$\newline$$ <li>Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.</li> $$\newline$$ <li>70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.</li> $$\newline$$ <li>No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.</li> $$\newline$$ <li>The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.</li> $\newline$ </ol>
What fraction of the class are interested in attending a 2-day event?
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer. $$\newline$$ Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.</li> $$\newline$$ <li>Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.</li> $$\newline$$ <li>70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.</li> $$\newline$$ <li>No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.</li> $$\newline$$ <li>The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.</li> $\newline$ </ol>
What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer. $$\newline$$ Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.</li> $$\newline$$ <li>Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.</li> $$\newline$$ <li>70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.</li> $$\newline$$ <li>No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.</li> $$\newline$$ <li>The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.</li> $\newline$ </ol>
How many female dancers are interested in attending a 2-day event?
10 players - P1, P2, ..., P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1,2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of around is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round. $$\newline$$ In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively. $$\newline$$ All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event. $$\newline$$ Distances covered by all the valid throws in the first round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>82.9</td></tr><tr><td>P3</td><td>81.5</td></tr><tr><td>P5</td><td>86.4</td></tr><tr><td>P6</td><td>82.5</td></tr><tr><td>P7</td><td>87.2</td></tr><tr><td>P9</td><td>84.1</td></tr></tbody></table> $$\newline$$ Distances covered by all the valid throws in the third round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>88.6</td></tr><tr><td>P3</td><td>79.0</td></tr><tr><td>P9</td><td>81.4</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal. $$\newline$$ ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double. $$\newline$$ iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount. $$\newline$$ iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round. $$\newline$$ v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was $1.0$ m.
10 players - P1, P2, ..., P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1,2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of around is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round. $$\newline$$ In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively. $$\newline$$ All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event. $$\newline$$ Distances covered by all the valid throws in the first round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>82.9</td></tr><tr><td>P3</td><td>81.5</td></tr><tr><td>P5</td><td>86.4</td></tr><tr><td>P6</td><td>82.5</td></tr><tr><td>P7</td><td>87.2</td></tr><tr><td>P9</td><td>84.1</td></tr></tbody></table> $$\newline$$ Distances covered by all the valid throws in the third round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>88.6</td></tr><tr><td>P3</td><td>79.0</td></tr><tr><td>P9</td><td>81.4</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal. $$\newline$$ ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double. $$\newline$$ iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount. $$\newline$$ iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round. $$\newline$$ v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was $1.0$ m.
10 players - P1, P2, ..., P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1,2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of around is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round. $$\newline$$ In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively. $$\newline$$ All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event. $$\newline$$ Distances covered by all the valid throws in the first round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>82.9</td></tr><tr><td>P3</td><td>81.5</td></tr><tr><td>P5</td><td>86.4</td></tr><tr><td>P6</td><td>82.5</td></tr><tr><td>P7</td><td>87.2</td></tr><tr><td>P9</td><td>84.1</td></tr></tbody></table> $$\newline$$ Distances covered by all the valid throws in the third round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>88.6</td></tr><tr><td>P3</td><td>79.0</td></tr><tr><td>P9</td><td>81.4</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal. $$\newline$$ ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double. $$\newline$$ iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount. $$\newline$$ iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round. $$\newline$$ v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was $1.0$ m.
10 players - P1, P2, ..., P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1,2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of around is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round. $$\newline$$ In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively. $$\newline$$ All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event. $$\newline$$ Distances covered by all the valid throws in the first round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>82.9</td></tr><tr><td>P3</td><td>81.5</td></tr><tr><td>P5</td><td>86.4</td></tr><tr><td>P6</td><td>82.5</td></tr><tr><td>P7</td><td>87.2</td></tr><tr><td>P9</td><td>84.1</td></tr></tbody></table> $$\newline$$ Distances covered by all the valid throws in the third round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>88.6</td></tr><tr><td>P3</td><td>79.0</td></tr><tr><td>P9</td><td>81.4</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal. $$\newline$$ ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double. $$\newline$$ iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount. $$\newline$$ iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round. $$\newline$$ v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was $1.0$ m.
What was the final score (in m) of the silver-medalist?
10 players - P1, P2, ..., P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1,2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of around is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round. $$\newline$$ In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively. $$\newline$$ All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event. $$\newline$$ Distances covered by all the valid throws in the first round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>82.9</td></tr><tr><td>P3</td><td>81.5</td></tr><tr><td>P5</td><td>86.4</td></tr><tr><td>P6</td><td>82.5</td></tr><tr><td>P7</td><td>87.2</td></tr><tr><td>P9</td><td>84.1</td></tr></tbody></table> $$\newline$$ Distances covered by all the valid throws in the third round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>88.6</td></tr><tr><td>P3</td><td>79.0</td></tr><tr><td>P9</td><td>81.4</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal. $$\newline$$ ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double. $$\newline$$ iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount. $$\newline$$ iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round. $$\newline$$ v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was $1.0$ m.
Which of the following can be the final score (in m) of P8?
10 players - P1, P2, ..., P10 - competed in an international javelin throw event. The number (after P) of a player reflects his rank at the beginning of the event, with rank 1 going to the topmost player. There were two phases in the event with the first phase consisting of rounds 1,2, and 3, and the second phase consisting of rounds 4, 5, and 6. A throw is measured in terms of the distance it covers (in meters, up to one decimal point accuracy), only if the throw is a 'valid' one. For an invalid throw, the distance is taken as zero. A player's score at the end of around is the maximum distance of all his throws up to that round. Players are re-ranked after every round based on their current scores. In case of a tie in scores, the player with a prevailing higher rank retains the higher rank. This ranking determines the order in which the players go for their throws in the next round. $$\newline$$ In each of the rounds in the first phase, the players throw in increasing order of their latest rank, i.e. the player ranked 1 at that point throws first, followed by the player ranked 2 at that point and so on. The top six players at the end of the first phase qualify for the second phase. In each of the rounds in the second phase, the players throw in decreasing order of their latest rank i.e. the player ranked 6 at that point throws first, followed by the player ranked 5 at that point and so on. The players ranked 1, 2, and 3 at the end of the sixth round receive gold, silver, and bronze medals respectively. $$\newline$$ All the valid throws of the event were of distinct distances (as per stated measurement accuracy). The tables below show distances (in meters) covered by all valid throws in the first and the third round in the event. $$\newline$$ Distances covered by all the valid throws in the first round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>82.9</td></tr><tr><td>P3</td><td>81.5</td></tr><tr><td>P5</td><td>86.4</td></tr><tr><td>P6</td><td>82.5</td></tr><tr><td>P7</td><td>87.2</td></tr><tr><td>P9</td><td>84.1</td></tr></tbody></table> $$\newline$$ Distances covered by all the valid throws in the third round $\newline$ <table class="question-table"><thead><tr><th>Player</th><th>Distance (in m)</th></tr></thead><tbody><tr><td>P1</td><td>88.6</td></tr><tr><td>P3</td><td>79.0</td></tr><tr><td>P9</td><td>81.4</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ i. Among the throws in the second round, only the last two were valid. Both the throws enabled these players to qualify for the second phase, with one of them qualifying with the least score. None of these players won any medal. $$\newline$$ ii. If a player throws first in a round AND he was also the last (among the players in the current round) to throw in the previous round, then the player is said to get a double. Two players got a double. $$\newline$$ iii. In each round of the second phase, exactly one player improved his score. Each of these improvements was by the same amount. $$\newline$$ iv. The gold and bronze medalists improved their scores in the fifth and the sixth rounds respectively. One medal winner improved his score in the fourth round. $$\newline$$ v. The difference between the final scores of the gold medalist and the silver medalist, as well as the difference between the final scores of the silver medalist and the bronze medalist was $1.0$ m.
By how much did the gold medalist improve his score (in m) in the second phase?
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below. $$\newline$$ If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it. $$\newline$$ A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal. $$\newline$$ The following facts are also known. $$\newline$$ <ol> $\newline$ <li>Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.</li> $$\newline$$ <li>Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.</li> $$\newline$$ <li>Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.</li> $$\newline$$ <li>Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.</li> $\newline$ </ol>
How many questions were DEFINITELY created by Amal?
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below. $$\newline$$ If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it. $$\newline$$ A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal. $$\newline$$ The following facts are also known. $$\newline$$ <ol> $\newline$ <li>Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.</li> $$\newline$$ <li>Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.</li> $$\newline$$ <li>Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.</li> $$\newline$$ <li>Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.</li> $\newline$ </ol>
How many questions were DEFINITELY created by Komal?
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below. $$\newline$$ If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it. $$\newline$$ A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal. $$\newline$$ The following facts are also known. $$\newline$$ <ol> $\newline$ <li>Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.</li> $$\newline$$ <li>Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.</li> $$\newline$$ <li>Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.</li> $$\newline$$ <li>Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.</li> $\newline$ </ol>
How many questions were DEFINITELY created by the SMEs?
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below. $$\newline$$ If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it. $$\newline$$ A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal. $$\newline$$ The following facts are also known. $$\newline$$ <ol> $\newline$ <li>Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.</li> $$\newline$$ <li>Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.</li> $$\newline$$ <li>Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.</li> $$\newline$$ <li>Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.</li> $\newline$ </ol>
How many questions were DEFINITELY disapproved by Bimal?
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below. $$\newline$$ If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it. $$\newline$$ A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal. $$\newline$$ The following facts are also known. $$\newline$$ <ol> $\newline$ <li>Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.</li> $$\newline$$ <li>Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.</li> $$\newline$$ <li>Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.</li> $$\newline$$ <li>Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.</li> $\newline$ </ol>
The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he reviewed. Which option best describes Amal's approval ratio?
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external "subject matter experts" (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below. $$\newline$$ If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it. $$\newline$$ A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal. $$\newline$$ The following facts are also known. $$\newline$$ <ol> $\newline$ <li>Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.</li> $$\newline$$ <li>Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.</li> $$\newline$$ <li>Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.</li> $$\newline$$ <li>Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.</li> $\newline$ </ol>
How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?
Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table. $$\newline$$ <table class="question-table"> <thead> <tr> <th>Finished product</th> <th>Raw materials required</th> </tr> </thead> <tbody> <tr> <td>Mango smoothie</td> <td>Mango, Milk</td> </tr> <tr> <td>Apple smoothie</td> <td>Apple, Milk</td> </tr> <tr> <td>Banana smoothie</td> <td>Banana, Milk</td> </tr> <tr> <td>Mixed fruit smoothie</td> <td>Mango, Apple, Banana, Milk</td> </tr> <tr> <td>Fruit salad</td> <td>Mango, Apple, Banana</td> </tr> </tbody> </table> $\newline$ <br> $\newline$ One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit. $$\newline$$ The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2. $$\newline$$ <table class="question-table"> <thead> <tr> <th>Business Hour</th> <th>Ganga</th> <th>Kaveri</th> <th>Narmada</th> </tr> </thead> <tbody> <tr> <td>Hour 1</td> <td>23</td> <td>19</td> <td>31</td> </tr> <tr> <td>Hour 2</td> <td>21</td> <td>22</td> <td>21</td> </tr> <tr> <td>Hour 3</td> <td>29</td> <td>30</td> <td>23</td> </tr> <tr> <td>Hour 4 (last hour)</td> <td>30</td> <td>27</td> <td>22</td> </tr> </tbody> </table> $$\newline$$ The following additional facts are known. $$\newline$$ <li>No one except possibly Ganga sold any Mango smoothie.</li> $$\newline$$ <li>Each woman sold either zero or one unit of any single finished product in any hour.</li> $$\newline$$ <li>Each woman had exactly one unit each of two different raw materials as leftovers.</li> $$\newline$$ <li>No one had any banana leftover.</li> $$\newline$$ </ol>
What BEST can be concluded about the number of units of fruit salad sold in the first hour?
Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table. $$\newline$$ <table class="question-table"> <thead> <tr> <th>Finished product</th> <th>Raw materials required</th> </tr> </thead> <tbody> <tr> <td>Mango smoothie</td> <td>Mango, Milk</td> </tr> <tr> <td>Apple smoothie</td> <td>Apple, Milk</td> </tr> <tr> <td>Banana smoothie</td> <td>Banana, Milk</td> </tr> <tr> <td>Mixed fruit smoothie</td> <td>Mango, Apple, Banana, Milk</td> </tr> <tr> <td>Fruit salad</td> <td>Mango, Apple, Banana</td> </tr> </tbody> </table> $\newline$ <br> $\newline$ One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit. $$\newline$$ The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2. $$\newline$$ <table class="question-table"> <thead> <tr> <th>Business Hour</th> <th>Ganga</th> <th>Kaveri</th> <th>Narmada</th> </tr> </thead> <tbody> <tr> <td>Hour 1</td> <td>23</td> <td>19</td> <td>31</td> </tr> <tr> <td>Hour 2</td> <td>21</td> <td>22</td> <td>21</td> </tr> <tr> <td>Hour 3</td> <td>29</td> <td>30</td> <td>23</td> </tr> <tr> <td>Hour 4 (last hour)</td> <td>30</td> <td>27</td> <td>22</td> </tr> </tbody> </table> $$\newline$$ The following additional facts are known. $$\newline$$ <li>No one except possibly Ganga sold any Mango smoothie.</li> $$\newline$$ <li>Each woman sold either zero or one unit of any single finished product in any hour.</li> $$\newline$$ <li>Each woman had exactly one unit each of two different raw materials as leftovers.</li> $$\newline$$ <li>No one had any banana leftover.</li> $$\newline$$ </ol>
Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table. $$\newline$$ <table class="question-table"> <thead> <tr> <th>Finished product</th> <th>Raw materials required</th> </tr> </thead> <tbody> <tr> <td>Mango smoothie</td> <td>Mango, Milk</td> </tr> <tr> <td>Apple smoothie</td> <td>Apple, Milk</td> </tr> <tr> <td>Banana smoothie</td> <td>Banana, Milk</td> </tr> <tr> <td>Mixed fruit smoothie</td> <td>Mango, Apple, Banana, Milk</td> </tr> <tr> <td>Fruit salad</td> <td>Mango, Apple, Banana</td> </tr> </tbody> </table> $\newline$ <br> $\newline$ One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit. $$\newline$$ The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2. $$\newline$$ <table class="question-table"> <thead> <tr> <th>Business Hour</th> <th>Ganga</th> <th>Kaveri</th> <th>Narmada</th> </tr> </thead> <tbody> <tr> <td>Hour 1</td> <td>23</td> <td>19</td> <td>31</td> </tr> <tr> <td>Hour 2</td> <td>21</td> <td>22</td> <td>21</td> </tr> <tr> <td>Hour 3</td> <td>29</td> <td>30</td> <td>23</td> </tr> <tr> <td>Hour 4 (last hour)</td> <td>30</td> <td>27</td> <td>22</td> </tr> </tbody> </table> $$\newline$$ The following additional facts are known. $$\newline$$ <li>No one except possibly Ganga sold any Mango smoothie.</li> $$\newline$$ <li>Each woman sold either zero or one unit of any single finished product in any hour.</li> $$\newline$$ <li>Each woman had exactly one unit each of two different raw materials as leftovers.</li> $$\newline$$ <li>No one had any banana leftover.</li> $$\newline$$ </ol>
If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. $$\newline$$ Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal. $$\newline$$ The following facts are also known. $$\newline$$ <li>F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.</li> $$\newline$$ <li>A was from the Automation area and did not have a paper scheduled in the October issue.</li> $$\newline$$ <li>None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.</li> $$\newline$$ <li>A and H were from different countries, but had their papers scheduled in exactly the same issues.</li> $$\newline$$ <li>C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.</li> $$\newline$$ <li>B, from the Logistics area, had a paper scheduled in the April issue of the journal.</li> $$\newline$$ <li>B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.</li> $$\newline$$ <li>D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.</li> $$\newline$$ <li>C and H belonged to different areas.</li> $\newline$ </ol>
What is the correct sequence of number of papers written by B, C, E and G, respectively?
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. $$\newline$$ Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal. $$\newline$$ The following facts are also known. $$\newline$$ <li>F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.</li> $$\newline$$ <li>A was from the Automation area and did not have a paper scheduled in the October issue.</li> $$\newline$$ <li>None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.</li> $$\newline$$ <li>A and H were from different countries, but had their papers scheduled in exactly the same issues.</li> $$\newline$$ <li>C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.</li> $$\newline$$ <li>B, from the Logistics area, had a paper scheduled in the April issue of the journal.</li> $$\newline$$ <li>B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.</li> $$\newline$$ <li>D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.</li> $$\newline$$ <li>C and H belonged to different areas.</li> $\newline$ </ol>
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. $$\newline$$ Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal. $$\newline$$ The following facts are also known. $$\newline$$ <li>F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.</li> $$\newline$$ <li>A was from the Automation area and did not have a paper scheduled in the October issue.</li> $$\newline$$ <li>None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.</li> $$\newline$$ <li>A and H were from different countries, but had their papers scheduled in exactly the same issues.</li> $$\newline$$ <li>C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.</li> $$\newline$$ <li>B, from the Logistics area, had a paper scheduled in the April issue of the journal.</li> $$\newline$$ <li>B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.</li> $$\newline$$ <li>D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.</li> $$\newline$$ <li>C and H belonged to different areas.</li> $\newline$ </ol>
Which of the following statement(s) MUST be true?<br><br>Statement A: Every issue had at least one paper by author(s) from each country.<br>Statement B: Every issue had at most two papers by author(s) from each area.
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. $$\newline$$ Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal. $$\newline$$ The following facts are also known. $$\newline$$ <li>F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.</li> $$\newline$$ <li>A was from the Automation area and did not have a paper scheduled in the October issue.</li> $$\newline$$ <li>None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.</li> $$\newline$$ <li>A and H were from different countries, but had their papers scheduled in exactly the same issues.</li> $$\newline$$ <li>C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.</li> $$\newline$$ <li>B, from the Logistics area, had a paper scheduled in the April issue of the journal.</li> $$\newline$$ <li>B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.</li> $$\newline$$ <li>D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.</li> $$\newline$$ <li>C and H belonged to different areas.</li> $\newline$ </ol>
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. $$\newline$$ Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal. $$\newline$$ The following facts are also known. $$\newline$$ <li>F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.</li> $$\newline$$ <li>A was from the Automation area and did not have a paper scheduled in the October issue.</li> $$\newline$$ <li>None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.</li> $$\newline$$ <li>A and H were from different countries, but had their papers scheduled in exactly the same issues.</li> $$\newline$$ <li>C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.</li> $$\newline$$ <li>B, from the Logistics area, had a paper scheduled in the April issue of the journal.</li> $$\newline$$ <li>B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.</li> $$\newline$$ <li>D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.</li> $$\newline$$ <li>C and H belonged to different areas.</li> $\newline$ </ol>
A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. $$\newline$$ Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal. $$\newline$$ The following facts are also known. $$\newline$$ <li>F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.</li> $$\newline$$ <li>A was from the Automation area and did not have a paper scheduled in the October issue.</li> $$\newline$$ <li>None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.</li> $$\newline$$ <li>A and H were from different countries, but had their papers scheduled in exactly the same issues.</li> $$\newline$$ <li>C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.</li> $$\newline$$ <li>B, from the Logistics area, had a paper scheduled in the April issue of the journal.</li> $$\newline$$ <li>B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.</li> $$\newline$$ <li>D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.</li> $$\newline$$ <li>C and H belonged to different areas.</li> $\newline$ </ol>
Which of the following is the correct sequence of number of papers by authors from Automation, Manufacturing and Logistics areas, respectively?
Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.
Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.
<table class="question-table"><thead><tr><td></td><td>No. of Friends</td><td>No. of<br>Acquaintances</td><td>No. of Strangers</td></tr></thead><tbody><tr><td>Amudha</td><td></td><td>1</td><td>4</td></tr><tr><td>Bharatan</td><td></td><td></td><td></td></tr><tr><td>Chandran</td><td></td><td>1</td><td></td></tr><tr><td>Dhinesh</td><td></td><td></td><td>2</td></tr><tr><td>Ezhil</td><td></td><td></td><td>1</td></tr><tr><td>Fani</td><td>1</td><td></td><td></td></tr><tr><td>Gowtham</td><td></td><td>3</td><td>2</td></tr></tbody></table>
The following additional facts are also known.
<ol>
<li>Amudha, Bharatan, and Chandran are mutual strangers.</li>
<li>Amudha, Dhinesh, and Fani are Ezhil's friends.</li>
<li>Chandran and Gowtham are friends.</li>
<li>Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.</li>
<li>Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.</li>
</ol>
Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.
Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.
<table class="question-table"><thead><tr><td></td><td>No. of Friends</td><td>No. of<br>Acquaintances</td><td>No. of Strangers</td></tr></thead><tbody><tr><td>Amudha</td><td></td><td>1</td><td>4</td></tr><tr><td>Bharatan</td><td></td><td></td><td></td></tr><tr><td>Chandran</td><td></td><td>1</td><td></td></tr><tr><td>Dhinesh</td><td></td><td></td><td>2</td></tr><tr><td>Ezhil</td><td></td><td></td><td>1</td></tr><tr><td>Fani</td><td>1</td><td></td><td></td></tr><tr><td>Gowtham</td><td></td><td>3</td><td>2</td></tr></tbody></table>
The following additional facts are also known.
<ol>
<li>Amudha, Bharatan, and Chandran are mutual strangers.</li>
<li>Amudha, Dhinesh, and Fani are Ezhil's friends.</li>
<li>Chandran and Gowtham are friends.</li>
<li>Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.</li>
<li>Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.</li>
</ol>
Which of these pairs share the same type of relationship?
Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.
Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.
<table class="question-table"><thead><tr><td></td><td>No. of Friends</td><td>No. of<br>Acquaintances</td><td>No. of Strangers</td></tr></thead><tbody><tr><td>Amudha</td><td></td><td>1</td><td>4</td></tr><tr><td>Bharatan</td><td></td><td></td><td></td></tr><tr><td>Chandran</td><td></td><td>1</td><td></td></tr><tr><td>Dhinesh</td><td></td><td></td><td>2</td></tr><tr><td>Ezhil</td><td></td><td></td><td>1</td></tr><tr><td>Fani</td><td>1</td><td></td><td></td></tr><tr><td>Gowtham</td><td></td><td>3</td><td>2</td></tr></tbody></table>
The following additional facts are also known.
<ol>
<li>Amudha, Bharatan, and Chandran are mutual strangers.</li>
<li>Amudha, Dhinesh, and Fani are Ezhil's friends.</li>
<li>Chandran and Gowtham are friends.</li>
<li>Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.</li>
<li>Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.</li>
</ol>
Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.
Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.
<table class="question-table"><thead><tr><td></td><td>No. of Friends</td><td>No. of<br>Acquaintances</td><td>No. of Strangers</td></tr></thead><tbody><tr><td>Amudha</td><td></td><td>1</td><td>4</td></tr><tr><td>Bharatan</td><td></td><td></td><td></td></tr><tr><td>Chandran</td><td></td><td>1</td><td></td></tr><tr><td>Dhinesh</td><td></td><td></td><td>2</td></tr><tr><td>Ezhil</td><td></td><td></td><td>1</td></tr><tr><td>Fani</td><td>1</td><td></td><td></td></tr><tr><td>Gowtham</td><td></td><td>3</td><td>2</td></tr></tbody></table>
The following additional facts are also known.
<ol>
<li>Amudha, Bharatan, and Chandran are mutual strangers.</li>
<li>Amudha, Dhinesh, and Fani are Ezhil's friends.</li>
<li>Chandran and Gowtham are friends.</li>
<li>Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.</li>
<li>Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.</li>
</ol>
Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.
Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.
<table class="question-table"><thead><tr><td></td><td>No. of Friends</td><td>No. of<br>Acquaintances</td><td>No. of Strangers</td></tr></thead><tbody><tr><td>Amudha</td><td></td><td>1</td><td>4</td></tr><tr><td>Bharatan</td><td></td><td></td><td></td></tr><tr><td>Chandran</td><td></td><td>1</td><td></td></tr><tr><td>Dhinesh</td><td></td><td></td><td>2</td></tr><tr><td>Ezhil</td><td></td><td></td><td>1</td></tr><tr><td>Fani</td><td>1</td><td></td><td></td></tr><tr><td>Gowtham</td><td></td><td>3</td><td>2</td></tr></tbody></table>
The following additional facts are also known.
<ol>
<li>Amudha, Bharatan, and Chandran are mutual strangers.</li>
<li>Amudha, Dhinesh, and Fani are Ezhil's friends.</li>
<li>Chandran and Gowtham are friends.</li>
<li>Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.</li>
<li>Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.</li>
</ol>
Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.
Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.
<table class="question-table"><thead><tr><td></td><td>No. of Friends</td><td>No. of<br>Acquaintances</td><td>No. of Strangers</td></tr></thead><tbody><tr><td>Amudha</td><td></td><td>1</td><td>4</td></tr><tr><td>Bharatan</td><td></td><td></td><td></td></tr><tr><td>Chandran</td><td></td><td>1</td><td></td></tr><tr><td>Dhinesh</td><td></td><td></td><td>2</td></tr><tr><td>Ezhil</td><td></td><td></td><td>1</td></tr><tr><td>Fani</td><td>1</td><td></td><td></td></tr><tr><td>Gowtham</td><td></td><td>3</td><td>2</td></tr></tbody></table>
The following additional facts are also known.
<ol>
<li>Amudha, Bharatan, and Chandran are mutual strangers.</li>
<li>Amudha, Dhinesh, and Fani are Ezhil's friends.</li>
<li>Chandran and Gowtham are friends.</li>
<li>Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.</li>
<li>Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.</li>
</ol>
How many people are either a friend or a friend-of-a-friend of Ezhil?
<p>A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.</p> $$\newline$$ <p>For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.</p> $$\newline$$ <p>For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.</p> $$\newline$$ <p>Answer the following questions INDEPENDENTLY of each other.</p>
Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car)arrive. At this moment, which among the following numbered car is parked next to car3?
<p>A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.</p> $$\newline$$ <p>For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.</p> $$\newline$$ <p>For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.</p> $$\newline$$ <p>Answer the following questions INDEPENDENTLY of each other.</p>
Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?
<p>A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.</p> $$\newline$$ <p>For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.</p> $$\newline$$ <p>For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.</p> $$\newline$$ <p>Answer the following questions INDEPENDENTLY of each other.</p>
Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?
<p>A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.</p> $$\newline$$ <p>For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.</p> $$\newline$$ <p>For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.</p> $$\newline$$ <p>Answer the following questions INDEPENDENTLY of each other.</p>
Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?
Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. $$\newline$$ The following facts are also known about these contracts. $$\newline$$ <ol> $\newline$ <li>Vendor Z had at least one contract in every year.</li> $$\newline$$ <li>Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.</li> $$\newline$$ <li>Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.</li> $$\newline$$ <li>There were five contracts in 2012.</li> $$\newline$$ <li>There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts.</li> $$\newline$$ <li>Institute C had one or more contracts in 2012 but did not have any contract in 2011.</li> $$\newline$$ <li>Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.</li> $\newline$ </ol>
In which of the following years were there two or more contracts?
Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. $$\newline$$ The following facts are also known about these contracts. $$\newline$$ <ol> $\newline$ <li>Vendor Z had at least one contract in every year.</li> $$\newline$$ <li>Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.</li> $$\newline$$ <li>Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.</li> $$\newline$$ <li>There were five contracts in 2012.</li> $$\newline$$ <li>There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts.</li> $$\newline$$ <li>Institute C had one or more contracts in 2012 but did not have any contract in 2011.</li> $$\newline$$ <li>Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.</li> $\newline$ </ol>
Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. $$\newline$$ The following facts are also known about these contracts. $$\newline$$ <ol> $\newline$ <li>Vendor Z had at least one contract in every year.</li> $$\newline$$ <li>Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.</li> $$\newline$$ <li>Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.</li> $$\newline$$ <li>There were five contracts in 2012.</li> $$\newline$$ <li>There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts.</li> $$\newline$$ <li>Institute C had one or more contracts in 2012 but did not have any contract in 2011.</li> $$\newline$$ <li>Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.</li> $\newline$ </ol>
In how many years during this period was there only one contract?
Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. $$\newline$$ The following facts are also known about these contracts. $$\newline$$ <ol> $\newline$ <li>Vendor Z had at least one contract in every year.</li> $$\newline$$ <li>Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.</li> $$\newline$$ <li>Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.</li> $$\newline$$ <li>There were five contracts in 2012.</li> $$\newline$$ <li>There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts.</li> $$\newline$$ <li>Institute C had one or more contracts in 2012 but did not have any contract in 2011.</li> $$\newline$$ <li>Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.</li> $\newline$ </ol>
What BEST can be concluded about the number of contracts in 2010?
Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. $$\newline$$ The following facts are also known about these contracts. $$\newline$$ <ol> $\newline$ <li>Vendor Z had at least one contract in every year.</li> $$\newline$$ <li>Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.</li> $$\newline$$ <li>Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.</li> $$\newline$$ <li>There were five contracts in 2012.</li> $$\newline$$ <li>There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts.</li> $$\newline$$ <li>Institute C had one or more contracts in 2012 but did not have any contract in 2011.</li> $$\newline$$ <li>Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.</li> $\newline$ </ol>
Which institutes had multiple contracts during the same year?
Four institutes, A, B, C, and D, had contracts with four vendors W, X, Y, and Z during the ten calendar years from 2010 to 2019. The contracts were either multi-year contracts running for several consecutive years or single-year contracts. No institute had more than one contract with the same vendor. However, in a calendar year, an institute may have had contracts with multiple vendors, and a vendor may have had contracts with multiple institutes. It is known that over the decade, the institutes each got into two contracts with two of these vendors, and each vendor got into two contracts with two of these institutes. $$\newline$$ The following facts are also known about these contracts. $$\newline$$ <ol> $\newline$ <li>Vendor Z had at least one contract in every year.</li> $$\newline$$ <li>Vendor X had one or more contracts in every year up to 2015, but no contract in any year after that.</li> $$\newline$$ <li>Vendor Y had contracts in 2010 and 2019. Vendor W had contracts only in 2012.</li> $$\newline$$ <li>There were five contracts in 2012.</li> $$\newline$$ <li>There were exactly four multi-year contracts. Institute B had a 7-year contract, D had a 4- year contract, and A and C had one 3-year contract each. The other four contracts were single year contracts.</li> $$\newline$$ <li>Institute C had one or more contracts in 2012 but did not have any contract in 2011.</li> $$\newline$$ <li>Institutes B and D each had exactly one contract in 2012. Institute D did not have any contract in 2010.</li> $\newline$ </ol>
Which institutes and vendors had more than one contracts in any year?
In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. $$\newline$$ The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. $$\newline$$ If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. $$\newline$$ If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. $$\newline$$ The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>English</th><th>Hindi</th><th>Mathematics</th><th>Science</th><th>Social Science</th></tr></thead><tbody><tr><td>Alva</td><td>80</td><td>75</td><td>70</td><td>75</td><td>60</td></tr><tr><td>Bithi</td><td>90</td><td>80</td><td>55</td><td>85</td><td>85</td></tr><tr><td>Carl</td><td>75</td><td>80</td><td>90</td><td>100</td><td>90</td></tr><tr><td>Deep</td><td>70</td><td>90</td><td>100</td><td>90</td><td>80</td></tr><tr><td>Esha</td><td>80</td><td>85</td><td>95</td><td>60</td><td>55</td></tr><tr><td>Foni</td><td>83</td><td>72</td><td>78</td><td>88</td><td>83</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ <ol><li>Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.</li> $$\newline$$ <li>The student who missed the Mathematics examination did not miss any other examination.</li> $$\newline$$ <li>One of the students who missed the Hindi examination did not miss any other examination.</li> $$\newline$$ <li>The other student who missed the Hindi examination also missed the Science examination.</li> $\newline$ </ol>
Who among the following did not appear for the Mathematics examination?
In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. $$\newline$$ The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. $$\newline$$ If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. $$\newline$$ If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. $$\newline$$ The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>English</th><th>Hindi</th><th>Mathematics</th><th>Science</th><th>Social Science</th></tr></thead><tbody><tr><td>Alva</td><td>80</td><td>75</td><td>70</td><td>75</td><td>60</td></tr><tr><td>Bithi</td><td>90</td><td>80</td><td>55</td><td>85</td><td>85</td></tr><tr><td>Carl</td><td>75</td><td>80</td><td>90</td><td>100</td><td>90</td></tr><tr><td>Deep</td><td>70</td><td>90</td><td>100</td><td>90</td><td>80</td></tr><tr><td>Esha</td><td>80</td><td>85</td><td>95</td><td>60</td><td>55</td></tr><tr><td>Foni</td><td>83</td><td>72</td><td>78</td><td>88</td><td>83</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ <ol><li>Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.</li> $$\newline$$ <li>The student who missed the Mathematics examination did not miss any other examination.</li> $$\newline$$ <li>One of the students who missed the Hindi examination did not miss any other examination.</li> $$\newline$$ <li>The other student who missed the Hindi examination also missed the Science examination.</li> $\newline$ </ol>
Which students did not appear for the English examination?
In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. $$\newline$$ The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. $$\newline$$ If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. $$\newline$$ If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. $$\newline$$ The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>English</th><th>Hindi</th><th>Mathematics</th><th>Science</th><th>Social Science</th></tr></thead><tbody><tr><td>Alva</td><td>80</td><td>75</td><td>70</td><td>75</td><td>60</td></tr><tr><td>Bithi</td><td>90</td><td>80</td><td>55</td><td>85</td><td>85</td></tr><tr><td>Carl</td><td>75</td><td>80</td><td>90</td><td>100</td><td>90</td></tr><tr><td>Deep</td><td>70</td><td>90</td><td>100</td><td>90</td><td>80</td></tr><tr><td>Esha</td><td>80</td><td>85</td><td>95</td><td>60</td><td>55</td></tr><tr><td>Foni</td><td>83</td><td>72</td><td>78</td><td>88</td><td>83</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ <ol><li>Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.</li> $$\newline$$ <li>The student who missed the Mathematics examination did not miss any other examination.</li> $$\newline$$ <li>One of the students who missed the Hindi examination did not miss any other examination.</li> $$\newline$$ <li>The other student who missed the Hindi examination also missed the Science examination.</li> $\newline$ </ol>
What BEST can be concluded about the students who did not appear for the Hindi examination?
In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. $$\newline$$ The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. $$\newline$$ If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. $$\newline$$ If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. $$\newline$$ The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>English</th><th>Hindi</th><th>Mathematics</th><th>Science</th><th>Social Science</th></tr></thead><tbody><tr><td>Alva</td><td>80</td><td>75</td><td>70</td><td>75</td><td>60</td></tr><tr><td>Bithi</td><td>90</td><td>80</td><td>55</td><td>85</td><td>85</td></tr><tr><td>Carl</td><td>75</td><td>80</td><td>90</td><td>100</td><td>90</td></tr><tr><td>Deep</td><td>70</td><td>90</td><td>100</td><td>90</td><td>80</td></tr><tr><td>Esha</td><td>80</td><td>85</td><td>95</td><td>60</td><td>55</td></tr><tr><td>Foni</td><td>83</td><td>72</td><td>78</td><td>88</td><td>83</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ <ol><li>Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.</li> $$\newline$$ <li>The student who missed the Mathematics examination did not miss any other examination.</li> $$\newline$$ <li>One of the students who missed the Hindi examination did not miss any other examination.</li> $$\newline$$ <li>The other student who missed the Hindi examination also missed the Science examination.</li> $\newline$ </ol>
What BEST can be concluded about the students who missed the Science examination?
In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. $$\newline$$ The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. $$\newline$$ If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. $$\newline$$ If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. $$\newline$$ The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>English</th><th>Hindi</th><th>Mathematics</th><th>Science</th><th>Social Science</th></tr></thead><tbody><tr><td>Alva</td><td>80</td><td>75</td><td>70</td><td>75</td><td>60</td></tr><tr><td>Bithi</td><td>90</td><td>80</td><td>55</td><td>85</td><td>85</td></tr><tr><td>Carl</td><td>75</td><td>80</td><td>90</td><td>100</td><td>90</td></tr><tr><td>Deep</td><td>70</td><td>90</td><td>100</td><td>90</td><td>80</td></tr><tr><td>Esha</td><td>80</td><td>85</td><td>95</td><td>60</td><td>55</td></tr><tr><td>Foni</td><td>83</td><td>72</td><td>78</td><td>88</td><td>83</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ <ol><li>Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.</li> $$\newline$$ <li>The student who missed the Mathematics examination did not miss any other examination.</li> $$\newline$$ <li>One of the students who missed the Hindi examination did not miss any other examination.</li> $$\newline$$ <li>The other student who missed the Hindi examination also missed the Science examination.</li> $\newline$ </ol>
How many out of these six students missed exactly one examination?
In a certain board examination, students were to appear for examination in five subjects: English, Hindi, Mathematics, Science and Social Science. Due to a certain emergency situation, a few of the examinations could not be conducted for some students. Hence, some students missed one examination and some others missed two examinations. Nobody missed more than two examinations. $$\newline$$ The board adopted the following policy for awarding marks to students. If a student appeared in all five examinations, then the marks awarded in each of the examinations were on the basis of the scores obtained by them in those examinations. $$\newline$$ If a student missed only one examination, then the marks awarded in that examination was the average of the best three among the four scores in the examinations they appeared for. $$\newline$$ If a student missed two examinations, then the marks awarded in each of these examinations was the average of the best two among the three scores in the examinations they appeared for. $$\newline$$ The marks obtained by six students in the examination are given in the table below. Each of them missed either one or two examinations. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>English</th><th>Hindi</th><th>Mathematics</th><th>Science</th><th>Social Science</th></tr></thead><tbody><tr><td>Alva</td><td>80</td><td>75</td><td>70</td><td>75</td><td>60</td></tr><tr><td>Bithi</td><td>90</td><td>80</td><td>55</td><td>85</td><td>85</td></tr><tr><td>Carl</td><td>75</td><td>80</td><td>90</td><td>100</td><td>90</td></tr><tr><td>Deep</td><td>70</td><td>90</td><td>100</td><td>90</td><td>80</td></tr><tr><td>Esha</td><td>80</td><td>85</td><td>95</td><td>60</td><td>55</td></tr><tr><td>Foni</td><td>83</td><td>72</td><td>78</td><td>88</td><td>83</td></tr></tbody></table> $$\newline$$ The following facts are also known. $$\newline$$ <ol><li>Four of these students appeared in each of the English, Hindi, Science, and Social Science examinations.</li> $$\newline$$ <li>The student who missed the Mathematics examination did not miss any other examination.</li> $$\newline$$ <li>One of the students who missed the Hindi examination did not miss any other examination.</li> $$\newline$$ <li>The other student who missed the Hindi examination also missed the Science examination.</li> $\newline$ </ol>
For how many students can we be definite about which examinations they missed?
The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: $$\newline$$ P1: timely arrival $$\newline$$ P2: behaviour $$\newline$$ P3: comfortable ride $$\newline$$ P4: driver's familiarity with the route $$\newline$$ P5: value for money</p> $$\newline$$ <p>Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters.</p> $$\newline$$ <p>The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:</p> $$\newline$$ <table class="question-table"><thead><tr><th></th><th>P1</th><th>P2</th><th>P3</th><th>P4</th><th>P5</th><th>Fixed Payment</th><th>Bonus</th></tr></thead><tbody><tr><td>Arun</td><td></td><td></td><td></td><td>4</td><td></td><td>Rs. 1000</td><td>Rs. 250 × Final Rating</td></tr><tr><td>Barun</td><td>3</td><td></td><td></td><td></td><td></td><td>Rs. 1200</td><td>Rs. 200 × Final Rating</td></tr><tr><td>Chandan</td><td></td><td></td><td>2</td><td></td><td></td><td>Rs. 1400</td><td>Rs. 100 × Final Rating</td></tr><tr><td>Damodaran</td><td></td><td>3</td><td></td><td></td><td></td><td>Rs. 1300</td><td>Rs. 150 × Final Rating</td></tr><tr><td>Eman</td><td></td><td></td><td></td><td></td><td>2</td><td>Rs. 1100</td><td>Rs. 200 × Final Rating</td></tr></tbody></table> $$\newline$$ <p>The following additional facts are known.</p> $$\newline$$ <ol> $$\newline$$ <li>Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.</li> $$\newline$$ <li>None of drivers has got the same rating in three parameters.</li></ol>
If Damodaran does not get a bonus, what is the maximum possible value of his final rating?
The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: $$\newline$$ P1: timely arrival $$\newline$$ P2: behaviour $$\newline$$ P3: comfortable ride $$\newline$$ P4: driver's familiarity with the route $$\newline$$ P5: value for money</p> $$\newline$$ <p>Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters.</p> $$\newline$$ <p>The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:</p> $$\newline$$ <table class="question-table"><thead><tr><th></th><th>P1</th><th>P2</th><th>P3</th><th>P4</th><th>P5</th><th>Fixed Payment</th><th>Bonus</th></tr></thead><tbody><tr><td>Arun</td><td></td><td></td><td></td><td>4</td><td></td><td>Rs. 1000</td><td>Rs. 250 × Final Rating</td></tr><tr><td>Barun</td><td>3</td><td></td><td></td><td></td><td></td><td>Rs. 1200</td><td>Rs. 200 × Final Rating</td></tr><tr><td>Chandan</td><td></td><td></td><td>2</td><td></td><td></td><td>Rs. 1400</td><td>Rs. 100 × Final Rating</td></tr><tr><td>Damodaran</td><td></td><td>3</td><td></td><td></td><td></td><td>Rs. 1300</td><td>Rs. 150 × Final Rating</td></tr><tr><td>Eman</td><td></td><td></td><td></td><td></td><td>2</td><td>Rs. 1100</td><td>Rs. 200 × Final Rating</td></tr></tbody></table> $$\newline$$ <p>The following additional facts are known.</p> $$\newline$$ <ol> $$\newline$$ <li>Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.</li> $$\newline$$ <li>None of drivers has got the same rating in three parameters.</li></ol>
If Eman gets a bonus, what is the minimum possible value of his final rating?
The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: $$\newline$$ P1: timely arrival $$\newline$$ P2: behaviour $$\newline$$ P3: comfortable ride $$\newline$$ P4: driver's familiarity with the route $$\newline$$ P5: value for money</p> $$\newline$$ <p>Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters.</p> $$\newline$$ <p>The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:</p> $$\newline$$ <table class="question-table"><thead><tr><th></th><th>P1</th><th>P2</th><th>P3</th><th>P4</th><th>P5</th><th>Fixed Payment</th><th>Bonus</th></tr></thead><tbody><tr><td>Arun</td><td></td><td></td><td></td><td>4</td><td></td><td>Rs. 1000</td><td>Rs. 250 × Final Rating</td></tr><tr><td>Barun</td><td>3</td><td></td><td></td><td></td><td></td><td>Rs. 1200</td><td>Rs. 200 × Final Rating</td></tr><tr><td>Chandan</td><td></td><td></td><td>2</td><td></td><td></td><td>Rs. 1400</td><td>Rs. 100 × Final Rating</td></tr><tr><td>Damodaran</td><td></td><td>3</td><td></td><td></td><td></td><td>Rs. 1300</td><td>Rs. 150 × Final Rating</td></tr><tr><td>Eman</td><td></td><td></td><td></td><td></td><td>2</td><td>Rs. 1100</td><td>Rs. 200 × Final Rating</td></tr></tbody></table> $$\newline$$ <p>The following additional facts are known.</p> $$\newline$$ <ol> $$\newline$$ <li>Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.</li> $$\newline$$ <li>None of drivers has got the same rating in three parameters.</li></ol>
If all five drivers get bonus, what is the minimum possible value of the monthly payment (in rupees) that a driver gets?
The local office of the APP-CAB company evaluates the performance of five cab drivers, Arun, Barun, Chandan, Damodaran, and Eman for their monthly payment based on ratings in five different parameters (P1 to P5) as given below: $$\newline$$ P1: timely arrival $$\newline$$ P2: behaviour $$\newline$$ P3: comfortable ride $$\newline$$ P4: driver's familiarity with the route $$\newline$$ P5: value for money</p> $$\newline$$ <p>Based on feedback from the customers, the office assigns a rating from 1 to 5 in each of these parameters. Each rating is an integer from a low value of 1 to a high value of 5. The final rating of a driver is the average of his ratings in these five parameters. The monthly payment of the drivers has two parts – a fixed payment and final rating-based bonus. If a driver gets a rating of 1 in any of the parameters, he is not eligible to get bonus. To be eligible for bonus a driver also needs to get a rating of five in at least one of the parameters.</p> $$\newline$$ <p>The partial information related to the ratings of the drivers in different parameters and the monthly payment structure (in rupees) is given in the table below:</p> $$\newline$$ <table class="question-table"><thead><tr><th></th><th>P1</th><th>P2</th><th>P3</th><th>P4</th><th>P5</th><th>Fixed Payment</th><th>Bonus</th></tr></thead><tbody><tr><td>Arun</td><td></td><td></td><td></td><td>4</td><td></td><td>Rs. 1000</td><td>Rs. 250 × Final Rating</td></tr><tr><td>Barun</td><td>3</td><td></td><td></td><td></td><td></td><td>Rs. 1200</td><td>Rs. 200 × Final Rating</td></tr><tr><td>Chandan</td><td></td><td></td><td>2</td><td></td><td></td><td>Rs. 1400</td><td>Rs. 100 × Final Rating</td></tr><tr><td>Damodaran</td><td></td><td>3</td><td></td><td></td><td></td><td>Rs. 1300</td><td>Rs. 150 × Final Rating</td></tr><tr><td>Eman</td><td></td><td></td><td></td><td></td><td>2</td><td>Rs. 1100</td><td>Rs. 200 × Final Rating</td></tr></tbody></table> $$\newline$$ <p>The following additional facts are known.</p> $$\newline$$ <ol> $$\newline$$ <li>Arun and Barun have got a rating of 5 in exactly one of the parameters. Chandan has got a rating of 5 in exactly two parameters.</li> $$\newline$$ <li>None of drivers has got the same rating in three parameters.</li></ol>
If all five drivers get bonus, what is the maximum possible value of the monthly payment (in rupees) that a driver gets?
In the table below the check marks indicate all languages spoken by five people: Paula, Quentin, Robert, Sally and Terence. For example, Paula speaks only Chinese and English.<br>
<br>
| | Arabic | Basque | Chinese | Dutch | English | French |
|---------|--------|--------|---------|-------|---------|--------|
| Paula | | | ✓ | | ✓ | |
| Quentin | | | | ✓ | ✓ | |
| Robert | ✓ | | | | | ✓ |
| Sally | | ✓ | | | ✓ | |
| Terence | | | ✓ | | | ✓ |
<br>
These five people form three teams, Team 1, Team 2 and Team 3. Each team has either 2 or 3 members. A team is said to speak a particular language if at least one of its members speak that language.<br>
<br>
The following facts are known.<br>
<ol>
<li>Each team speaks exactly four languages and has the same number of members.</li>
<li>English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team.</li>
<li>None of the teams include both Quentin and Robert.</li>
<li>Paula and Sally are together in exactly two teams.</li>
<li>Robert is in Team 1 and Quentin is in Team 3.</li>
</ol>
Who among the following four is not a member of Team 2?
In the table below the check marks indicate all languages spoken by five people: Paula, Quentin, Robert, Sally and Terence. For example, Paula speaks only Chinese and English.<br>
<br>
| | Arabic | Basque | Chinese | Dutch | English | French |
|---------|--------|--------|---------|-------|---------|--------|
| Paula | | | ✓ | | ✓ | |
| Quentin | | | | ✓ | ✓ | |
| Robert | ✓ | | | | | ✓ |
| Sally | | ✓ | | | ✓ | |
| Terence | | | ✓ | | | ✓ |
<br>
These five people form three teams, Team 1, Team 2 and Team 3. Each team has either 2 or 3 members. A team is said to speak a particular language if at least one of its members speak that language.<br>
<br>
The following facts are known.<br>
<ol>
<li>Each team speaks exactly four languages and has the same number of members.</li>
<li>English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team.</li>
<li>None of the teams include both Quentin and Robert.</li>
<li>Paula and Sally are together in exactly two teams.</li>
<li>Robert is in Team 1 and Quentin is in Team 3.</li>
</ol>
Who among the following four people is a part of exactly two teams?
In the table below the check marks indicate all languages spoken by five people: Paula, Quentin, Robert, Sally and Terence. For example, Paula speaks only Chinese and English.<br>
<br>
| | Arabic | Basque | Chinese | Dutch | English | French |
|---------|--------|--------|---------|-------|---------|--------|
| Paula | | | ✓ | | ✓ | |
| Quentin | | | | ✓ | ✓ | |
| Robert | ✓ | | | | | ✓ |
| Sally | | ✓ | | | ✓ | |
| Terence | | | ✓ | | | ✓ |
<br>
These five people form three teams, Team 1, Team 2 and Team 3. Each team has either 2 or 3 members. A team is said to speak a particular language if at least one of its members speak that language.<br>
<br>
The following facts are known.<br>
<ol>
<li>Each team speaks exactly four languages and has the same number of members.</li>
<li>English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team.</li>
<li>None of the teams include both Quentin and Robert.</li>
<li>Paula and Sally are together in exactly two teams.</li>
<li>Robert is in Team 1 and Quentin is in Team 3.</li>
</ol>
Who among the five people is a member of all teams?
In the table below the check marks indicate all languages spoken by five people: Paula, Quentin, Robert, Sally and Terence. For example, Paula speaks only Chinese and English.<br>
<br>
| | Arabic | Basque | Chinese | Dutch | English | French |
|---------|--------|--------|---------|-------|---------|--------|
| Paula | | | ✓ | | ✓ | |
| Quentin | | | | ✓ | ✓ | |
| Robert | ✓ | | | | | ✓ |
| Sally | | ✓ | | | ✓ | |
| Terence | | | ✓ | | | ✓ |
<br>
These five people form three teams, Team 1, Team 2 and Team 3. Each team has either 2 or 3 members. A team is said to speak a particular language if at least one of its members speak that language.<br>
<br>
The following facts are known.<br>
<ol>
<li>Each team speaks exactly four languages and has the same number of members.</li>
<li>English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team.</li>
<li>None of the teams include both Quentin and Robert.</li>
<li>Paula and Sally are together in exactly two teams.</li>
<li>Robert is in Team 1 and Quentin is in Team 3.</li>
</ol>
Apart from Chinese and English, which languages are spoken by Team 1?
The first year students in a business school are split into six sections. In $2019$ the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common endterm (ET) worth $100$ marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions. $$\newline$$ Each of MT and ET had at least four questions that were worth $5$ marks, at least three questions that were worth $10$ marks, and at least two questions that were worth $15$ marks. In both MT and ET, all the $5$-mark questions preceded the $10$-mark questions, and all the $15$ - mark questions followed the $10$-mark questions. $$\newline$$ The following additional facts are known. $$\newline$$ i. Annie prepared the fifth question for both MT and ET. For MT, this question carried $5$ marks. $$\newline$$ ii. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT. $$\newline$$ iii. All questions prepared by a faculty member appeared consecutively in MT as well as ET. $$\newline$$ iv. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both. $$\newline$$ v. Fakir prepared the first question of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.
The first year students in a business school are split into six sections. In $2019$ the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common endterm (ET) worth $100$ marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions. $$\newline$$ Each of MT and ET had at least four questions that were worth $5$ marks, at least three questions that were worth $10$ marks, and at least two questions that were worth $15$ marks. In both MT and ET, all the $5$-mark questions preceded the $10$-mark questions, and all the $15$ - mark questions followed the $10$-mark questions. $$\newline$$ The following additional facts are known. $$\newline$$ i. Annie prepared the fifth question for both MT and ET. For MT, this question carried $5$ marks. $$\newline$$ ii. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT. $$\newline$$ iii. All questions prepared by a faculty member appeared consecutively in MT as well as ET. $$\newline$$ iv. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both. $$\newline$$ v. Fakir prepared the first question of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.
How many 5-mark questions were there in MT and ET combined?
The first year students in a business school are split into six sections. In $2019$ the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common endterm (ET) worth $100$ marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions. $$\newline$$ Each of MT and ET had at least four questions that were worth $5$ marks, at least three questions that were worth $10$ marks, and at least two questions that were worth $15$ marks. In both MT and ET, all the $5$-mark questions preceded the $10$-mark questions, and all the $15$ - mark questions followed the $10$-mark questions. $$\newline$$ The following additional facts are known. $$\newline$$ i. Annie prepared the fifth question for both MT and ET. For MT, this question carried $5$ marks. $$\newline$$ ii. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT. $$\newline$$ iii. All questions prepared by a faculty member appeared consecutively in MT as well as ET. $$\newline$$ iv. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both. $$\newline$$ v. Fakir prepared the first question of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.
The first year students in a business school are split into six sections. In $2019$ the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common endterm (ET) worth $100$ marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions. $$\newline$$ Each of MT and ET had at least four questions that were worth $5$ marks, at least three questions that were worth $10$ marks, and at least two questions that were worth $15$ marks. In both MT and ET, all the $5$-mark questions preceded the $10$-mark questions, and all the $15$ - mark questions followed the $10$-mark questions. $$\newline$$ The following additional facts are known. $$\newline$$ i. Annie prepared the fifth question for both MT and ET. For MT, this question carried $5$ marks. $$\newline$$ ii. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT. $$\newline$$ iii. All questions prepared by a faculty member appeared consecutively in MT as well as ET. $$\newline$$ iv. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both. $$\newline$$ v. Fakir prepared the first question of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.
Which of the following questions did Beti prepare in ET?
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items. $$\newline$$ The following additional facts are known. $$\newline$$ <li>i) No composer who assigned item to Princess, assigned any item to Queen.</li> $$\newline$$ <li>ii) No composer who assigned item to Rani, assigned any item to Samragni.</li> $$\newline$$ <li>iii) The first performance was by Princess; this item was assigned by Badal.</li> $$\newline$$ <li>iv) The last performance was by Rani; this item was assigned by Gagan.</li> $$\newline$$ <li>v) The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.</li>
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items. $$\newline$$ The following additional facts are known. $$\newline$$ <li>i) No composer who assigned item to Princess, assigned any item to Queen.</li> $$\newline$$ <li>ii) No composer who assigned item to Rani, assigned any item to Samragni.</li> $$\newline$$ <li>iii) The first performance was by Princess; this item was assigned by Badal.</li> $$\newline$$ <li>iv) The last performance was by Rani; this item was assigned by Gagan.</li> $$\newline$$ <li>v) The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.</li>
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items. $$\newline$$ The following additional facts are known. $$\newline$$ <li>i) No composer who assigned item to Princess, assigned any item to Queen.</li> $$\newline$$ <li>ii) No composer who assigned item to Rani, assigned any item to Samragni.</li> $$\newline$$ <li>iii) The first performance was by Princess; this item was assigned by Badal.</li> $$\newline$$ <li>iv) The last performance was by Rani; this item was assigned by Gagan.</li> $$\newline$$ <li>v) The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.</li>
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items. $$\newline$$ The following additional facts are known. $$\newline$$ <li>i) No composer who assigned item to Princess, assigned any item to Queen.</li> $$\newline$$ <li>ii) No composer who assigned item to Rani, assigned any item to Samragni.</li> $$\newline$$ <li>iii) The first performance was by Princess; this item was assigned by Badal.</li> $$\newline$$ <li>iv) The last performance was by Rani; this item was assigned by Gagan.</li> $$\newline$$ <li>v) The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.</li>
Which pair of performances were composed by the same composer?
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers. $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>A and B are to be placed in consecutively numbered shelves in increasing order.</li> $$\newline$$ <li>I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.</li> $$\newline$$ <li>D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.</li> $$\newline$$ <li>K is to be placed in shelf number 16.</li> $$\newline$$ <li>L and J are items of the same type, while H is an item of a different type.</li> $$\newline$$ <li>C is a candy and is to be placed in a shelf preceded by two empty shelves.</li> $$\newline$$ <li>L is to be placed in a shelf preceded by exactly one empty shelf.</li> $\newline$ </ol>
In how many different ways can the items be arranged on the shelves?
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers. $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>A and B are to be placed in consecutively numbered shelves in increasing order.</li> $$\newline$$ <li>I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.</li> $$\newline$$ <li>D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.</li> $$\newline$$ <li>K is to be placed in shelf number 16.</li> $$\newline$$ <li>L and J are items of the same type, while H is an item of a different type.</li> $$\newline$$ <li>C is a candy and is to be placed in a shelf preceded by two empty shelves.</li> $$\newline$$ <li>L is to be placed in a shelf preceded by exactly one empty shelf.</li> $\newline$ </ol>
Which of the following items is not a type of biscuit?
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers. $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>A and B are to be placed in consecutively numbered shelves in increasing order.</li> $$\newline$$ <li>I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.</li> $$\newline$$ <li>D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.</li> $$\newline$$ <li>K is to be placed in shelf number 16.</li> $$\newline$$ <li>L and J are items of the same type, while H is an item of a different type.</li> $$\newline$$ <li>C is a candy and is to be placed in a shelf preceded by two empty shelves.</li> $$\newline$$ <li>L is to be placed in a shelf preceded by exactly one empty shelf.</li> $\newline$ </ol>
Which of the following can represent the numbers of the empty shelves in a possible arrangement?
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers. $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>A and B are to be placed in consecutively numbered shelves in increasing order.</li> $$\newline$$ <li>I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.</li> $$\newline$$ <li>D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.</li> $$\newline$$ <li>K is to be placed in shelf number 16.</li> $$\newline$$ <li>L and J are items of the same type, while H is an item of a different type.</li> $$\newline$$ <li>C is a candy and is to be placed in a shelf preceded by two empty shelves.</li> $$\newline$$ <li>L is to be placed in a shelf preceded by exactly one empty shelf.</li> $\newline$ </ol>
Which of the following statements is necessarily true?
Seven candidates, Akil, Balaram, Chitra, Divya, Erina, Fatima, and Ganeshan, were invited to interview for a position. Candidates
were required to reach the venue before 8 am. Immediately upon arrival, they were sent to one of three interview rooms: 101,
102, and 103. The following venue log shows the arrival times for these candidates. Some of the names have not been recorded
in the log and have been marked as '?'.
<table class="question-table"><thead><tr><th>Time</th><th>7:10 am</th><th>7:15 am</th><th>7:25 am</th><th>7:30 am</th><th>7:40 am</th><th>7:45 am</th></tr></thead><tbody><tr><td>Person</td><td>Akil, ?</td><td>?</td><td>?</td><td>Chitra</td><td>Fatima</td><td>?</td></tr></tbody></table>
Additionally here are some statements from the candidates:
Balaram: I was the third person to enter Room 101.
Chitra: I was the last person to enter the room I was allotted to.
Erina: I was the only person in the room I was allotted to.
Fatima: Three people including Akil were already in the room that I was allotted to when I entered it.
Ganeshan: I was one among the two candidates allotted to Room 102.
What best can be said about the room to which Divya was allotted?
Seven candidates, Akil, Balaram, Chitra, Divya, Erina, Fatima, and Ganeshan, were invited to interview for a position. Candidates
were required to reach the venue before 8 am. Immediately upon arrival, they were sent to one of three interview rooms: 101,
102, and 103. The following venue log shows the arrival times for these candidates. Some of the names have not been recorded
in the log and have been marked as '?'.
<table class="question-table"><thead><tr><th>Time</th><th>7:10 am</th><th>7:15 am</th><th>7:25 am</th><th>7:30 am</th><th>7:40 am</th><th>7:45 am</th></tr></thead><tbody><tr><td>Person</td><td>Akil, ?</td><td>?</td><td>?</td><td>Chitra</td><td>Fatima</td><td>?</td></tr></tbody></table>
Additionally here are some statements from the candidates:
Balaram: I was the third person to enter Room 101.
Chitra: I was the last person to enter the room I was allotted to.
Erina: I was the only person in the room I was allotted to.
Fatima: Three people including Akil were already in the room that I was allotted to when I entered it.
Ganeshan: I was one among the two candidates allotted to Room 102.
Seven candidates, Akil, Balaram, Chitra, Divya, Erina, Fatima, and Ganeshan, were invited to interview for a position. Candidates
were required to reach the venue before 8 am. Immediately upon arrival, they were sent to one of three interview rooms: 101,
102, and 103. The following venue log shows the arrival times for these candidates. Some of the names have not been recorded
in the log and have been marked as '?'.
<table class="question-table"><thead><tr><th>Time</th><th>7:10 am</th><th>7:15 am</th><th>7:25 am</th><th>7:30 am</th><th>7:40 am</th><th>7:45 am</th></tr></thead><tbody><tr><td>Person</td><td>Akil, ?</td><td>?</td><td>?</td><td>Chitra</td><td>Fatima</td><td>?</td></tr></tbody></table>
Additionally here are some statements from the candidates:
Balaram: I was the third person to enter Room 101.
Chitra: I was the last person to enter the room I was allotted to.
Erina: I was the only person in the room I was allotted to.
Fatima: Three people including Akil were already in the room that I was allotted to when I entered it.
Ganeshan: I was one among the two candidates allotted to Room 102.
Seven candidates, Akil, Balaram, Chitra, Divya, Erina, Fatima, and Ganeshan, were invited to interview for a position. Candidates
were required to reach the venue before 8 am. Immediately upon arrival, they were sent to one of three interview rooms: 101,
102, and 103. The following venue log shows the arrival times for these candidates. Some of the names have not been recorded
in the log and have been marked as '?'.
<table class="question-table"><thead><tr><th>Time</th><th>7:10 am</th><th>7:15 am</th><th>7:25 am</th><th>7:30 am</th><th>7:40 am</th><th>7:45 am</th></tr></thead><tbody><tr><td>Person</td><td>Akil, ?</td><td>?</td><td>?</td><td>Chitra</td><td>Fatima</td><td>?</td></tr></tbody></table>
Additionally here are some statements from the candidates:
Balaram: I was the third person to enter Room 101.
Chitra: I was the last person to enter the room I was allotted to.
Erina: I was the only person in the room I was allotted to.
Fatima: Three people including Akil were already in the room that I was allotted to when I entered it.
Ganeshan: I was one among the two candidates allotted to Room 102.
If Ganeshan entered the venue before Divya, when did Balaram enter the venue?
An agency entrusted to accredit colleges looks at four parameters: faculty quality (F), reputation (R), placement quality (P), and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points: A (50 points), B (40 points), C (30 points), D (20 points), and F (0 points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are 0.1, 0.2, 0.3 and 0.4 in some order, but the order is not disclosed. $\newline$ Accreditation is awarded based on the following scheme: $$\newline$$ <table class="question-table"><thead><tr><th>Range</th><th>Accreditation</th></tr></thead><tbody><tr><td>Overall score ≥ 45</td><td>AAA</td></tr><tr><td>35 ≤ Overall score < 45</td><td>BAA</td></tr><tr><td>25 ≤ Overall score < 35</td><td>BBA</td></tr><tr><td>15 ≤ Overall score < 25</td><td>BBB</td></tr><tr><td>Overall score < 15</td><td>Junk</td></tr></tbody></table> $$\newline$$ Eight colleges apply for accreditation, and receive the following grades in the four parameters (F, R, P, and I): $$\newline$$ <table class="question-table"><thead><tr><th></th><th>F</th><th>R</th><th>P</th><th>I</th></tr></thead><tbody><tr><td>A-one</td><td>A</td><td>A</td><td>A</td><td>B</td></tr><tr><td>Best Ed</td><td>B</td><td>C</td><td>D</td><td>D</td></tr><tr><td>Cosmopolitan</td><td>B</td><td>D</td><td>D</td><td>C</td></tr><tr><td>Dominance</td><td>D</td><td>D</td><td>B</td><td>C</td></tr><tr><td>Education Aid</td><td>A</td><td>A</td><td>B</td><td>A</td></tr><tr><td>Fancy</td><td>A</td><td>A</td><td>B</td><td>B</td></tr><tr><td>Global</td><td>C</td><td>F</td><td>D</td><td>D</td></tr><tr><td>High Q</td><td>C</td><td>D</td><td>D</td><td>B</td></tr></tbody></table> $$\newline$$ It is further known that in terms of overall scores: $$\newline$$ <ol> $\newline$ <li>High Q is better than Best Ed;</li> $$\newline$$ <li>Best Ed is better than Cosmopolitan; and</li> $$\newline$$ <li>Education Aid is better than A-one.</li> $$\newline$$ </ol>
How many colleges receive the accreditation of AAA?
Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes $X, Y,$ and $Z$. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:
1. Three students are from $X$, three are from $Y$, and the remaining two students, both female, are from $Z$.
2. Both the male students from $Y$ minor in Finance, while the female student from $Y$ majors in Operations.
3. Only one male student majors in Operations, while three female students minor in Marketing.
4. One female and two male students major in Finance.
5. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
6. Barun is from $Y$ and majors in Operations. Chetan is from $X$ and majors in Finance.
7. Daisy minors in Operations.
Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes $X, Y,$ and $Z$. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:
1. Three students are from $X$, three are from $Y$, and the remaining two students, both female, are from $Z$.
2. Both the male students from $Y$ minor in Finance, while the female student from $Y$ majors in Operations.
3. Only one male student majors in Operations, while three female students minor in Marketing.
4. One female and two male students major in Finance.
5. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
6. Barun is from $Y$ and majors in Operations. Chetan is from $X$ and majors in Finance.
7. Daisy minors in Operations.
Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes $X, Y,$ and $Z$. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:
1. Three students are from $X$, three are from $Y$, and the remaining two students, both female, are from $Z$.
2. Both the male students from $Y$ minor in Finance, while the female student from $Y$ majors in Operations.
3. Only one male student majors in Operations, while three female students minor in Marketing.
4. One female and two male students major in Finance.
5. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
6. Barun is from $Y$ and majors in Operations. Chetan is from $X$ and majors in Finance.
7. Daisy minors in Operations.
Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes $X, Y,$ and $Z$. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:
1. Three students are from $X$, three are from $Y$, and the remaining two students, both female, are from $Z$.
2. Both the male students from $Y$ minor in Finance, while the female student from $Y$ majors in Operations.
3. Only one male student majors in Operations, while three female students minor in Marketing.
4. One female and two male students major in Finance.
5. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
6. Barun is from $Y$ and majors in Operations. Chetan is from $X$ and majors in Finance.
7. Daisy minors in Operations.
<p>If Chitra majors in Finance, which subject does Bandita major in?</p>
Fuel contamination levels at each of 20 petrol pumps $P1, P2, \ldots, P20$ were recorded as either high, medium, or low.
1. Contamination levels at three pumps among $P1 - P5$ were recorded as high.
2. $P6$ was the only pump among $P1 - P10$ where the contamination level was recorded as low.
3. $P7$ and $P8$ were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps $P16 - P20$.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
Fuel contamination levels at each of 20 petrol pumps $P1, P2, \ldots, P20$ were recorded as either high, medium, or low.
1. Contamination levels at three pumps among $P1 - P5$ were recorded as high.
2. $P6$ was the only pump among $P1 - P10$ where the contamination level was recorded as low.
3. $P7$ and $P8$ were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps $P16 - P20$.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
<p>What best can be said about the number of pumps at which the contamination levels were recorded as medium?</p>
Fuel contamination levels at each of 20 petrol pumps $P1, P2, \ldots, P20$ were recorded as either high, medium, or low.
1. Contamination levels at three pumps among $P1 - P5$ were recorded as high.
2. $P6$ was the only pump among $P1 - P10$ where the contamination level was recorded as low.
3. $P7$ and $P8$ were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps $P16 - P20$.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
<p>If the contamination level at P11 was recorded as low, then which of the following MUST be true?</p>
Fuel contamination levels at each of 20 petrol pumps $P1, P2, \ldots, P20$ were recorded as either high, medium, or low.
1. Contamination levels at three pumps among $P1 - P5$ were recorded as high.
2. $P6$ was the only pump among $P1 - P10$ where the contamination level was recorded as low.
3. $P7$ and $P8$ were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps $P16 - P20$.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
<p>If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?</p>
<p>Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:</p><ol><li>The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.</li><li>The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.</li><li>60% of the politicians are in the administration committee, and 20% are in the teaching committee. </li></ol>
<p>Based on the given information, which of the following statements MUST be FALSE?</p>
<p>Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:</p><ol><li>The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.</li><li>The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.</li><li>60% of the politicians are in the administration committee, and 20% are in the teaching committee. </li></ol>
<p>What is the number of bureaucrats in the administration committee?</p>
<p>Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:</p><ol><li>The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.</li><li>The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.</li><li>60% of the politicians are in the administration committee, and 20% are in the teaching committee. </li></ol>
<p>What is the number of educationalists in the research committee?</p>
<p>Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:</p><ol><li>The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.</li><li>The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.</li><li>60% of the politicians are in the administration committee, and 20% are in the teaching committee. </li></ol>
<p>Which of the following CANNOT be determined uniquely based on the given information?</p>
<p>A company administers a written test comprising of three sections of 20 marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.</p><p>Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:</p><ol><li>No two candidates had the same composite score.</li><li>Ajay was the unique highest scorer in WE.</li><li>Among the four recruited, Geeta had the lowest composite score.</li><li>Indu was recruited.</li><li>Danish, Harini, and Indu had scored the same marks the in GA.</li><li>Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.</li></ol>
<img src="https://balti.aftergrad.in/questions/VjRDBdTI8wHtX3B" width="400px"/>
<p>Which of the following statements MUST be true?<br/>1. Jatin's composite score was more than that of Danish.<br/>2. Indu scored less than Chetna in DI.<br/>3. Jatin scored more than Indu in GA.</p>
<p>A company administers a written test comprising of three sections of 20 marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.</p><p>Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:</p><ol><li>No two candidates had the same composite score.</li><li>Ajay was the unique highest scorer in WE.</li><li>Among the four recruited, Geeta had the lowest composite score.</li><li>Indu was recruited.</li><li>Danish, Harini, and Indu had scored the same marks the in GA.</li><li>Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.</li></ol>
<img src="https://balti.aftergrad.in/questions/VjRDBdTI8wHtX3B" width="400px"/>
<p>Which of the following statements MUST be FALSE?</p>
<p>A company administers a written test comprising of three sections of 20 marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.</p><p>Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:</p><ol><li>No two candidates had the same composite score.</li><li>Ajay was the unique highest scorer in WE.</li><li>Among the four recruited, Geeta had the lowest composite score.</li><li>Indu was recruited.</li><li>Danish, Harini, and Indu had scored the same marks the in GA.</li><li>Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.</li></ol>
<img src="https://balti.aftergrad.in/questions/VjRDBdTI8wHtX3B" width="400px"/>
<p>If all the candidates except Ajay and Danish had different marks in DI, and Bala's composite score was less than Chetna's composite score, then what is the maximum marks that Bala could have scored in DI?</p>
<p>A company administers a written test comprising of three sections of 20 marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.</p><p>Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:</p><ol><li>No two candidates had the same composite score.</li><li>Ajay was the unique highest scorer in WE.</li><li>Among the four recruited, Geeta had the lowest composite score.</li><li>Indu was recruited.</li><li>Danish, Harini, and Indu had scored the same marks the in GA.</li><li>Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.</li></ol>
<img src="https://balti.aftergrad.in/questions/VjRDBdTI8wHtX3B" width="400px"/>
<p>If all the candidates scored different marks in WE then what is the maximum marks that Harini could have scored in WE?</p>
