Out of $10$ countries -- Country $1$ through Country $10$-- Country $9$ has the highest gross domestic product (GDP), and Country $10$ has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country $1$ through Country $8$ for the year $2024$. $$\newline$$ - Column $1$ gives the country's identity. $$\newline$$ - Column $2$ gives the country's GDP as a fraction of the GDP of Country 9. $$\newline$$ - Column $3$ gives the country's GDP per capita as a fraction of the GDP per capita of Country10. $$\newline$$ - Column $4$ gives the country's annual GDP growth rate. $$\newline$$ - Column $5$ gives the country's annual population growth rate. $$\newline$$ <img src="https://balti.aftergrad.in/questions/x0fbwwGULKsMFn5" width="400px"/> $$\newline$$ Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.
Which one among the countries 1 through 8, has the smallest population in 2024?
Out of $10$ countries -- Country $1$ through Country $10$-- Country $9$ has the highest gross domestic product (GDP), and Country $10$ has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country $1$ through Country $8$ for the year $2024$. $$\newline$$ - Column $1$ gives the country's identity. $$\newline$$ - Column $2$ gives the country's GDP as a fraction of the GDP of Country 9. $$\newline$$ - Column $3$ gives the country's GDP per capita as a fraction of the GDP per capita of Country10. $$\newline$$ - Column $4$ gives the country's annual GDP growth rate. $$\newline$$ - Column $5$ gives the country's annual population growth rate. $$\newline$$ <img src="https://balti.aftergrad.in/questions/x0fbwwGULKsMFn5" width="400px"/> $$\newline$$ Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.
The ratio of Country 4’s GDP to Country 5’s GDP in 2026 will be closest to
Out of $10$ countries -- Country $1$ through Country $10$-- Country $9$ has the highest gross domestic product (GDP), and Country $10$ has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country $1$ through Country $8$ for the year $2024$. $$\newline$$ - Column $1$ gives the country's identity. $$\newline$$ - Column $2$ gives the country's GDP as a fraction of the GDP of Country 9. $$\newline$$ - Column $3$ gives the country's GDP per capita as a fraction of the GDP per capita of Country10. $$\newline$$ - Column $4$ gives the country's annual GDP growth rate. $$\newline$$ - Column $5$ gives the country's annual population growth rate. $$\newline$$ <img src="https://balti.aftergrad.in/questions/x0fbwwGULKsMFn5" width="400px"/> $$\newline$$ Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.
Which one among the countries 1, 4, 5, and 7 will have the largest population in 2027?
Out of $10$ countries -- Country $1$ through Country $10$-- Country $9$ has the highest gross domestic product (GDP), and Country $10$ has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country $1$ through Country $8$ for the year $2024$. $$\newline$$ - Column $1$ gives the country's identity. $$\newline$$ - Column $2$ gives the country's GDP as a fraction of the GDP of Country 9. $$\newline$$ - Column $3$ gives the country's GDP per capita as a fraction of the GDP per capita of Country10. $$\newline$$ - Column $4$ gives the country's annual GDP growth rate. $$\newline$$ - Column $5$ gives the country's annual population growth rate. $$\newline$$ <img src="https://balti.aftergrad.in/questions/x0fbwwGULKsMFn5" width="400px"/> $$\newline$$ Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.
For how many countries among Country 1 through Country 8 will the GDP per capita in 2027 be lower than that in 2024?
The table given below shows the amount, in grams, of carbohydrate, protein, fat and all other nutrients, per 100 grams of nutrients in seven food grains. The first column shows the foodgrain category and the second column its codename. The table has some missing values. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GQdIW9xUGI5li3N" width="600px"/> $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>Both the pseudo-cereals had higher amounts of carbohydrate as well as higher amounts of protein than any millet.</li> $$\newline$$ <li>Both the cereals had higher amounts of carbohydrate than any pseudo-cereal.</li> $$\newline$$ <li>All the missing values of carbohydrate amounts (in grams) for all the foodgrains are non-zero multiples of 5.</li> $$\newline$$ <li>All the missing values of protein, fat and other nutrients amounts (in grams) for all the foodgrains are non-zero multiples of 4.</li> $$\newline$$ <li>P1 contained double the amount of protein that M3 contains.</li> $\newline$ </ol>
How many foodgrains had a higher amount of carbohydrate per 100 grams of nutrients than M1?
The table given below shows the amount, in grams, of carbohydrate, protein, fat and all other nutrients, per 100 grams of nutrients in seven food grains. The first column shows the foodgrain category and the second column its codename. The table has some missing values. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GQdIW9xUGI5li3N" width="600px"/> $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>Both the pseudo-cereals had higher amounts of carbohydrate as well as higher amounts of protein than any millet.</li> $$\newline$$ <li>Both the cereals had higher amounts of carbohydrate than any pseudo-cereal.</li> $$\newline$$ <li>All the missing values of carbohydrate amounts (in grams) for all the foodgrains are non-zero multiples of 5.</li> $$\newline$$ <li>All the missing values of protein, fat and other nutrients amounts (in grams) for all the foodgrains are non-zero multiples of 4.</li> $$\newline$$ <li>P1 contained double the amount of protein that M3 contains.</li> $\newline$ </ol>
How many grams of protein were there in 100 grams of nutrients in M2?
The table given below shows the amount, in grams, of carbohydrate, protein, fat and all other nutrients, per 100 grams of nutrients in seven food grains. The first column shows the foodgrain category and the second column its codename. The table has some missing values. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GQdIW9xUGI5li3N" width="600px"/> $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>Both the pseudo-cereals had higher amounts of carbohydrate as well as higher amounts of protein than any millet.</li> $$\newline$$ <li>Both the cereals had higher amounts of carbohydrate than any pseudo-cereal.</li> $$\newline$$ <li>All the missing values of carbohydrate amounts (in grams) for all the foodgrains are non-zero multiples of 5.</li> $$\newline$$ <li>All the missing values of protein, fat and other nutrients amounts (in grams) for all the foodgrains are non-zero multiples of 4.</li> $$\newline$$ <li>P1 contained double the amount of protein that M3 contains.</li> $\newline$ </ol>
How many grams of other nutrients were there in 100 grams of nutrients in M3?
The table given below shows the amount, in grams, of carbohydrate, protein, fat and all other nutrients, per 100 grams of nutrients in seven food grains. The first column shows the foodgrain category and the second column its codename. The table has some missing values. $$\newline$$ <img src="https://balti.aftergrad.in/questions/GQdIW9xUGI5li3N" width="600px"/> $$\newline$$ The following additional facts are known. $$\newline$$ <ol> $\newline$ <li>Both the pseudo-cereals had higher amounts of carbohydrate as well as higher amounts of protein than any millet.</li> $$\newline$$ <li>Both the cereals had higher amounts of carbohydrate than any pseudo-cereal.</li> $$\newline$$ <li>All the missing values of carbohydrate amounts (in grams) for all the foodgrains are non-zero multiples of 5.</li> $$\newline$$ <li>All the missing values of protein, fat and other nutrients amounts (in grams) for all the foodgrains are non-zero multiples of 4.</li> $$\newline$$ <li>P1 contained double the amount of protein that M3 contains.</li> $\newline$ </ol>
What is the median of the number of grams of protein in 100 grams of nutrients among these food grains?
In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months, January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.
<ol>
<li>In every month, both online and offline registration numbers were multiples of 10.</li>
<li>In January, the number of offline registrations was twice that of online registrations.</li>
<li>In April, the number of online registrations was twice that of offline registrations.</li>
<li>The number of online registrations in March was the same as the number of offline registrations in February.</li>
<li>The number of online registrations was the largest in May.</li>
</ol>
<img src="https://balti.aftergrad.in/questions/WmqdRM0XsKMRC29" width="400px"/>
What was the total number of registrations in April?
In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months, January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.
<ol>
<li>In every month, both online and offline registration numbers were multiples of 10.</li>
<li>In January, the number of offline registrations was twice that of online registrations.</li>
<li>In April, the number of online registrations was twice that of offline registrations.</li>
<li>The number of online registrations in March was the same as the number of offline registrations in February.</li>
<li>The number of online registrations was the largest in May.</li>
</ol>
<img src="https://balti.aftergrad.in/questions/WmqdRM0XsKMRC29" width="400px"/>
What was the number of online registrations in January?
In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months, January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.
<ol>
<li>In every month, both online and offline registration numbers were multiples of 10.</li>
<li>In January, the number of offline registrations was twice that of online registrations.</li>
<li>In April, the number of online registrations was twice that of offline registrations.</li>
<li>The number of online registrations in March was the same as the number of offline registrations in February.</li>
<li>The number of online registrations was the largest in May.</li>
</ol>
<img src="https://balti.aftergrad.in/questions/WmqdRM0XsKMRC29" width="400px"/>
Which of the following statements can be true?<br><br>I. The number of offline registrations was the smallest In May.<br> $$\newline$$ II. The total number of registrations was the smallest in February.
In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months, January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.
<ol>
<li>In every month, both online and offline registration numbers were multiples of 10.</li>
<li>In January, the number of offline registrations was twice that of online registrations.</li>
<li>In April, the number of online registrations was twice that of offline registrations.</li>
<li>The number of online registrations in March was the same as the number of offline registrations in February.</li>
<li>The number of online registrations was the largest in May.</li>
</ol>
<img src="https://balti.aftergrad.in/questions/WmqdRM0XsKMRC29" width="400px"/>
What was the number of online registrations in January?
In a coaching class, some students register online, and some others register offline. No student registers both online and offline; hence the total registration number is the sum of online and offline registrations. The following facts and table pertain to these registration numbers for the five months, January to May of 2023. The table shows the minimum, maximum, median registration numbers of these five months, separately for online, offline and total number of registrations. The following additional facts are known.
<ol>
<li>In every month, both online and offline registration numbers were multiples of 10.</li>
<li>In January, the number of offline registrations was twice that of online registrations.</li>
<li>In April, the number of online registrations was twice that of offline registrations.</li>
<li>The number of online registrations in March was the same as the number of offline registrations in February.</li>
<li>The number of online registrations was the largest in May.</li>
</ol>
<img src="https://balti.aftergrad.in/questions/WmqdRM0XsKMRC29" width="400px"/>
Which pair of months definitely had the same total number of registrations? $\newline$ I. January and April $\newline$ II. February and May
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>
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>
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 Akhil attains a total score of 24, then what is the total score of Bimal?
Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers – Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5. $$\newline$$ The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively. $$\newline$$ The summary statistics of these ratings for the five workers is given below. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>Ullas</th><th>Vasu</th><th>Waman</th><th>Xavier</th><th>Yusuf</th></tr></thead><tbody><tr><td>Mean rating</td><td>2.2</td><td>3.8</td><td>3.4</td><td>3.6</td><td>2.6</td></tr><tr><td>Median rating</td><td>2</td><td>4</td><td>4</td><td>4</td><td>3</td></tr><tr><td>Modal rating</td><td>2</td><td>4</td><td>5</td><td>5</td><td>1 and 4</td></tr><tr><td>Range of rating*</td><td>3</td><td>3</td><td>4</td><td>4</td><td>3</td></tr></tbody></table> $$\newline$$ *Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker. $$\newline$$ The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers. $$\newline$$ (a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu. $$\newline$$ (b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
How many individual ratings cannot be determined from the above information? (in numerial value)
Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers – Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5. $$\newline$$ The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively. $$\newline$$ The summary statistics of these ratings for the five workers is given below. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>Ullas</th><th>Vasu</th><th>Waman</th><th>Xavier</th><th>Yusuf</th></tr></thead><tbody><tr><td>Mean rating</td><td>2.2</td><td>3.8</td><td>3.4</td><td>3.6</td><td>2.6</td></tr><tr><td>Median rating</td><td>2</td><td>4</td><td>4</td><td>4</td><td>3</td></tr><tr><td>Modal rating</td><td>2</td><td>4</td><td>5</td><td>5</td><td>1 and 4</td></tr><tr><td>Range of rating*</td><td>3</td><td>3</td><td>4</td><td>4</td><td>3</td></tr></tbody></table> $$\newline$$ *Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker. $$\newline$$ The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers. $$\newline$$ (a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu. $$\newline$$ (b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
To how many workers did R2 give a rating of 4? (in numerial value)
Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers – Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5. $$\newline$$ The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively. $$\newline$$ The summary statistics of these ratings for the five workers is given below. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>Ullas</th><th>Vasu</th><th>Waman</th><th>Xavier</th><th>Yusuf</th></tr></thead><tbody><tr><td>Mean rating</td><td>2.2</td><td>3.8</td><td>3.4</td><td>3.6</td><td>2.6</td></tr><tr><td>Median rating</td><td>2</td><td>4</td><td>4</td><td>4</td><td>3</td></tr><tr><td>Modal rating</td><td>2</td><td>4</td><td>5</td><td>5</td><td>1 and 4</td></tr><tr><td>Range of rating*</td><td>3</td><td>3</td><td>4</td><td>4</td><td>3</td></tr></tbody></table> $$\newline$$ *Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker. $$\newline$$ The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers. $$\newline$$ (a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu. $$\newline$$ (b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
What rating did R1 give to Xavier? (in numerial value)
Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers – Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5. $$\newline$$ The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively. $$\newline$$ The summary statistics of these ratings for the five workers is given below. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>Ullas</th><th>Vasu</th><th>Waman</th><th>Xavier</th><th>Yusuf</th></tr></thead><tbody><tr><td>Mean rating</td><td>2.2</td><td>3.8</td><td>3.4</td><td>3.6</td><td>2.6</td></tr><tr><td>Median rating</td><td>2</td><td>4</td><td>4</td><td>4</td><td>3</td></tr><tr><td>Modal rating</td><td>2</td><td>4</td><td>5</td><td>5</td><td>1 and 4</td></tr><tr><td>Range of rating*</td><td>3</td><td>3</td><td>4</td><td>4</td><td>3</td></tr></tbody></table> $$\newline$$ *Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker. $$\newline$$ The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers. $$\newline$$ (a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu. $$\newline$$ (b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
What is the median of the ratings given by R3 to the five workers? (in numerial value)
Five restaurants, coded R1, R2, R3, R4 and R5 gave integer ratings to five gig workers – Ullas, Vasu, Waman, Xavier and Yusuf, on a scale of 1 to 5. $$\newline$$ The means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively. $$\newline$$ The summary statistics of these ratings for the five workers is given below. $$\newline$$ <table class="question-table"><thead><tr><th></th><th>Ullas</th><th>Vasu</th><th>Waman</th><th>Xavier</th><th>Yusuf</th></tr></thead><tbody><tr><td>Mean rating</td><td>2.2</td><td>3.8</td><td>3.4</td><td>3.6</td><td>2.6</td></tr><tr><td>Median rating</td><td>2</td><td>4</td><td>4</td><td>4</td><td>3</td></tr><tr><td>Modal rating</td><td>2</td><td>4</td><td>5</td><td>5</td><td>1 and 4</td></tr><tr><td>Range of rating*</td><td>3</td><td>3</td><td>4</td><td>4</td><td>3</td></tr></tbody></table> $$\newline$$ *Range of ratings is defined as the difference between the maximum and minimum ratings awarded to a worker. $$\newline$$ The following is partial information about ratings of 1 and 5 awarded by the restaurants to the workers. $$\newline$$ (a) R1 awarded a rating of 5 to Waman, as did R2 to Xavier, R3 to Waman and Xavier, and R5 to Vasu. $$\newline$$ (b) R1 awarded a rating of 1 to Ullas, as did R2 to Waman and Yusuf, and R3 to Yusuf.
Which among the following restaurants gave its median rating to exactly one of the workers?
All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade; others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained. $$\newline$$ <ol> $\newline$ <li>The numbers of non-CS students who took AI and ML were in the ratio 2: 5.</li> $$\newline$$ <li>The number of non-CS students who took either AI or ML was equal to the number of CS students.</li> $$\newline$$ <li>The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.</li> $$\newline$$ <li>In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3: 2 for ML.</li> $$\newline$$ <li>No CS student failed in AI, while no non-CS student got an A grade in AI.</li> $$\newline$$ <li>The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4:5:2.</li> $$\newline$$ <li>The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was 3: 1.</li> $$\newline$$ <li>30 students failed in ML.</li> $\newline$ </ol>
All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade; others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained. $$\newline$$ <ol> $\newline$ <li>The numbers of non-CS students who took AI and ML were in the ratio 2: 5.</li> $$\newline$$ <li>The number of non-CS students who took either AI or ML was equal to the number of CS students.</li> $$\newline$$ <li>The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.</li> $$\newline$$ <li>In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3: 2 for ML.</li> $$\newline$$ <li>No CS student failed in AI, while no non-CS student got an A grade in AI.</li> $$\newline$$ <li>The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4:5:2.</li> $$\newline$$ <li>The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was 3: 1.</li> $$\newline$$ <li>30 students failed in ML.</li> $\newline$ </ol>
All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade; others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained. $$\newline$$ <ol> $\newline$ <li>The numbers of non-CS students who took AI and ML were in the ratio 2: 5.</li> $$\newline$$ <li>The number of non-CS students who took either AI or ML was equal to the number of CS students.</li> $$\newline$$ <li>The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.</li> $$\newline$$ <li>In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3: 2 for ML.</li> $$\newline$$ <li>No CS student failed in AI, while no non-CS student got an A grade in AI.</li> $$\newline$$ <li>The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4:5:2.</li> $$\newline$$ <li>The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was 3: 1.</li> $$\newline$$ <li>30 students failed in ML.</li> $\newline$ </ol>
All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade; others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained. $$\newline$$ <ol> $\newline$ <li>The numbers of non-CS students who took AI and ML were in the ratio 2: 5.</li> $$\newline$$ <li>The number of non-CS students who took either AI or ML was equal to the number of CS students.</li> $$\newline$$ <li>The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.</li> $$\newline$$ <li>In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3: 2 for ML.</li> $$\newline$$ <li>No CS student failed in AI, while no non-CS student got an A grade in AI.</li> $$\newline$$ <li>The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4:5:2.</li> $$\newline$$ <li>The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was 3: 1.</li> $$\newline$$ <li>30 students failed in ML.</li> $\newline$ </ol>
All the first-year students in the computer science (CS) department in a university take both the courses (i) AI and (ii) ML. Students from other departments (non-CS students) can also take one of these two courses, but not both. Students who fail in a course get an F grade; others pass and are awarded A or B or C grades depending on their performance. The following are some additional facts about the number of students who took these two courses this year and the grades they obtained. $$\newline$$ <ol> $\newline$ <li>The numbers of non-CS students who took AI and ML were in the ratio 2: 5.</li> $$\newline$$ <li>The number of non-CS students who took either AI or ML was equal to the number of CS students.</li> $$\newline$$ <li>The numbers of non-CS students who failed in the two courses were the same and their total is equal to the number of CS students who got a C grade in ML.</li> $$\newline$$ <li>In both the courses, 50% of the students who passed got a B grade. But, while the numbers of students who got A and C grades were the same for AI, they were in the ratio 3: 2 for ML.</li> $$\newline$$ <li>No CS student failed in AI, while no non-CS student got an A grade in AI.</li> $$\newline$$ <li>The numbers of CS students who got A, B and C grades respectively in AI were in the ratio 3 : 5 : 2, while in ML the ratio was 4:5:2.</li> $$\newline$$ <li>The ratio of the total number of non-CS students failing in one of the two courses to the number of CS students failing in one of the two courses was 3: 1.</li> $$\newline$$ <li>30 students failed in ML.</li> $\newline$ </ol>
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There were equal numbers of domestic and foreign products.</li> $$\newline$$ <li>Half of the domestic products were FDA approved cosmetic products.</li> $$\newline$$ <li>None of the foreign products had both the approvals, while 60 domestic products had both the approvals.</li> $$\newline$$ <li>There were 140 nutrition products, half of them were foreign products.</li> $$\newline$$ <li>There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products</li> $$\newline$$ </ol>
How many foreign products were FDA approved cosmetic products?
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There were equal numbers of domestic and foreign products.</li> $$\newline$$ <li>Half of the domestic products were FDA approved cosmetic products.</li> $$\newline$$ <li>None of the foreign products had both the approvals, while 60 domestic products had both the approvals.</li> $$\newline$$ <li>There were 140 nutrition products, half of them were foreign products.</li> $$\newline$$ <li>There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products</li> $$\newline$$ </ol>
How many cosmetic products did not have FDA approval?
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There were equal numbers of domestic and foreign products.</li> $$\newline$$ <li>Half of the domestic products were FDA approved cosmetic products.</li> $$\newline$$ <li>None of the foreign products had both the approvals, while 60 domestic products had both the approvals.</li> $$\newline$$ <li>There were 140 nutrition products, half of them were foreign products.</li> $$\newline$$ <li>There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products</li> $$\newline$$ </ol>
Which among the following options best represents the number of domestic cosmetic products that had both the approvals?
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There were equal numbers of domestic and foreign products.</li> $$\newline$$ <li>Half of the domestic products were FDA approved cosmetic products.</li> $$\newline$$ <li>None of the foreign products had both the approvals, while 60 domestic products had both the approvals.</li> $$\newline$$ <li>There were 140 nutrition products, half of them were foreign products.</li> $$\newline$$ <li>There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products</li> $$\newline$$ </ol>
If $70$ cosmetic products did not have EU approval, then how many nutrition products had both the approvals?
A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals - FDA or EU. $$\newline$$ The following facts are also known: $$\newline$$ <ol> $\newline$ <li>There were equal numbers of domestic and foreign products.</li> $$\newline$$ <li>Half of the domestic products were FDA approved cosmetic products.</li> $$\newline$$ <li>None of the foreign products had both the approvals, while 60 domestic products had both the approvals.</li> $$\newline$$ <li>There were 140 nutrition products, half of them were foreign products.</li> $$\newline$$ <li>There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products</li> $$\newline$$ </ol>
If $50$ nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?
A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below. $$\newline$$ 1. Over the two days, all three of them met the same total number of households, and each of them sold a total of $100$ items. $$\newline$$ 2. On both days, Lahur met the same number of households and sold the same number of items. $$\newline$$ 3. Hokli could not sell any item on the second day because the first household he met on that day complained against him. $$\newline$$ 4. Tohri met $30$ more households on the second day than on the first day. $$\newline$$ 5. Tohri's success rate was twice that of Lahur's on the first day, and it was $75 \%$ of Lahur's on the second day.
What was the total number of households met by Tohri, Hokli and Lahur on the first day?
A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below. $$\newline$$ 1. Over the two days, all three of them met the same total number of households, and each of them sold a total of $100$ items. $$\newline$$ 2. On both days, Lahur met the same number of households and sold the same number of items. $$\newline$$ 3. Hokli could not sell any item on the second day because the first household he met on that day complained against him. $$\newline$$ 4. Tohri met $30$ more households on the second day than on the first day. $$\newline$$ 5. Tohri's success rate was twice that of Lahur's on the first day, and it was $75 \%$ of Lahur's on the second day.
How many TRICCEK items were sold by Tohri on the first day?
A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below. $$\newline$$ 1. Over the two days, all three of them met the same total number of households, and each of them sold a total of $100$ items. $$\newline$$ 2. On both days, Lahur met the same number of households and sold the same number of items. $$\newline$$ 3. Hokli could not sell any item on the second day because the first household he met on that day complained against him. $$\newline$$ 4. Tohri met $30$ more households on the second day than on the first day. $$\newline$$ 5. Tohri's success rate was twice that of Lahur's on the first day, and it was $75 \%$ of Lahur's on the second day.
How many households did Lahur meet on the second day?
A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below. $$\newline$$ 1. Over the two days, all three of them met the same total number of households, and each of them sold a total of $100$ items. $$\newline$$ 2. On both days, Lahur met the same number of households and sold the same number of items. $$\newline$$ 3. Hokli could not sell any item on the second day because the first household he met on that day complained against him. $$\newline$$ 4. Tohri met $30$ more households on the second day than on the first day. $$\newline$$ 5. Tohri's success rate was twice that of Lahur's on the first day, and it was $75 \%$ of Lahur's on the second day.
How many households did Tohri meet on the first day?
A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below. $$\newline$$ 1. Over the two days, all three of them met the same total number of households, and each of them sold a total of $100$ items. $$\newline$$ 2. On both days, Lahur met the same number of households and sold the same number of items. $$\newline$$ 3. Hokli could not sell any item on the second day because the first household he met on that day complained against him. $$\newline$$ 4. Tohri met $30$ more households on the second day than on the first day. $$\newline$$ 5. Tohri's success rate was twice that of Lahur's on the first day, and it was $75 \%$ of Lahur's on the second day.
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 total number of units of milk the three women had in the beginning?
XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery.<br><br>The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day. $$\newline$$ It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Day</th><th>Cumulative orders booked</th><th>Orders delivered on day</th><th>Cumulative orders lost</th></tr></thead><tbody><tr><td>13th</td><td>219</td><td>11</td><td>91</td></tr><tr><td>14th</td><td>249</td><td>27</td><td>92</td></tr><tr><td>15th</td><td>277</td><td>23</td><td>94</td></tr><tr><td>16th</td><td>302</td><td>11</td><td>106</td></tr><tr><td>17th</td><td>327</td><td>21</td><td>118</td></tr><tr><td>18th</td><td>332</td><td>13</td><td>120</td></tr><tr><td>19th</td><td>337</td><td>14</td><td>129</td></tr></tbody></table><br><br>
Among the following days, the largest fraction of orders booked on which day was lost?
XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery.<br><br>The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day. $$\newline$$ It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Day</th><th>Cumulative orders booked</th><th>Orders delivered on day</th><th>Cumulative orders lost</th></tr></thead><tbody><tr><td>13th</td><td>219</td><td>11</td><td>91</td></tr><tr><td>14th</td><td>249</td><td>27</td><td>92</td></tr><tr><td>15th</td><td>277</td><td>23</td><td>94</td></tr><tr><td>16th</td><td>302</td><td>11</td><td>106</td></tr><tr><td>17th</td><td>327</td><td>21</td><td>118</td></tr><tr><td>18th</td><td>332</td><td>13</td><td>120</td></tr><tr><td>19th</td><td>337</td><td>14</td><td>129</td></tr></tbody></table><br><br>
On which of the following days was the number of orders booked the highest?
XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery.<br><br>The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day. $$\newline$$ It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Day</th><th>Cumulative orders booked</th><th>Orders delivered on day</th><th>Cumulative orders lost</th></tr></thead><tbody><tr><td>13th</td><td>219</td><td>11</td><td>91</td></tr><tr><td>14th</td><td>249</td><td>27</td><td>92</td></tr><tr><td>15th</td><td>277</td><td>23</td><td>94</td></tr><tr><td>16th</td><td>302</td><td>11</td><td>106</td></tr><tr><td>17th</td><td>327</td><td>21</td><td>118</td></tr><tr><td>18th</td><td>332</td><td>13</td><td>120</td></tr><tr><td>19th</td><td>337</td><td>14</td><td>129</td></tr></tbody></table><br><br>
The delivery ratio for a given day is defined as the ratio of the number of orders booked on that day which are delivered on the next day to the number of orders booked on the second day after booking. On which of the following days, was the delivery ratio the highest?
XYZ organization got into the business of delivering groceries to home at the beginning of the last month. They have a two-day delivery promise. However, their deliveries are unreliable. An order booked on a particular day may be delivered the next day or the day after. If the order is not delivered at the end of two days, then the order is declared as lost at the end of the second day. XYZ then does not deliver the order, but informs the customer, marks the order as lost, returns the payment and pays a penalty for non-delivery.<br><br>The following table provides details about the operations of XYZ for a week of the last month. The first column gives the date, the second gives the cumulative number of orders that were booked up to and including that day. The third column represents the number of orders delivered on that day. The last column gives the cumulative number of orders that were lost up to and including that day. $$\newline$$ It is known that the numbers of orders that were booked on the 11th, 12th, and 13th of the last month that took two days to deliver were 4, 6, and 8 respectively. $$\newline$$ <br><br><table class="question-table"><thead><tr><th>Day</th><th>Cumulative orders booked</th><th>Orders delivered on day</th><th>Cumulative orders lost</th></tr></thead><tbody><tr><td>13th</td><td>219</td><td>11</td><td>91</td></tr><tr><td>14th</td><td>249</td><td>27</td><td>92</td></tr><tr><td>15th</td><td>277</td><td>23</td><td>94</td></tr><tr><td>16th</td><td>302</td><td>11</td><td>106</td></tr><tr><td>17th</td><td>327</td><td>21</td><td>118</td></tr><tr><td>18th</td><td>332</td><td>13</td><td>120</td></tr><tr><td>19th</td><td>337</td><td>14</td><td>129</td></tr></tbody></table><br><br>
The average time taken to deliver orders booked on a particular day is computed as follows. Let the number of orders delivered the next day be $x$ and the number of orders delivered the day after be $y$. Then the average time to deliver order is $(x+2y)/(x+y)$. $\newline$ On which of the following days was the average time taken to deliver orders booked the least?
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. $$\newline$$ In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. $$\newline$$ The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election. $$\newline$$ <table class="question-table"><thead><tr><th>Constituency</th><th>A</th><th>B</th><th>C</th><th>D</th></tr></thead><tbody><tr><td>No. of candidates contesting</td><td>10</td><td>12</td><td>5</td><td>8</td></tr><tr><td>Total No. of valid votes polled</td><td>5,00,000</td><td>3,25,000</td><td>6,00,030</td><td></td></tr><tr><td>No. of votes polled by the winning candidate</td><td>2,75,000</td><td>48,750</td><td></td><td></td></tr><tr><td>No. of votes polled by the first runner up</td><td>95,000</td><td></td><td></td><td>37,500</td></tr><tr><td>No. of votes polled by the second runner up</td><td></td><td></td><td></td><td>30,000</td></tr><tr><td>% of valid votes polled by the third runner up</td><td></td><td></td><td></td><td>10%</td></tr></tbody></table> $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>The first runner up polled 10,000 more votes than the second runner up in constituency A.</li> $$\newline$$ <li>None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.</li> $$\newline$$ <li>The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.</li></ol>
What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. $$\newline$$ In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. $$\newline$$ The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election. $$\newline$$ <table class="question-table"><thead><tr><th>Constituency</th><th>A</th><th>B</th><th>C</th><th>D</th></tr></thead><tbody><tr><td>No. of candidates contesting</td><td>10</td><td>12</td><td>5</td><td>8</td></tr><tr><td>Total No. of valid votes polled</td><td>5,00,000</td><td>3,25,000</td><td>6,00,030</td><td></td></tr><tr><td>No. of votes polled by the winning candidate</td><td>2,75,000</td><td>48,750</td><td></td><td></td></tr><tr><td>No. of votes polled by the first runner up</td><td>95,000</td><td></td><td></td><td>37,500</td></tr><tr><td>No. of votes polled by the second runner up</td><td></td><td></td><td></td><td>30,000</td></tr><tr><td>% of valid votes polled by the third runner up</td><td></td><td></td><td></td><td>10%</td></tr></tbody></table> $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>The first runner up polled 10,000 more votes than the second runner up in constituency A.</li> $$\newline$$ <li>None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.</li> $$\newline$$ <li>The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.</li></ol>
How many candidates who contested in constituency B lost their security deposit?
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. $$\newline$$ In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. $$\newline$$ The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election. $$\newline$$ <table class="question-table"><thead><tr><th>Constituency</th><th>A</th><th>B</th><th>C</th><th>D</th></tr></thead><tbody><tr><td>No. of candidates contesting</td><td>10</td><td>12</td><td>5</td><td>8</td></tr><tr><td>Total No. of valid votes polled</td><td>5,00,000</td><td>3,25,000</td><td>6,00,030</td><td></td></tr><tr><td>No. of votes polled by the winning candidate</td><td>2,75,000</td><td>48,750</td><td></td><td></td></tr><tr><td>No. of votes polled by the first runner up</td><td>95,000</td><td></td><td></td><td>37,500</td></tr><tr><td>No. of votes polled by the second runner up</td><td></td><td></td><td></td><td>30,000</td></tr><tr><td>% of valid votes polled by the third runner up</td><td></td><td></td><td></td><td>10%</td></tr></tbody></table> $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>The first runner up polled 10,000 more votes than the second runner up in constituency A.</li> $$\newline$$ <li>None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.</li> $$\newline$$ <li>The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.</li></ol>
What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. $$\newline$$ In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. $$\newline$$ The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election. $$\newline$$ <table class="question-table"><thead><tr><th>Constituency</th><th>A</th><th>B</th><th>C</th><th>D</th></tr></thead><tbody><tr><td>No. of candidates contesting</td><td>10</td><td>12</td><td>5</td><td>8</td></tr><tr><td>Total No. of valid votes polled</td><td>5,00,000</td><td>3,25,000</td><td>6,00,030</td><td></td></tr><tr><td>No. of votes polled by the winning candidate</td><td>2,75,000</td><td>48,750</td><td></td><td></td></tr><tr><td>No. of votes polled by the first runner up</td><td>95,000</td><td></td><td></td><td>37,500</td></tr><tr><td>No. of votes polled by the second runner up</td><td></td><td></td><td></td><td>30,000</td></tr><tr><td>% of valid votes polled by the third runner up</td><td></td><td></td><td></td><td>10%</td></tr></tbody></table> $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>The first runner up polled 10,000 more votes than the second runner up in constituency A.</li> $$\newline$$ <li>None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.</li> $$\newline$$ <li>The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.</li></ol>
What was the number of valid votes polled in constituency D?
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. $$\newline$$ In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. $$\newline$$ The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election. $$\newline$$ <table class="question-table"><thead><tr><th>Constituency</th><th>A</th><th>B</th><th>C</th><th>D</th></tr></thead><tbody><tr><td>No. of candidates contesting</td><td>10</td><td>12</td><td>5</td><td>8</td></tr><tr><td>Total No. of valid votes polled</td><td>5,00,000</td><td>3,25,000</td><td>6,00,030</td><td></td></tr><tr><td>No. of votes polled by the winning candidate</td><td>2,75,000</td><td>48,750</td><td></td><td></td></tr><tr><td>No. of votes polled by the first runner up</td><td>95,000</td><td></td><td></td><td>37,500</td></tr><tr><td>No. of votes polled by the second runner up</td><td></td><td></td><td></td><td>30,000</td></tr><tr><td>% of valid votes polled by the third runner up</td><td></td><td></td><td></td><td>10%</td></tr></tbody></table> $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>The first runner up polled 10,000 more votes than the second runner up in constituency A.</li> $$\newline$$ <li>None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.</li> $$\newline$$ <li>The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.</li></ol>
The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. $\newline$ Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?
In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. $$\newline$$ In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits. $$\newline$$ The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election. $$\newline$$ <table class="question-table"><thead><tr><th>Constituency</th><th>A</th><th>B</th><th>C</th><th>D</th></tr></thead><tbody><tr><td>No. of candidates contesting</td><td>10</td><td>12</td><td>5</td><td>8</td></tr><tr><td>Total No. of valid votes polled</td><td>5,00,000</td><td>3,25,000</td><td>6,00,030</td><td></td></tr><tr><td>No. of votes polled by the winning candidate</td><td>2,75,000</td><td>48,750</td><td></td><td></td></tr><tr><td>No. of votes polled by the first runner up</td><td>95,000</td><td></td><td></td><td>37,500</td></tr><tr><td>No. of votes polled by the second runner up</td><td></td><td></td><td></td><td>30,000</td></tr><tr><td>% of valid votes polled by the third runner up</td><td></td><td></td><td></td><td>10%</td></tr></tbody></table> $$\newline$$ The following additional facts are known: $$\newline$$ <ol> $\newline$ <li>The first runner up polled 10,000 more votes than the second runner up in constituency A.</li> $$\newline$$ <li>None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.</li> $$\newline$$ <li>The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.</li></ol>
For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?
A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments - 'Apparel', 'Electronics', and 'HomeDecor'. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table. $$\newline$$ <table class="question-table"><thead><tr><td></td><td colspan="2">Delhi</td><td colspan="2">Mumbai</td><td colspan="2">Bengaluru</td><td colspan="2">Kolkata</td></tr><tr><td>Sales Amounts (Crore Rupees)</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td></tr></thead><tbody><tr><td>Apparels</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>54</td></tr><tr><td>Electronics</td><td>78</td><td>98</td><td>82</td><td>102</td><td>90</td><td>70</td><td>80</td><td>100</td></tr><tr><td>Home Decor</td><td></td><td>100</td><td></td><td>72</td><td></td><td>80</td><td></td><td>54</td></tr></tbody></table><br><br>The following additional information is known. $$\newline$$ <ol> $\newline$ <li>The sales amounts in the Apparel departments were the same for Delhi and Kolkata in2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments were the same for Mumbai and Kolkata in 2018.</li> $$\newline$$ <li>The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.</li> $$\newline$$ <li>The total sales amounts of the four Home Decor departments increased by Rs 70 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from 2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019 from 2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.</li></ol>
In the Home Decor departments, which cities had the highest sales amounts in 2018 and 2019, respectively?
A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments - 'Apparel', 'Electronics', and 'HomeDecor'. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table. $$\newline$$ <table class="question-table"><thead><tr><td></td><td colspan="2">Delhi</td><td colspan="2">Mumbai</td><td colspan="2">Bengaluru</td><td colspan="2">Kolkata</td></tr><tr><td>Sales Amounts (Crore Rupees)</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td></tr></thead><tbody><tr><td>Apparels</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>54</td></tr><tr><td>Electronics</td><td>78</td><td>98</td><td>82</td><td>102</td><td>90</td><td>70</td><td>80</td><td>100</td></tr><tr><td>Home Decor</td><td></td><td>100</td><td></td><td>72</td><td></td><td>80</td><td></td><td>54</td></tr></tbody></table><br><br>The following additional information is known. $$\newline$$ <ol> $\newline$ <li>The sales amounts in the Apparel departments were the same for Delhi and Kolkata in2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments were the same for Mumbai and Kolkata in 2018.</li> $$\newline$$ <li>The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.</li> $$\newline$$ <li>The total sales amounts of the four Home Decor departments increased by Rs 70 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from 2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019 from 2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.</li></ol>
What was the increase in sales amount, in Crore Rupees, in the Apparel department of Mumbai from 2018 to 2019?
A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments - 'Apparel', 'Electronics', and 'HomeDecor'. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table. $$\newline$$ <table class="question-table"><thead><tr><td></td><td colspan="2">Delhi</td><td colspan="2">Mumbai</td><td colspan="2">Bengaluru</td><td colspan="2">Kolkata</td></tr><tr><td>Sales Amounts (Crore Rupees)</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td></tr></thead><tbody><tr><td>Apparels</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>54</td></tr><tr><td>Electronics</td><td>78</td><td>98</td><td>82</td><td>102</td><td>90</td><td>70</td><td>80</td><td>100</td></tr><tr><td>Home Decor</td><td></td><td>100</td><td></td><td>72</td><td></td><td>80</td><td></td><td>54</td></tr></tbody></table><br><br>The following additional information is known. $$\newline$$ <ol> $\newline$ <li>The sales amounts in the Apparel departments were the same for Delhi and Kolkata in2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments were the same for Mumbai and Kolkata in 2018.</li> $$\newline$$ <li>The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.</li> $$\newline$$ <li>The total sales amounts of the four Home Decor departments increased by Rs 70 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from 2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019 from 2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.</li></ol>
Among all the 12 departments (i.e., the 3 departments in each of the 4 cities), what was the maximum percentage increase in sales amount from 2018 to 2019?
A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments - 'Apparel', 'Electronics', and 'HomeDecor'. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table. $$\newline$$ <table class="question-table"><thead><tr><td></td><td colspan="2">Delhi</td><td colspan="2">Mumbai</td><td colspan="2">Bengaluru</td><td colspan="2">Kolkata</td></tr><tr><td>Sales Amounts (Crore Rupees)</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td><td>2018</td><td>2019</td></tr></thead><tbody><tr><td>Apparels</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>54</td></tr><tr><td>Electronics</td><td>78</td><td>98</td><td>82</td><td>102</td><td>90</td><td>70</td><td>80</td><td>100</td></tr><tr><td>Home Decor</td><td></td><td>100</td><td></td><td>72</td><td></td><td>80</td><td></td><td>54</td></tr></tbody></table><br><br>The following additional information is known. $$\newline$$ <ol> $\newline$ <li>The sales amounts in the Apparel departments were the same for Delhi and Kolkata in2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments were the same for Mumbai and Kolkata in 2018.</li> $$\newline$$ <li>The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.</li> $$\newline$$ <li>The total sales amounts of the four Home Decor departments increased by Rs 70 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Home Decor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from 2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019 from 2018.</li> $$\newline$$ <li>The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.</li></ol>
What was the total sales amount, in Crore Rupees, in 2019 for the chain of departmental stores?
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
<img src="https://balti.aftergrad.in/questions/oc0seIMCy7gOprO" width="500px"/>
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
<table class="question-table"><thead><tr><th></th><th>IPC Crimes</th><th>SLL Crimes</th><th>Other Crimes</th></tr></thead><tbody><tr><td>Delhi</td><td>*</td><td>*</td><td>*</td></tr><tr><td>Goa</td><td>*</td><td>4</td><td>*</td></tr><tr><td>Haryana</td><td>8</td><td>6</td><td>*</td></tr><tr><td>Karnataka</td><td>3</td><td>2</td><td>*</td></tr><tr><td>Kerala</td><td>*</td><td>9</td><td>*</td></tr><tr><td>Maharashtra</td><td>3</td><td>4</td><td>8</td></tr><tr><td>Puducherry</td><td>13</td><td>29</td><td>*</td></tr><tr><td>Tamil Nadu</td><td>11</td><td>7</td><td>*</td></tr><tr><td>Telangana</td><td>6</td><td>9</td><td>8</td></tr><tr><td>West Bengal</td><td>17</td><td>*</td><td>16</td></tr></tbody></table>
What is the rank of Kerala in the 'IPC crimes' category?
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
<img src="https://balti.aftergrad.in/questions/oc0seIMCy7gOprO" width="500px"/>
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
<table class="question-table"><thead><tr><th></th><th>IPC Crimes</th><th>SLL Crimes</th><th>Other Crimes</th></tr></thead><tbody><tr><td>Delhi</td><td>*</td><td>*</td><td>*</td></tr><tr><td>Goa</td><td>*</td><td>4</td><td>*</td></tr><tr><td>Haryana</td><td>8</td><td>6</td><td>*</td></tr><tr><td>Karnataka</td><td>3</td><td>2</td><td>*</td></tr><tr><td>Kerala</td><td>*</td><td>9</td><td>*</td></tr><tr><td>Maharashtra</td><td>3</td><td>4</td><td>8</td></tr><tr><td>Puducherry</td><td>13</td><td>29</td><td>*</td></tr><tr><td>Tamil Nadu</td><td>11</td><td>7</td><td>*</td></tr><tr><td>Telangana</td><td>6</td><td>9</td><td>8</td></tr><tr><td>West Bengal</td><td>17</td><td>*</td><td>16</td></tr></tbody></table>
In the two states where the highest total number of cases are registered, the ratio of the total number of cases in IPC crimes to the total number in SLL crimes is closest to
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
<img src="https://balti.aftergrad.in/questions/oc0seIMCy7gOprO" width="500px"/>
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
<table class="question-table"><thead><tr><th></th><th>IPC Crimes</th><th>SLL Crimes</th><th>Other Crimes</th></tr></thead><tbody><tr><td>Delhi</td><td>*</td><td>*</td><td>*</td></tr><tr><td>Goa</td><td>*</td><td>4</td><td>*</td></tr><tr><td>Haryana</td><td>8</td><td>6</td><td>*</td></tr><tr><td>Karnataka</td><td>3</td><td>2</td><td>*</td></tr><tr><td>Kerala</td><td>*</td><td>9</td><td>*</td></tr><tr><td>Maharashtra</td><td>3</td><td>4</td><td>8</td></tr><tr><td>Puducherry</td><td>13</td><td>29</td><td>*</td></tr><tr><td>Tamil Nadu</td><td>11</td><td>7</td><td>*</td></tr><tr><td>Telangana</td><td>6</td><td>9</td><td>8</td></tr><tr><td>West Bengal</td><td>17</td><td>*</td><td>16</td></tr></tbody></table>
Which of the following is DEFINITELY true about the ranks of states/UT in the ‘other crimes’ category?
i) Tamil Nadu: 2
ii) Puducherry: 3
The Ministry of Home Affairs is analysing crimes committed by foreigners in different states and union territories (UT) of India. All cases refer to the ones registered against foreigners in 2016.
The number of cases – classified into three categories: IPC crimes, SLL crimes and other crimes – for nine states/UTs are shown in the figure below. These nine belong to the top ten states/UTs in terms of the total number of cases registered. The remaining state (among top ten) is West Bengal, where all the 520 cases registered were SLL crimes.
<img src="https://balti.aftergrad.in/questions/oc0seIMCy7gOprO" width="500px"/>
The table below shows the ranks of the ten states/UTs mentioned above among ALL states/UTs of India in terms of the number of cases registered in each of the three category of crimes. A state/UT is given rank r for a category of crimes if there are (r-1) states/UTs having a larger number of cases registered in the same category. For example, if two states have the same number of cases in a category, and exactly three other states/UTs have larger numbers of cases registered in the same category, then both the states are given rank 4 in that category. Missing ranks in the table are denoted by *.
<table class="question-table"><thead><tr><th></th><th>IPC Crimes</th><th>SLL Crimes</th><th>Other Crimes</th></tr></thead><tbody><tr><td>Delhi</td><td>*</td><td>*</td><td>*</td></tr><tr><td>Goa</td><td>*</td><td>4</td><td>*</td></tr><tr><td>Haryana</td><td>8</td><td>6</td><td>*</td></tr><tr><td>Karnataka</td><td>3</td><td>2</td><td>*</td></tr><tr><td>Kerala</td><td>*</td><td>9</td><td>*</td></tr><tr><td>Maharashtra</td><td>3</td><td>4</td><td>8</td></tr><tr><td>Puducherry</td><td>13</td><td>29</td><td>*</td></tr><tr><td>Tamil Nadu</td><td>11</td><td>7</td><td>*</td></tr><tr><td>Telangana</td><td>6</td><td>9</td><td>8</td></tr><tr><td>West Bengal</td><td>17</td><td>*</td><td>16</td></tr></tbody></table>
What is the sum of the ranks of Delhi in the three categories of crimes?
The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates. $$\newline$$ A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates. $$\newline$$ The following facts are known about the outlet on a particular day: $$\newline$$ 1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C. $$\newline$$ 2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3. $$\newline$$ 3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9. $$\newline$$ 4. The outlet received 88000 units of L by selling A during the day. $$\newline$$ 5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C. $$\newline$$ 6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.
How many units of currency A did the outlet buy on that day?
The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates. $$\newline$$ A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates. $$\newline$$ The following facts are known about the outlet on a particular day: $$\newline$$ 1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C. $$\newline$$ 2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3. $$\newline$$ 3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9. $$\newline$$ 4. The outlet received 88000 units of L by selling A during the day. $$\newline$$ 5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C. $$\newline$$ 6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.
How many units of currency C did the outlet sell on that day?
The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates. $$\newline$$ A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates. $$\newline$$ The following facts are known about the outlet on a particular day: $$\newline$$ 1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C. $$\newline$$ 2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3. $$\newline$$ 3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9. $$\newline$$ 4. The outlet received 88000 units of L by selling A during the day. $$\newline$$ 5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C. $$\newline$$ 6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.
What was the base exchange rate of currency B with respect to currency L on that day?
The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates. $$\newline$$ A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates. $$\newline$$ The following facts are known about the outlet on a particular day: $$\newline$$ 1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C. $$\newline$$ 2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3. $$\newline$$ 3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9. $$\newline$$ 4. The outlet received 88000 units of L by selling A during the day. $$\newline$$ 5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C. $$\newline$$ 6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.
What was the buying exchange rate of currency C with respect to currency L on that day?
There are only four brands of entry level smartphones called Azra, Bysi, Cxqi, and Dipq in a country. Details about their market
share, unit selling price, and profitability (defined as the profit as a percentage of the revenue) for the year 2016 are given in the
table below:
<table class="question-table"><thead><tr><td>Brand</td><td>Market Share (%)</td><td>Unit Selling Price (Rs.)</td><td>Profitability (%)</td></tr></thead><tbody><tr><td>Azra</td><td>40</td><td>15,000</td><td>10</td></tr><tr><td>Bysi</td><td>25</td><td>20,000</td><td>30</td></tr><tr><td>Cxqi</td><td>15</td><td>30,000</td><td>40</td></tr><tr><td>Dipq</td><td>20</td><td>25,000</td><td>30</td></tr></tbody></table>
In 2017, sales volume of entry level smartphones grew by 40% as compared to that in 2016. Cxqi offered a 40% discount on its
unit selling price in 2017, which resulted in a 15% increase in its market share. Each of the other three brands lost 5% market
share. However, the profitability of Cxqi came down to half of its value in 2016. The unit selling prices of the other three brands
and their profitability values remained the same in 2017 as they were in 2016.
The brand that had the highest revenue in 2016 is:
There are only four brands of entry level smartphones called Azra, Bysi, Cxqi, and Dipq in a country. Details about their market
share, unit selling price, and profitability (defined as the profit as a percentage of the revenue) for the year 2016 are given in the
table below:
<table class="question-table"><thead><tr><td>Brand</td><td>Market Share (%)</td><td>Unit Selling Price (Rs.)</td><td>Profitability (%)</td></tr></thead><tbody><tr><td>Azra</td><td>40</td><td>15,000</td><td>10</td></tr><tr><td>Bysi</td><td>25</td><td>20,000</td><td>30</td></tr><tr><td>Cxqi</td><td>15</td><td>30,000</td><td>40</td></tr><tr><td>Dipq</td><td>20</td><td>25,000</td><td>30</td></tr></tbody></table>
In 2017, sales volume of entry level smartphones grew by 40% as compared to that in 2016. Cxqi offered a 40% discount on its
unit selling price in 2017, which resulted in a 15% increase in its market share. Each of the other three brands lost 5% market
share. However, the profitability of Cxqi came down to half of its value in 2016. The unit selling prices of the other three brands
and their profitability values remained the same in 2017 as they were in 2016.
There are only four brands of entry level smartphones called Azra, Bysi, Cxqi, and Dipq in a country. Details about their market
share, unit selling price, and profitability (defined as the profit as a percentage of the revenue) for the year 2016 are given in the
table below:
<table class="question-table"><thead><tr><td>Brand</td><td>Market Share (%)</td><td>Unit Selling Price (Rs.)</td><td>Profitability (%)</td></tr></thead><tbody><tr><td>Azra</td><td>40</td><td>15,000</td><td>10</td></tr><tr><td>Bysi</td><td>25</td><td>20,000</td><td>30</td></tr><tr><td>Cxqi</td><td>15</td><td>30,000</td><td>40</td></tr><tr><td>Dipq</td><td>20</td><td>25,000</td><td>30</td></tr></tbody></table>
In 2017, sales volume of entry level smartphones grew by 40% as compared to that in 2016. Cxqi offered a 40% discount on its
unit selling price in 2017, which resulted in a 15% increase in its market share. Each of the other three brands lost 5% market
share. However, the profitability of Cxqi came down to half of its value in 2016. The unit selling prices of the other three brands
and their profitability values remained the same in 2017 as they were in 2016.
There are only four brands of entry level smartphones called Azra, Bysi, Cxqi, and Dipq in a country. Details about their market
share, unit selling price, and profitability (defined as the profit as a percentage of the revenue) for the year 2016 are given in the
table below:
<table class="question-table"><thead><tr><td>Brand</td><td>Market Share (%)</td><td>Unit Selling Price (Rs.)</td><td>Profitability (%)</td></tr></thead><tbody><tr><td>Azra</td><td>40</td><td>15,000</td><td>10</td></tr><tr><td>Bysi</td><td>25</td><td>20,000</td><td>30</td></tr><tr><td>Cxqi</td><td>15</td><td>30,000</td><td>40</td></tr><tr><td>Dipq</td><td>20</td><td>25,000</td><td>30</td></tr></tbody></table>
In 2017, sales volume of entry level smartphones grew by 40% as compared to that in 2016. Cxqi offered a 40% discount on its
unit selling price in 2017, which resulted in a 15% increase in its market share. Each of the other three brands lost 5% market
share. However, the profitability of Cxqi came down to half of its value in 2016. The unit selling prices of the other three brands
and their profitability values remained the same in 2017 as they were in 2016.
The complete list of brands whose profits went up in 2017 from 2016 is:
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>
What is the weight of the faculty quality parameter?
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>
What is the highest overall score among the eight colleges?
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 have overall scores between 31 and 40, both inclusive?
