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Q1:

CAT 2024 Slot 1

Logical Reasoning > Optimization

Hard

Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya's and Ramya's campaigns and the type of campaigns they run. Each campaign is said to have a level of $1$ if it is a staid campaign and a level of $2$ if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate. $$\newline$$ If Amiya and Ramya both run campaigns focusing on issues, then $\newline$ - The percentage of students voting in the election will be $20$ times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then $20 \times(2+2) \%$, that is, $80 \%$ of the students will vote in the election. $\newline$ - Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive $1 / 3$ of the votes cast, and Ramya will receive the other $2 / 3$. $$\newline$$ The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent. $\newline$ - If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then $10 \%$ of the students who would have otherwise voted for Amiya will vote for Ramya, and another $10 \%$ who would have otherwise voted for Amiya, will not vote at all. $\newline$ - If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then $20 \%$ of the students who would have otherwise voted for Ramya will vote for Amiya, and another $5 \%$ who would have otherwise voted for Ramya, will not vote at all. $\newline$ - If both run campaigns attacking each other, then $10 \%$ of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?

$60\%$

$64\%$

$40\%$

$36\%$

Correct Answer

Option 4

Correct Answer

Explanation →

Q2:

CAT 2024 Slot 1

Logical Reasoning > Optimization

Hard

Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya's and Ramya's campaigns and the type of campaigns they run. Each campaign is said to have a level of $1$ if it is a staid campaign and a level of $2$ if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate. $$\newline$$ If Amiya and Ramya both run campaigns focusing on issues, then $\newline$ - The percentage of students voting in the election will be $20$ times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then $20 \times(2+2) \%$, that is, $80 \%$ of the students will vote in the election. $\newline$ - Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive $1 / 3$ of the votes cast, and Ramya will receive the other $2 / 3$. $$\newline$$ The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent. $\newline$ - If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then $10 \%$ of the students who would have otherwise voted for Amiya will vote for Ramya, and another $10 \%$ who would have otherwise voted for Amiya, will not vote at all. $\newline$ - If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then $20 \%$ of the students who would have otherwise voted for Ramya will vote for Amiya, and another $5 \%$ who would have otherwise voted for Ramya, will not vote at all. $\newline$ - If both run campaigns attacking each other, then $10 \%$ of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

What is the minimum percentage of students who will vote in the election?

$32\%$

$40\%$

$36\%$

$38\%$

Correct Answer

Option 3

Correct Answer

Explanation →

Q3:

CAT 2024 Slot 1

Logical Reasoning > Optimization

Hard

Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya's and Ramya's campaigns and the type of campaigns they run. Each campaign is said to have a level of $1$ if it is a staid campaign and a level of $2$ if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate. $$\newline$$ If Amiya and Ramya both run campaigns focusing on issues, then $\newline$ - The percentage of students voting in the election will be $20$ times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then $20 \times(2+2) \%$, that is, $80 \%$ of the students will vote in the election. $\newline$ - Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive $1 / 3$ of the votes cast, and Ramya will receive the other $2 / 3$. $$\newline$$ The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent. $\newline$ - If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then $10 \%$ of the students who would have otherwise voted for Amiya will vote for Ramya, and another $10 \%$ who would have otherwise voted for Amiya, will not vote at all. $\newline$ - If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then $20 \%$ of the students who would have otherwise voted for Ramya will vote for Amiya, and another $5 \%$ who would have otherwise voted for Ramya, will not vote at all. $\newline$ - If both run campaigns attacking each other, then $10 \%$ of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

If Amiya runs a campaign focusing on issues, then what is the maximum percentage of votes that she $\newline$ can get?

40%

36%

48%

44%

Correct Answer

Option 3

Correct Answer

Explanation →

Q4:

CAT 2024 Slot 1

Logical Reasoning > Optimization

Hard

Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya's and Ramya's campaigns and the type of campaigns they run. Each campaign is said to have a level of $1$ if it is a staid campaign and a level of $2$ if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate. $$\newline$$ If Amiya and Ramya both run campaigns focusing on issues, then $\newline$ - The percentage of students voting in the election will be $20$ times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then $20 \times(2+2) \%$, that is, $80 \%$ of the students will vote in the election. $\newline$ - Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive $1 / 3$ of the votes cast, and Ramya will receive the other $2 / 3$. $$\newline$$ The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent. $\newline$ - If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then $10 \%$ of the students who would have otherwise voted for Amiya will vote for Ramya, and another $10 \%$ who would have otherwise voted for Amiya, will not vote at all. $\newline$ - If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then $20 \%$ of the students who would have otherwise voted for Ramya will vote for Amiya, and another $5 \%$ who would have otherwise voted for Ramya, will not vote at all. $\newline$ - If both run campaigns attacking each other, then $10 \%$ of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

If Ramya runs a campaign attacking Amiya, then what is the minimum percentage of votes that she is guaranteed to get?

30%

15%

12%

18%

Correct Answer

Option 2

Correct Answer

Explanation →

Q5:

CAT 2024 Slot 1

Logical Reasoning > Optimization

Hard

Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya's and Ramya's campaigns and the type of campaigns they run. Each campaign is said to have a level of $1$ if it is a staid campaign and a level of $2$ if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate. $$\newline$$ If Amiya and Ramya both run campaigns focusing on issues, then $\newline$ - The percentage of students voting in the election will be $20$ times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then $20 \times(2+2) \%$, that is, $80 \%$ of the students will vote in the election. $\newline$ - Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive $1 / 3$ of the votes cast, and Ramya will receive the other $2 / 3$. $$\newline$$ The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent. $\newline$ - If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then $10 \%$ of the students who would have otherwise voted for Amiya will vote for Ramya, and another $10 \%$ who would have otherwise voted for Amiya, will not vote at all. $\newline$ - If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then $20 \%$ of the students who would have otherwise voted for Ramya will vote for Amiya, and another $5 \%$ who would have otherwise voted for Ramya, will not vote at all. $\newline$ - If both run campaigns attacking each other, then $10 \%$ of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.

What is the maximum possible voting margin with which one of the candidates can win?

20%

29%

26%

28%

Correct Answer

Option 2

Correct Answer

Explanation →

Q6:

CAT 2023 Slot 2

Logical Reasoning > Optimization

Hard

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. $$\newline$$ Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. $$\newline$$ The following information is also known. $$\newline$$ <ol><li>Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).</li> $$\newline$$ <li>Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.</li> $$\newline$$ <li>Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.</li> $$\newline$$ <li>The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.</li></ol>

What was the total amount spent on tickets (in Rs.) by Bipasha?

100

120

110

90

Correct Answer

Option 3

Correct Answer

Explanation →

Q7:

CAT 2023 Slot 2

Logical Reasoning > Optimization

Hard

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. $$\newline$$ Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. $$\newline$$ The following information is also known. $$\newline$$ <ol><li>Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).</li> $$\newline$$ <li>Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.</li> $$\newline$$ <li>Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.</li> $$\newline$$ <li>The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.</li></ol>

Which were all the rides that Anjali completed by 2:00 pm?

Ride-1 and Ride-4

Ride-1, Ride-2, and Ride-4

Ride-1, Ride-2, and Ride-3

Ride-1 and Ride-3

Correct Answer

Option 3

Correct Answer

Explanation →

Q8:

CAT 2023 Slot 2

Logical Reasoning > Optimization

Hard

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. $$\newline$$ Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. $$\newline$$ The following information is also known. $$\newline$$ <ol><li>Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).</li> $$\newline$$ <li>Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.</li> $$\newline$$ <li>Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.</li> $$\newline$$ <li>The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.</li></ol>

Which ride was taken by all three visitors?

Ride-4

Ride-2

Ride-3

Ride-1

Correct Answer

Option 4

Correct Answer

Explanation →

Q9:

CAT 2023 Slot 2

Logical Reasoning > Optimization

Hard

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. $$\newline$$ Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. $$\newline$$ The following information is also known. $$\newline$$ <ol><li>Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).</li> $$\newline$$ <li>Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.</li> $$\newline$$ <li>Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.</li> $$\newline$$ <li>The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.</li></ol>

How many rides did Anjali and Chitra take in total?

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q10:

CAT 2023 Slot 2

Logical Reasoning > Optimization

Hard

Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. $$\newline$$ Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly. $$\newline$$ The following information is also known. $$\newline$$ <ol><li>Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).</li> $$\newline$$ <li>Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.</li> $$\newline$$ <li>Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.</li> $$\newline$$ <li>The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.</li></ol>

What was the total amount spent on tickets (in Rs.) by Anjali?

Entered answer:

Correct Answer

140

Correct Answer

Explanation →

Q11:

CAT 2023 Slot 1

Logical Reasoning > Optimization

Hard

A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.<p> $$\newline$$ There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.</p> $$\newline$$ <p>On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.</p> $$\newline$$ <p>Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.</p> $$\newline$$ <p>The following additional information is known about that day.</p> $$\newline$$ <ol> $$\newline$$ <li>All slots were full.</li> $$\newline$$ <li>The number of US applications was the same in all the slots. The same was true for the other three categories.</li> $$\newline$$ <li>50% of the applications were US applications.</li> $$\newline$$ <li>All applicants except Ira, Vijay and Nandini arrived on time.</li> $$\newline$$ <li>Vijay was called to a counter at 9:25 am.</li></ol>

How many UK applications were scheduled on that day? (in numerial value)

Entered answer:

Correct Answer

0

Correct Answer

Explanation →

Q12:

CAT 2023 Slot 1

Logical Reasoning > Optimization

Hard

A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.<p> $$\newline$$ There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.</p> $$\newline$$ <p>On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.</p> $$\newline$$ <p>Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.</p> $$\newline$$ <p>The following additional information is known about that day.</p> $$\newline$$ <ol> $$\newline$$ <li>All slots were full.</li> $$\newline$$ <li>The number of US applications was the same in all the slots. The same was true for the other three categories.</li> $$\newline$$ <li>50% of the applications were US applications.</li> $$\newline$$ <li>All applicants except Ira, Vijay and Nandini arrived on time.</li> $$\newline$$ <li>Vijay was called to a counter at 9:25 am.</li></ol>

What is the maximum possible value of the total time (in minutes, nearest to its integer value) required to process all applications in the Others category on that day? (in numerial value)

Entered answer:

Correct Answer

200

Correct Answer

Explanation →

Q13:

CAT 2023 Slot 1

Logical Reasoning > Optimization

Hard

A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.<p> $$\newline$$ There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.</p> $$\newline$$ <p>On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.</p> $$\newline$$ <p>Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.</p> $$\newline$$ <p>The following additional information is known about that day.</p> $$\newline$$ <ol> $$\newline$$ <li>All slots were full.</li> $$\newline$$ <li>The number of US applications was the same in all the slots. The same was true for the other three categories.</li> $$\newline$$ <li>50% of the applications were US applications.</li> $$\newline$$ <li>All applicants except Ira, Vijay and Nandini arrived on time.</li> $$\newline$$ <li>Vijay was called to a counter at 9:25 am.</li></ol>

Which of the following is the closest to the time when Nandini's application process got over?

9:45 am

9:37 am

9:50 am

9:35 am

Correct Answer

Option 1

Correct Answer

Explanation →

Q14:

CAT 2023 Slot 1

Logical Reasoning > Optimization

Hard

A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.<p> $$\newline$$ There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.</p> $$\newline$$ <p>On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.</p> $$\newline$$ <p>Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.</p> $$\newline$$ <p>The following additional information is known about that day.</p> $$\newline$$ <ol> $$\newline$$ <li>All slots were full.</li> $$\newline$$ <li>The number of US applications was the same in all the slots. The same was true for the other three categories.</li> $$\newline$$ <li>50% of the applications were US applications.</li> $$\newline$$ <li>All applicants except Ira, Vijay and Nandini arrived on time.</li> $$\newline$$ <li>Vijay was called to a counter at 9:25 am.</li></ol>

Which of the following statements is false?

The application process of Mahira was completed before Nandini's.

The application process of Mahira started after Nandini's.

The application process of Osman was completed before 9:45 am.

The application process of Osman was completed before Vijay's.

Correct Answer

Option 2

Correct Answer

Explanation →

Q15:

CAT 2023 Slot 1

Logical Reasoning > Optimization

Hard

A visa processing office (VPO) accepts visa applications in four categories – US, UK, Schengen, and Others. The applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.<p> $$\newline$$ There are ten counters in the office, four dedicated to US applications, and two each for UK applications, Schengen applications and Others applications. Applicants are called in for processing sequentially on a first-come-first-served basis whenever a counter gets freed for their category. The processing time for an application is the same within each category. But it may vary across the categories. Each US and UK application requires 10 minutes of processing time. Depending on the number of applications in a category and time required to process an application for that category, it is possible that an applicant for a slot may be processed later.</p> $$\newline$$ <p>On a particular day, Ira, Vijay and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next.</p> $$\newline$$ <p>Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category.</p> $$\newline$$ <p>The following additional information is known about that day.</p> $$\newline$$ <ol> $$\newline$$ <li>All slots were full.</li> $$\newline$$ <li>The number of US applications was the same in all the slots. The same was true for the other three categories.</li> $$\newline$$ <li>50% of the applications were US applications.</li> $$\newline$$ <li>All applicants except Ira, Vijay and Nandini arrived on time.</li> $$\newline$$ <li>Vijay was called to a counter at 9:25 am.</li></ol>

When did the application processing for all US applicants get over on that day?

3:40 pm

2:05 pm

2:00 pm

2:25 pm

Correct Answer

Option 2

Correct Answer

Explanation →

Q16:

CAT 2020 Slot 2

Logical Reasoning > Optimization

Medium

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. $$\newline$$ Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots. $$\newline$$ The following additional facts are also known. $$\newline$$ <ol><li>Seminars by students from Economics are scheduled in each of the four slots.</li> $$\newline$$ <li>A's is the only seminar that is scheduled at 10:00 am. A is guided by R.</li> $$\newline$$ <li>F is an Anthropology student whose seminar is scheduled at 10:30 am.</li> $$\newline$$ <li>The seminar of a Sociology student is scheduled at 9:00 am.</li> $$\newline$$ <li>B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.</li> $$\newline$$ <li>P, who is guiding both B and C, has students scheduled in the first two slots.</li> $$\newline$$ <li>A and G are scheduled in two consecutive slots.</li></ol>

Which one of the following statements is necessarily true?

Three seminars are scheduled in the first slot.

Two seminars are scheduled in the first slot.

Only one seminar is scheduled in the second slot.

Three seminars are scheduled in the last slot.

Correct Answer

Option 2

Correct Answer

Explanation →

Q17:

CAT 2020 Slot 2

Logical Reasoning > Optimization

Medium

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. $$\newline$$ Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots. $$\newline$$ The following additional facts are also known. $$\newline$$ <ol><li>Seminars by students from Economics are scheduled in each of the four slots.</li> $$\newline$$ <li>A's is the only seminar that is scheduled at 10:00 am. A is guided by R.</li> $$\newline$$ <li>F is an Anthropology student whose seminar is scheduled at 10:30 am.</li> $$\newline$$ <li>The seminar of a Sociology student is scheduled at 9:00 am.</li> $$\newline$$ <li>B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.</li> $$\newline$$ <li>P, who is guiding both B and C, has students scheduled in the first two slots.</li> $$\newline$$ <li>A and G are scheduled in two consecutive slots.</li></ol>

Who all are NOT guiding any Economics students?

P, Q and S

P, R and S

Q, R and S

P, Q and R

Correct Answer

Option 1

Correct Answer

Explanation →

Q18:

CAT 2020 Slot 2

Logical Reasoning > Optimization

Medium

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. $$\newline$$ Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots. $$\newline$$ The following additional facts are also known. $$\newline$$ <ol><li>Seminars by students from Economics are scheduled in each of the four slots.</li> $$\newline$$ <li>A's is the only seminar that is scheduled at 10:00 am. A is guided by R.</li> $$\newline$$ <li>F is an Anthropology student whose seminar is scheduled at 10:30 am.</li> $$\newline$$ <li>The seminar of a Sociology student is scheduled at 9:00 am.</li> $$\newline$$ <li>B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.</li> $$\newline$$ <li>P, who is guiding both B and C, has students scheduled in the first two slots.</li> $$\newline$$ <li>A and G are scheduled in two consecutive slots.</li></ol>

Which one of the following statements is necessarily true?

B is scheduled in the first slot.

H is an Economics student.

Q is guiding G.

S is guiding F.

Correct Answer

Option 2

Correct Answer

Explanation →

Q19:

CAT 2020 Slot 2

Logical Reasoning > Optimization

Medium

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. $$\newline$$ Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots. $$\newline$$ The following additional facts are also known. $$\newline$$ <ol><li>Seminars by students from Economics are scheduled in each of the four slots.</li> $$\newline$$ <li>A's is the only seminar that is scheduled at 10:00 am. A is guided by R.</li> $$\newline$$ <li>F is an Anthropology student whose seminar is scheduled at 10:30 am.</li> $$\newline$$ <li>The seminar of a Sociology student is scheduled at 9:00 am.</li> $$\newline$$ <li>B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.</li> $$\newline$$ <li>P, who is guiding both B and C, has students scheduled in the first two slots.</li> $$\newline$$ <li>A and G are scheduled in two consecutive slots.</li></ol>

If D is scheduled in a slot later than Q's, then which of the following two statement(s) is (are) true?<br/><br/>(i) E and H are guided by T.<br/>(ii) G is guided by Q.

Only (i)

Both (i) and (ii)

Only (ii)

Neither (i) nor (ii)

Correct Answer

Option 2

Correct Answer

Explanation →

Q20:

CAT 2020 Slot 2

Logical Reasoning > Optimization

Medium

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. $$\newline$$ Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots. $$\newline$$ The following additional facts are also known. $$\newline$$ <ol><li>Seminars by students from Economics are scheduled in each of the four slots.</li> $$\newline$$ <li>A's is the only seminar that is scheduled at 10:00 am. A is guided by R.</li> $$\newline$$ <li>F is an Anthropology student whose seminar is scheduled at 10:30 am.</li> $$\newline$$ <li>The seminar of a Sociology student is scheduled at 9:00 am.</li> $$\newline$$ <li>B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.</li> $$\newline$$ <li>P, who is guiding both B and C, has students scheduled in the first two slots.</li> $$\newline$$ <li>A and G are scheduled in two consecutive slots.</li></ol>

If E and Q are both scheduled in the same slot, then which of the following statements BEST describes the relationship between D, H, and T?

At least one of D and H is guided by T.

Neither D nor H is guided by T.

Both D and H are guided by T.

Exactly one of D and H is guided by T.

Correct Answer

Option 1

Correct Answer

Explanation →

Q21:

CAT 2020 Slot 2

Logical Reasoning > Optimization

Medium

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. $$\newline$$ Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be Scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots. $$\newline$$ The following additional facts are also known. $$\newline$$ <ol><li>Seminars by students from Economics are scheduled in each of the four slots.</li> $$\newline$$ <li>A's is the only seminar that is scheduled at 10:00 am. A is guided by R.</li> $$\newline$$ <li>F is an Anthropology student whose seminar is scheduled at 10:30 am.</li> $$\newline$$ <li>The seminar of a Sociology student is scheduled at 9:00 am.</li> $$\newline$$ <li>B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.</li> $$\newline$$ <li>P, who is guiding both B and C, has students scheduled in the first two slots.</li> $$\newline$$ <li>A and G are scheduled in two consecutive slots.</li></ol>

If D is scheduled in the slot immediately before Q's, then which of the following is NOT necessarily true?

D is guided by T.

G is guided by Q.

F is guided by S.

E is guided by R.

Correct Answer

Option 4

Correct Answer

Explanation →

Q22:

CAT 2019 Slot 2

Logical Reasoning > Optimization

Medium

Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for 10 minutes and charges Rs. 100/-. Dr. Kane sees each patient for 15 minutes and charges Rs. 200/-, while Dr. Wayne sees each patient for 25 minutes and charges Rs. 300/-. $$\newline$$ <p>The clinic has three rooms numbered 1, 2 and 3 which are assigned to the three doctors as per the following table. $$\newline$$ </p><table class="question-table"><thead><tr><th>Room No.</th><th>Monday & Tuesday</th><th>Wednesday & Thursday</th><th>Friday & Saturday</th></tr></thead><tbody><tr><td>1</td><td>Ben</td><td>Wayne</td><td>Wayne</td></tr><tr><td>2</td><td>Kane</td><td>Ben</td><td>Ben</td></tr><tr><td>3</td><td>Wayne</td><td>Kane</td><td>Kane</td></tr></tbody></table><p>The clinic is open from 9 a.m. to 11.30 a.m. every Monday to Saturday.</p><p>On arrival each patient is handed a numbered token indicating their position in the queue, starting with token number 1 every day. As soon as any doctor becomes free, the next patient in the queue enters that emptied room for consultation. If at any time, more than one room is free then the waiting patient enters the room with the smallest number. For example, if the next two patients in the queue have token numbers 7 and 8 and if rooms numbered 1 and 3 are free, then patient with token number 7 enters room number 1 and patient with token number 8 enters room number 3.</p>

What is the maximum number of patients that the clinic can cater to on any single day?

30

12

15

31

Correct Answer

Option 4

Correct Answer

Explanation →

Q23:

CAT 2019 Slot 2

Logical Reasoning > Optimization

Medium

Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for 10 minutes and charges Rs. 100/-. Dr. Kane sees each patient for 15 minutes and charges Rs. 200/-, while Dr. Wayne sees each patient for 25 minutes and charges Rs. 300/-. $$\newline$$ <p>The clinic has three rooms numbered 1, 2 and 3 which are assigned to the three doctors as per the following table. $$\newline$$ </p><table class="question-table"><thead><tr><th>Room No.</th><th>Monday & Tuesday</th><th>Wednesday & Thursday</th><th>Friday & Saturday</th></tr></thead><tbody><tr><td>1</td><td>Ben</td><td>Wayne</td><td>Wayne</td></tr><tr><td>2</td><td>Kane</td><td>Ben</td><td>Ben</td></tr><tr><td>3</td><td>Wayne</td><td>Kane</td><td>Kane</td></tr></tbody></table><p>The clinic is open from 9 a.m. to 11.30 a.m. every Monday to Saturday.</p><p>On arrival each patient is handed a numbered token indicating their position in the queue, starting with token number 1 every day. As soon as any doctor becomes free, the next patient in the queue enters that emptied room for consultation. If at any time, more than one room is free then the waiting patient enters the room with the smallest number. For example, if the next two patients in the queue have token numbers 7 and 8 and if rooms numbered 1 and 3 are free, then patient with token number 7 enters room number 1 and patient with token number 8 enters room number 3.</p>

The queue is never empty on one particular Saturday. Which of the three doctors would earn the maximum amount in consultation charges on that day?

Dr. Ben

Dr. Wayne

Both Dr. Wayne and Dr. Kane

Dr. Kane

Correct Answer

Option 4

Correct Answer

Explanation →

Q24:

CAT 2019 Slot 2

Logical Reasoning > Optimization

Medium

Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for 10 minutes and charges Rs. 100/-. Dr. Kane sees each patient for 15 minutes and charges Rs. 200/-, while Dr. Wayne sees each patient for 25 minutes and charges Rs. 300/-. $$\newline$$ <p>The clinic has three rooms numbered 1, 2 and 3 which are assigned to the three doctors as per the following table. $$\newline$$ </p><table class="question-table"><thead><tr><th>Room No.</th><th>Monday & Tuesday</th><th>Wednesday & Thursday</th><th>Friday & Saturday</th></tr></thead><tbody><tr><td>1</td><td>Ben</td><td>Wayne</td><td>Wayne</td></tr><tr><td>2</td><td>Kane</td><td>Ben</td><td>Ben</td></tr><tr><td>3</td><td>Wayne</td><td>Kane</td><td>Kane</td></tr></tbody></table><p>The clinic is open from 9 a.m. to 11.30 a.m. every Monday to Saturday.</p><p>On arrival each patient is handed a numbered token indicating their position in the queue, starting with token number 1 every day. As soon as any doctor becomes free, the next patient in the queue enters that emptied room for consultation. If at any time, more than one room is free then the waiting patient enters the room with the smallest number. For example, if the next two patients in the queue have token numbers 7 and 8 and if rooms numbered 1 and 3 are free, then patient with token number 7 enters room number 1 and patient with token number 8 enters room number 3.</p>

Mr. Singh visited the clinic on Monday, Wednesday, and Friday of a particular week, arriving at 8:50 a.m. on each of the three days. His token number was 13 on all three days. On which day was he at the clinic for the maximum duration?

Monday

Wednesday

Same duration on all three days

Friday

Correct Answer

Option 1

Correct Answer

Explanation →

Q25:

CAT 2019 Slot 2

Logical Reasoning > Optimization

Medium

Three doctors, Dr. Ben, Dr. Kane and Dr. Wayne visit a particular clinic Monday to Saturday to see patients. Dr. Ben sees each patient for 10 minutes and charges Rs. 100/-. Dr. Kane sees each patient for 15 minutes and charges Rs. 200/-, while Dr. Wayne sees each patient for 25 minutes and charges Rs. 300/-. $$\newline$$ <p>The clinic has three rooms numbered 1, 2 and 3 which are assigned to the three doctors as per the following table. $$\newline$$ </p><table class="question-table"><thead><tr><th>Room No.</th><th>Monday & Tuesday</th><th>Wednesday & Thursday</th><th>Friday & Saturday</th></tr></thead><tbody><tr><td>1</td><td>Ben</td><td>Wayne</td><td>Wayne</td></tr><tr><td>2</td><td>Kane</td><td>Ben</td><td>Ben</td></tr><tr><td>3</td><td>Wayne</td><td>Kane</td><td>Kane</td></tr></tbody></table><p>The clinic is open from 9 a.m. to 11.30 a.m. every Monday to Saturday.</p><p>On arrival each patient is handed a numbered token indicating their position in the queue, starting with token number 1 every day. As soon as any doctor becomes free, the next patient in the queue enters that emptied room for consultation. If at any time, more than one room is free then the waiting patient enters the room with the smallest number. For example, if the next two patients in the queue have token numbers 7 and 8 and if rooms numbered 1 and 3 are free, then patient with token number 7 enters room number 1 and patient with token number 8 enters room number 3.</p>

On a slow Thursday, only two patients are waiting at $9$ a.m. After that two patients keep arriving at exact $15$ minute intervals starting at $9:15$ a.m. -- i.e. at $9:15$ a.m., $9:30$ a.m., $9:45$ a.m. etc. Then the total duration in minutes when all three doctors are simultaneously free is

0

15

10

30

Correct Answer

Option 1

Correct Answer

Explanation →