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CAT 2023 Slot 2 DILR · Set 4 of 4Logical ReasoningHard DifficultyQ16–Q20 · 3 MCQ + 2 TITA

CAT 2023 Slot 2 DILR Set 4: Optimization (5 Questions) with Solutions

The Optimization set from the official CAT 2023 Slot 2 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2023 Slot 2 DILR · Questions 16–20
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.
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.
The following information is also known.
1
Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).
2
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.
3
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.
4
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.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q16. Optimization

MCQ · +3 / −1
What was the total amount spent on tickets (in Rs.) by Bipasha?
  1. A) 100
  2. B) 120
  3. C) 110
  4. D) 90
Correct Answer
C) 110
Step-by-step solution
📌 Core Concept
Ticket spending is fixed by the clues, so Bipasha's three rides can be identified from her timings, the equal-expense clue and the ride-closing rules.
🔢 Step-by-Step Solution
1
Chitra spent Rs. 50 with no waiting and finished by 11 am. Anjali waited for Chitra to finish Ride-1 at 11 am, so Chitra was on Ride-1 from 10 to 11. Rs. 50 as a total with Ride-1 (Rs. 20) means Ride-3 (Rs. 30). Chitra's spend is therefore Rs.
50
2. By 12:15 pm all three had spent the same amount, so Bipasha had spent Rs. 50 by 12:15.
3
Bipasha began her first ride at 11:30 am. That ride runs until 12:30, so her second ticket cannot be bought before 12:30. Her only ticket by 12:15 is the 11:30 ride, so her first ride costs Rs. 50 and is Ride-2 (11:30 to 12:30).
4
Clue 4 says Bipasha took a 1-hour break after her second ride, then queued behind Anjali for the last ride. Her second ride ends no earlier than 1:30, so she joins that queue no earlier than 2:30. Her last ride cannot be Ride-3, which must finish by 1 pm, and cannot be Ride-2, which she has already taken.
5
It also cannot be Ride-1. Anjali took Ride-1 at 11 am, which is long before Bipasha could join a queue, and Bipasha would have to wait for Anjali's Ride-1 ride. So the ride they share last is Ride-4 (Rs. 40).
6
Bipasha's middle ride cannot be Ride-3, because the last Ride-3 gate is 12:00 and she is still on Ride-2 until 12:30. It cannot be Ride-2 or Ride-4, which she takes first and last. So it is Ride-1 (Rs. 20).
7
Bipasha's spend is 50 + 20 + 40 = Rs.
110
### Why Not the Others
100, 120 and 90 do not match the ride set Ride-2, Ride-1 and Ride-4 that the clues force.
Quick Check
Bipasha rides Ride-2 from 11:30 to 12:30, Ride-1 from 12:30 to 1:30, takes a break until 2:30, then queues for Ride-4. This is consistent with all four clues.
Correct Answer: C

Q17. Optimization

MCQ · +3 / −1
Which were all the rides that Anjali completed by 2:00 pm?
  1. A) Ride-1 and Ride-4
  2. B) Ride-1, Ride-2, and Ride-4
  3. C) Ride-1, Ride-2, and Ride-3
  4. D) Ride-1 and Ride-3
Correct Answer
C) Ride-1, Ride-2, and Ride-3
Step-by-step solution
📌 Core Concept
Anjali's timeline comes from the ticket-spend clue and the rule that she waited only once.
🔢 Step-by-Step Solution
1
Clue 2: Anjali arrived at Ride-1 at 10:30, waited until 11:00, and rode from 11 to 12. This was the only ride where she waited, so she took no ride before it (see step 2).
2
Clue 3: Her ticket spend by 12:15 equals Chitra's Rs.
50
Ride-1 cost Rs. 20, so exactly Rs. 30 more was spent by 12:15. A ride before Ride-1 would also have been paid for by then, so the Rs. 30 is not a prior ride. It is Ride-3 starting at 12:00. The 12:00 start also respects Ride-3's cutoff of a 1 pm finish.
3
Anjali then goes straight on without waiting. Ride-2 is open at 1:00 (Bipasha left it at 12:30), so she rides Ride-2 from 1 to 2. Buying Ride-2 at 12:00 instead would push her spend past Rs. 50 by 12:15.
4
Clue 4: Her last ride, which Bipasha takes after her, is Ride-4 from 2 to 3. It starts at 2:00, so it is not completed by 2 pm.
5
By 2:00 pm Anjali has completed Ride-1 (12:00), Ride-3 (1:00) and Ride-2 (2:00).
Why Not the Others
Options A and B include Ride-4, which Anjali only finishes at 3:00.
Option D omits Ride-2, which she finishes at 2:00.
Correct Answer: C

Q18. Optimization

MCQ · +3 / −1
Which ride was taken by all three visitors?
  1. A) Ride-4
  2. B) Ride-2
  3. C) Ride-3
  4. D) Ride-1
Correct Answer
D) Ride-1
Step-by-step solution
📌 Core Concept
Once each visitor's ride list is built from the clues, the common ride can be read off directly.
🔢 Step-by-Step Solution
1
Chitra: Clue 1 gives Rs. 50 with no waiting, and Clue 2 shows she was on Ride-1 from 10 to 11. So Chitra took Ride-3 (9 to 10) and Ride-1 (10 to 11), which cost 30 + 20 = 50.
2
Anjali: Ride-1 (11 to 12), Ride-3 (12 to 1), Ride-2 (1 to 2) and Ride-4 (2 to 3). The Rs. 50 spent by 12:15 (Clue 3) forces Ride-3 at 12:00, and Clue 4 makes Ride-4 her last ride.
3
Bipasha: Ride-2 (11:30 to 12:30), which is her only ticket by 12:15 and costs Rs.
50
Then Ride-1 (12:30 to 1:30), a 1-hour coffee break, and Ride-4 (3 to 4) after waiting for Anjali, as Clue 4 says.
4
Compare the lists:
Ride-1: Chitra, Anjali, Bipasha.
Ride-2: Anjali, Bipasha.
Ride-3: Chitra, Anjali.
Ride-4: Anjali, Bipasha.
5
Only Ride-1 appears in all three lists.
Why Not the Others
Ride-4 and Ride-2 were not taken by Chitra.
Ride-3 was not taken by Bipasha, since its last ride must finish by 1 pm and her free slot started at 12:30.
Correct Answer: D

Q19. Optimization

TITA · +3 / 0
How many rides did Anjali and Chitra take in total?
Correct Answer
6
Step-by-step solution
📌 Core Concept
The number of rides for each visitor follows from their timelines. Chitra's is fixed by Clues 1 and 2, and Anjali's by Clues 2 to 4.
🔢 Step-by-Step Solution
1
Chitra spent Rs. 50 without waiting. Anjali waited from 10:30 to 11:00 for Chitra to finish Ride-1, so Chitra was on Ride-1 from 10 to 11. Rs. 50 therefore means Ride-1 (20) plus Ride-3 (30, from 9 to 10). Chitra took 2 rides.
2
Anjali rode Ride-1 from 11 to 12 and had spent Rs. 50 by 12:15, the same as Chitra. The extra Rs. 30 is Ride-3 at 12:00, since a ride before Ride-1 would conflict with her only waiting at Ride-1. This gives Ride-3 from 12 to 1.
3
She continues without waiting: Ride-2 from 1 to 2.
4
Clues 3 and 4 make Ride-4 her last ride, shared with Bipasha. Bipasha waits 30 minutes for Anjali to finish it, so Anjali rides Ride-4 from 2 to 3. Anjali took 4 rides.
5
Total for Anjali and Chitra: 4 + 2 = 6.
Quick Check
Anjali's four rides are Ride-1, Ride-3, Ride-2 and Ride-4. Each starts as soon as the previous one ends, so she waits only at Ride-1, as Clue 2 requires.
Correct Answer: 6

Q20. Optimization

TITA · +3 / 0
What was the total amount spent on tickets (in Rs.) by Anjali?
Correct Answer
140
Step-by-step solution
📌 Core Concept
The spend-matching clue and the waiting rule fix Anjali's rides, and her ticket total is the sum of their prices.
🔢 Step-by-Step Solution
1
Clue 2: Anjali rode Ride-1 from 11 to 12 (Rs. 20) after waiting from 10:30. This was the only ride where she waited.
2
Clue 3: By 12:15 all three had spent the same, and Chitra's spend was Rs.
50
So Anjali had spent Rs. 30 beyond Ride-1 by 12:15. A ride before 10:30 would also have been paid for by then, so the Rs. 30 is Ride-3 at 12:00 (12 to 1). This is also a valid time for Ride-3, which must finish by 1 pm.
3
Ride-2 is the next ride: she goes in at 1:00 with no waiting, after Bipasha left at 12:30, and rides until 2:00 (Rs. 50).
4
Clue 4: Her last ride is the one Bipasha later takes after waiting 30 minutes. Ride-1 and Ride-2 were already taken by Anjali, and Ride-3 is closed after 1 pm. So it is Ride-4 from 2 to 3 (Rs. 40).
5
Total: 20 + 30 + 50 + 40 = 140.
Quick Check
Anjali's Rs. 50 by 12:15 matches Chitra's, and 140 is the sum of all four ticket prices (20 + 50 + 30 + 40).
Correct Answer: 140
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CAT 2023 Slot 2 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Lucknow

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