CAT 2025 Slot 1 DILR Set 5 Q19–Q22

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2025 Slot 1, with 4 questions (Grids & Matrices). Answers are CAT's official key.

The set

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means "Yes", two taps mean "No", and three taps mean "Maybe".

A total of 40 taps were heard across the five questions. Each question received at least one "Yes", one "No", and one "Maybe."

The following information is known.
1. Alia tapped a total of 6 times and received 9 taps to her question. She responded "Yes" to the questions asked by both Clive and Dilshan.
2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded "No" to Badal.
3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions.
4. No one responded "Yes" more than twice.
5. No one's answer to Alia's question matched the answer that Alia gave to that person's question. This was also true for Ehsaan.
6. Clive tapped more times in total than Badal.

Question 19

How many taps did Clive receive for his question?

TITA: type in the answer. There are no options and no negative marking.

Answer: 7 Grids & Matrices TITA

Solution

  1. Each question gets 4 responses with at least one of each, so it receives 7, 8 or 9 taps. With 40 in total, \(9 + c + 3x = 40\) forces Clive \(= 7\) (Y,Y,N,M) and Badal, Dilshan, Ehsaan \(= 8\) each (Y,N,N,M).
  2. Clive's question received 7 taps.

Question 20

Which two people tapped an equal number of times in total?
  1. A
    Alia and Badal
  2. B
    Clive and Ehsaan
  3. C
    Badal and Dilshan
  4. D
    Dilshan and Clive

Answer: (A) Alia and Badal Grids & Matrices MCQ

Solution

  1. Each question gets 4 responses with at least one of each, so it receives 7, 8 or 9 taps. With 40 in total, \(9 + c + 3x = 40\) forces Clive \(= 7\) (Y,Y,N,M) and Badal, Dilshan, Ehsaan \(= 8\) each (Y,N,N,M).
  2. Alia tapped 6 with Yes to Clive and Dilshan; the other two total 4 and can't include a third Yes, so she said No to Badal and Ehsaan. Dilshan tapped 11 with No (2) to Badal, so he said Maybe to Alia, Clive and Ehsaan.
  3. Alia's question (Y,N,M,M): Clive and Dilshan can't say Yes and Badal and Ehsaan can't say No, so Clive said No. Ehsaan's question: Dilshan said M, so Ehsaan's answer to Dilshan isn't M; Dilshan's question then needs it to be N.
  4. Ehsaan's total 9 forces him to say M to Alia, M to Badal and Y to Clive. Then Badal said Yes to Alia, Clive said Yes to Badal, and Badal said No to Clive. Since Ehsaan said Y to Clive, Clive says N to Ehsaan and Badal Y.
  5. Badal and Clive give N and M to Dilshan; Clive > Badal with a total of 14 forces Badal = 6 (N) and Clive = 8 (M). Totals: A 6, B 6, C 8, D 11, E 9.
  6. Alia and Badal both tapped 6 times.

Question 21

What was Clive's response to Ehsaan's question?
  1. A
    Yes
  2. B
    Maybe
  3. C
    Cannot be determined
  4. D
    No

Answer: (D) No Grids & Matrices MCQ

Solution

  1. Each question gets 4 responses with at least one of each, so it receives 7, 8 or 9 taps. With 40 in total, \(9 + c + 3x = 40\) forces Clive \(= 7\) (Y,Y,N,M) and Badal, Dilshan, Ehsaan \(= 8\) each (Y,N,N,M).
  2. Alia tapped 6 with Yes to Clive and Dilshan; the other two total 4 and can't include a third Yes, so she said No to Badal and Ehsaan. Dilshan tapped 11 with No (2) to Badal, so he said Maybe to Alia, Clive and Ehsaan.
  3. Alia's question (Y,N,M,M): Clive and Dilshan can't say Yes and Badal and Ehsaan can't say No, so Clive said No. Ehsaan's question: Dilshan said M, so Ehsaan's answer to Dilshan isn't M; Dilshan's question then needs it to be N.
  4. Ehsaan's total 9 forces him to say M to Alia, M to Badal and Y to Clive. Then Badal said Yes to Alia, Clive said Yes to Badal, and Badal said No to Clive. Since Ehsaan said Y to Clive, Clive says N to Ehsaan and Badal Y.
  5. Badal and Clive give N and M to Dilshan; Clive > Badal with a total of 14 forces Badal = 6 (N) and Clive = 8 (M). Totals: A 6, B 6, C 8, D 11, E 9.
  6. Clive answered No to Ehsaan.

Question 22

How many "Yes" responses were received across all the questions?

TITA: type in the answer. There are no options and no negative marking.

Answer: 6 Grids & Matrices TITA

Solution

  1. Each question gets 4 responses with at least one of each, so it receives 7, 8 or 9 taps. With 40 in total, \(9 + c + 3x = 40\) forces Clive \(= 7\) (Y,Y,N,M) and Badal, Dilshan, Ehsaan \(= 8\) each (Y,N,N,M).
  2. Clive's question has 2 Yes and every other question has exactly 1, so the total is \(2 + 4 = 6\).

Same concept in other years

See every question on Pairwise interactions within a group (calls, replies, relationships).

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