CAT 2025 Slot 1 · DILR · Question 19

CAT 2025 Slot 1 previous year question on Sports and Scores Based Sets, with the answer and a step-by-step solution.

Sports and Scores Based SetsLOGICAL REASONING - High LevelType in the answer (TITA)Medium

Set 5: Five Friends, Five Questions, Forty Taps — this question belongs to a set. Read the full set with all 4 questions →

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.

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.

Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded "No" to Badal.

Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions.

No one responded "Yes" more than twice.

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.

Clive tapped more times in total than Badal.

How many taps did Clive receive for his question?

Answer & solution

Answer: 7

Every question draws four responses, each worth 1, 2 or 3 taps.

Each question must include at least one of each response, so three of the four taps are fixed at 1, 2 and 3 — a total of 6 — and the fourth adds 1, 2 or 3.

So each question's tally is 7, 8 or 9.

The five tallies add to the 40 taps heard altogether.

Clue 1 fixes Alia's tally at 9, leaving 31 across the other four.

Clue 3 makes Badal's, Dilshan's and Ehsaan's tallies equal, say k each, with Clive's being t.

So 3k+t=31 with both k and t between 7 and 9.

Taking k=7 gives t=10, which is too large, and k=9 gives t=4, which is too small.

Only k=8 works, giving t=7.

Clive received 7 taps for his question.

Shortcut. The at-least-one-of-each rule pins every question into the narrow band 7 to 9, and five such numbers summing to 40 average exactly 8. With Alia already one above the average at 9, something must sit one below — and clue 3 forces that to be Clive.

CAT 2025 Slot 1 · DILR · Question 19

More Sports and Scores Based Sets questions