CAT 2025 Slot 1 · DILR · Question 20

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 LevelMultiple choiceHard

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.

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
Pick an option, then check.
Answer & solution

Answer: Option A

The totals tapped by the five people also add to 40, since every tap is somebody's response.

Clues 1 and 2 give Alia 6, Dilshan 11 and Ehsaan 9, leaving 14 to share between Badal and Clive.

Clue 6 puts Clive above Badal, so Badal is at most 6.

Dilshan's 11 taps over four answers must be 3+3+3+2, and clue 2 makes the 2 his answer to Badal, so he answered 3 to everyone else.

Alia's 6 taps include the two single taps she gave Clive and Dilshan, leaving 4 across Badal and Ehsaan; clue 4 caps her at two "Yes" answers, so neither of those can be 1 and both must be 2.

Clue 5 now bites on Alia's question: Clive cannot answer 1, Dilshan cannot answer 1, and Badal and Ehsaan cannot answer 2.

Alia's question totals 9, so its four answers are 1, 2, 3 and 3; Dilshan's is 3, which forces Clive's to be 2 and leaves 1 and 3 for Badal and Ehsaan.

Applying clue 5 to Ehsaan's question in the same way forces Ehsaan's answers to be 3 to Alia, 3 to Badal, 1 to Clive and 2 to Dilshan, which is his total of 9.

Working the remaining questions through, Badal answers 1, 2, 2 and 1 for a total of 6, while Clive answers 2, 1, 3 and 2 for a total of 8.

That satisfies clue 6, and Alia and Badal both total 6 — the first option.

Shortcut. Dilshan's 11 is the entry point, since 11 from four answers capped at 3 can only be 3+3+3+2. Once his row is fixed, clue 5 turns Alia's and Ehsaan's questions into simple elimination.

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