CAT 2025 Slot 1 · DILR · Set 5: Five Friends, Five Questions, Forty Taps

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.

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.

Ehsaan's question drew 8 taps, so its four answers are 1, 2, 3 and 2.

Alia answered 2, as established from her total of 6 and the cap on her "Yes" responses.

Dilshan answered 3, since his only non-3 answer went to Badal.

That leaves Badal and Clive to supply the remaining 1 and 2.

Clue 5 says nobody's answer to Ehsaan's question matched Ehsaan's answer to that person's question.

Ehsaan answered 1 to Clive's question, so Clive's answer to Ehsaan cannot be 1.

Clive therefore answered 2, and Badal answered 1.

Two taps mean "No", so Clive's response was "No" — the fourth option.

Shortcut. Clue 5 is a mismatch rule, so it eliminates rather than confirms. With only two values left to place and one of them blocked for Clive, the answer drops out immediately.

The completed grid of responses settles this by counting.

Alia answered 2 to Badal, 1 to Clive, 1 to Dilshan and 2 to Ehsaan.

Badal answered 1 to Alia, 2 to Clive, 2 to Dilshan and 1 to Ehsaan.

Clive answered 2 to Alia, 1 to Badal, 3 to Dilshan and 2 to Ehsaan.

Dilshan answered 3 to Alia, 2 to Badal, 3 to Clive and 3 to Ehsaan.

Ehsaan answered 3 to Alia, 3 to Badal, 1 to Clive and 2 to Dilshan.

A "Yes" is a single tap, so count the 1s: Alia gave two, Badal gave two, Clive gave one and Ehsaan gave one.

Dilshan gave none, since his answers were three 3s and a 2.

The total is 2+2+1+1=6 "Yes" responses.

Shortcut. Each question needs at least one "Yes", giving a floor of 5, and clue 4 caps each person at two, giving a ceiling of 10. The tally of question totals — one 9, three 8s and one 7 — leaves only a little room above the floor, and the grid lands on 6.