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CAT 2025 Slot 1 DILR · Set 5 of 5Logical ReasoningHard DifficultyQ19–Q22 · 2 MCQ + 2 TITA

CAT 2025 Slot 1 DILR Set 5: Math Puzzles (4 Questions) with Solutions

The Math Puzzles set from the official CAT 2025 Slot 1 DILR paper: the caselet, all 4 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 2025 Slot 1 DILR · Questions 19–22
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.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q19. Math Puzzles

TITA · +3 / 0
How many taps did Clive receive for his question?
Correct Answer
7
Step-by-step solution
📌 Core Concept
Each question gets four responses, and every question has at least one Yes (1 tap), one No (2 taps) and one Maybe (3 taps). That fixes the possible totals for a question, and the overall total of 40 then pins down Clive's.
🔢 Step-by-Step Solution
1
The four responses must contain 1, 2 and 3 plus one repeated value rr. So a question's total is 6+r6+r, which can only be 7, 8 or 9.
2
Clue 1 says Alia's question received 9.
3
Clue 3 says Badal, Dilshan and Ehsaan each received the same total xx. Let Clive's total be cc. Then 9+3x+c=409+3x+c=40, so 3x+c=313x+c=31.
4
Both xx and cc must be in {7,8,9}\{7,8,9\}. If x=7x=7, then c=10c=10, which is impossible. If x=9x=9, then c=4c=4, which is impossible. So x=8x=8 and c=7c=7.
5
Clive's question therefore received 7 taps, made up of Yes, Yes, No, Maybe.
Quick Check
9+8+8+8+7=409+8+8+8+7=40, which matches the total.
Correct Answer: 7

Q20. Math Puzzles

MCQ · +3 / −1
Which two people tapped an equal number of times in total?
  1. A) Clive and Ehsaan
  2. B) Dilshan and Clive
  3. C) Badal and Dilshan
  4. D) Alia and Badal
Correct Answer
D) Alia and Badal
Step-by-step solution
📌 Core Concept
The question totals (9, 8, 8, 8, 7) fix what each person received. Clues 1, 2 and 5 then fix every response, and each person's total follows.
🔢 Step-by-Step Solution
1
Question totals: Alia 9, Badal, Dilshan and Ehsaan 8 each, Clive 7. A total of 8 means Yes, No, No, Maybe. A total of 9 means Yes, No, Maybe, Maybe. A total of 7 means Yes, Yes, No, Maybe.
2
Alia tapped 6, and she said Yes (1) to Clive and Dilshan. Her other two responses sum to 4. They cannot be 1+3, because that needs a third Yes. So she said No to Badal and Ehsaan.
3
Clue 5 says no one's answer to Alia matched Alia's answer to them. So Clive and Dilshan did not say Yes to Alia, and Badal and Ehsaan did not say No. Alia's received set (Yes, No, Maybe, Maybe) then gives: Badal and Ehsaan answered Yes or Maybe, and Clive and Dilshan answered No or Maybe.
4
Dilshan tapped 11. He said No (2) to Badal, so his other three responses sum to 9, and all three are Maybe. So Dilshan said Maybe to Alia, Clive and Ehsaan. Clive then said No to Alia, since one of Clive and Dilshan said No and the other said Maybe.
5
Ehsaan tapped 9. Dilshan said Maybe to Ehsaan, so by clue 5 Ehsaan did not say Maybe to Dilshan. That leaves Ehsaan's answer to Dilshan as No. Ehsaan's responses to Alia and Badal are Yes or Maybe, and his response to Clive is Yes or No. The only way to total 9 is Maybe, Maybe, Yes. So Ehsaan said Maybe to Alia, Maybe to Badal and Yes to Clive.
6
Badal then received Maybe from Ehsaan, so Clive said Yes to Badal. Clive's question needs one Yes and one No from Badal and Ehsaan. Ehsaan said Yes, so Badal said No to Clive.
7
Ehsaan's question needs one Yes and one No from Badal and Clive. Clive's No to Ehsaan is forced by clue 5, since Ehsaan said Yes to Clive. So Badal said Yes to Ehsaan. Alia's Yes must then come from Badal, so Badal said Yes to Alia.
8
Badal's totals so far are Alia 1, Clive 2, Ehsaan 1, which is 4. Clive's so far are Alia 2, Badal 1, Ehsaan 2, which is 5. Both answered Dilshan with No or Maybe, one each. Their totals sum to 14 and Clive's is larger (clue 6), so Clive said Maybe (total 8) and Badal said No (total 6).
9
Totals: Alia 6, Badal 6, Clive 8, Dilshan 11, Ehsaan 9. Alia and Badal are equal.
Why Not the Others
A) Clive 8 and Ehsaan 9 differ.
B) Dilshan 11 and Clive 8 differ.
C) Badal 6 and Dilshan 11 differ.
Correct Answer: D

Q21. Math Puzzles

MCQ · +3 / −1
What was Clive’s response to Ehsaan’s question?
  1. A) Yes
  2. B) Maybe
  3. C) No
  4. D) Cannot be determined
Correct Answer
C) No
Step-by-step solution
📌 Core Concept
Clive's answer to Ehsaan is either Yes or No. Clue 5 (applied to Ehsaan) and the tap totals decide which.
🔢 Step-by-Step Solution
1
Question totals are Alia 9, Badal, Dilshan and Ehsaan 8 each, and Clive 7. So Ehsaan's question got Yes, No, No, Maybe.
2
Alia said No to Ehsaan (she tapped 6, with Yes to Clive and Dilshan, and at most two Yes answers per person). Dilshan tapped 11, so he said No to Badal and Maybe to everyone else. That includes Maybe to Ehsaan. The remaining two answers to Ehsaan, from Badal and Clive, are therefore one Yes and one No.
3
Ehsaan tapped 9. His answers to Alia and Badal can only be Yes or Maybe, his answer to Dilshan cannot be Maybe (Dilshan said Maybe to him, clue 5), and his answer to Clive can only be Yes or No. The only combination totalling 9 is Maybe to Alia, Maybe to Badal, No to Dilshan and Yes to Clive.
4
Clue 5 applies to Ehsaan, so no one's answer to Ehsaan matches Ehsaan's answer to them. Ehsaan said Yes to Clive, so Clive's answer to Ehsaan is not Yes.
5
Clive's answer is therefore No, and Badal's answer to Ehsaan is Yes.
Why Not the Others
A) Clive cannot say Yes, because Ehsaan said Yes to Clive.
B) Maybe would leave Ehsaan's question without the required Yes, No and No.
D) The clues fix it, so it can be determined.
Correct Answer: C

Q22. Math Puzzles

TITA · +3 / 0
How many “Yes” responses were received across all the questions?
Correct Answer
6
Step-by-step solution
📌 Core Concept
Every question has a fixed set of responses once its total is known. Counting the Yes responses in each set gives the answer without having to fill in the whole grid.
🔢 Step-by-Step Solution
1
Each question has four responses with at least one Yes, No and Maybe, so a question's total is 7, 8 or 9. With 9+3x+c=409+3x+c=40 and Alia's question at 9, the totals are Alia 9, Badal 8, Dilshan 8, Ehsaan 8 and Clive 7.
2
A total of 9 is 1+2+3+31+2+3+3, which has one Yes. A total of 8 is 1+2+2+31+2+2+3, which has one Yes. A total of 7 is 1+1+2+31+1+2+3, which has two Yes responses.
3
Yes counts per question: Alia 1, Badal 1, Dilshan 1, Ehsaan 1, Clive 2.
4
Total Yes responses: 1+1+1+1+2=61+1+1+1+2=6.
Quick Check
Clue 4 allows at most two Yes from any one person. The full arrangement has Yes from Alia (to Clive and Dilshan), from Badal (to Alia and Ehsaan) and from Ehsaan (to Clive), which gives 6 and breaks no clue.
Correct Answer: 6
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CAT 2025 Slot 1 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Kozhikode

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