CAT 2025 Question Paper | DILR Slot 1

CAT Questions

CAT 2025 DILR was similar to CAT 2022 in pattern. All the four sets had 5 questions this year too. There were 6 TITA Questions. Atleast two sets were doable in each slot and one of the four sets was extremely tough. Choice of Sets became a crucial factor. Overall this section was at a medium to high level of difficulty.

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?

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Video Explanation

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Explanatory Answer

Let's start with the grid as shown below.
We know that everyone receives taps from four others. They recieve one Yes (1 tap), one No (2 taps) and one Maybe (3 taps).
So, everyone recieves 6 taps at least. Then, the number of times the fourth person taps to them decides the total number of taps recieved by them.
Therefore, when Alia recieved 9 taps that should have been (1,2,3,3) taps from the other four freinds.

Let us say that Clive recieved 'c' number of taps. Let Badal, Dilshan and Eshan recieve 'b' number of taps each.
Obeserve that 'c', the taps recieved by Clive has to be one of (1,2,3,1), (1,2,3,2) or (1,2,3,3). So Clive's score 'c' can be 7, 8 or 9.
Total taps = Total Taps recieved = 40.
Taps recieved by Alia, Badal, Clive, Dilshan, and Ehsaan = 40.
9 + b + c + b + b = 40
3b = 31 - c
b & c have to be positive integers, therefore, the only value that c can take is 8, and b takes 7.
So, Alia recieved 9 (1,2,3,3), Clive recieved 7 (1,2,3,1) and the other three recieved 8 (1,2,3,2) taps.

Alia tapped 6 times all together for 4 people. This means her breakup of taps would have been (1,1,2,2)
This is because, the moment you use a 3, the other three numbers must be 1. Like (1,1,1,3). But we are clearly told a person can't tap more than two Yes'.
Dilshan tapped a total of 11 times. This means the combination of his taps should have been (3,3,3,2).
Eshan tapped a total of 9 times. This means the combination of his taps should have been (2,2,2,3) or (1,2,3,3).
Let's talk about why (2,2,2,3) is an impossibility...
That's because Eshan like Alia does not give the same response as the one he recieves from a friend.
Eshan recieves two 2's. If he taps three 2's. One of the 2's tapped will be to the person who tapped 2 to Eshan!!
So Eshan taps 9 times as (1,2,3,3).

We know that Clive tapped more number of times than Badal.
Taps by Alia, Badal, Clive, Dilshan, and Ehsaan = 40.
6 + Badal + Clive + 11 + 9 = 40.
Badal + Clive = 14. Badal can't go below 6! Because, a 5 (or a smaller number) must use at least three 1's, like (1,1,1,2)
Hence, Badal = 6 (1,1,2,2) and Clive = 8.
Though, there are different ways of combining Clive's 8, remember that the total count of Yes', No's and Maybe's recieved, must match with the total count of Yes', No's and Maybe's tapped.
There are 6, 8 and 6 number of Yes', No's and Maybe's recieved. Therefore, Clive's 8 can only be (1,2,2,3).

With all of this information and the facts stated, we can have the grid looking like:

Received	Tapped
	Alia	Badal	Clive	Dilshan	Eshan	Total
Alia	x					9 (1, 2, 3, 3)
Badal		x		2		8 (1,2,3,2)
Clive	1		x			7 (1,2,3,1)
Dilshan	1			x		8 (1,2,3,2)
Eshan					x	8 (1,2,3,2)
Total	6 (1,1,2,2)	6 (1,1,2,2)	8 (1,2,2,3)	11 (3,3,3,2)	9 (1,2,3,3)	40

From the column of Alia's taps. Alia must tap Badal and Eshan 2 each.
Dilshan's column must be filled with remaining 3's.
Alia's row is also easy to fill. She can't recieve a 2 from Badal (Badal tapped her 2). She can't recieve a 3 from Badal (Badal never tapped a 3).
Alia recieves a 1 from Badal.

Alia has to recieve a 3 from Eshan. Because Eshan tapped her 2. So she can't recieve a 2 from him.
Alis finally has to recieve a 2 from Clive.

Received	Tapped
	Alia	Badal	Clive	Dilshan	Eshan	Total
Alia	x	1	2	3	3	9 (1, 2, 3, 3)
Badal	2	x		2		8 (1,2,3,2)
Clive	1		x	3		7 (1,2,3,1)
Dilshan	1			x		8 (1,2,3,2)
Eshan	2			3	x	8 (1,2,3,2)
Total	6 (1,1,2,2)	6 (1,1,2,2)	8 (1,2,2,3)	11 (3,3,3,2)	9 (1,2,3,3)	40

From here, abstract the problem and fill the grid like a Sudoku.
Dilshan tapped Eshan a 3. So Eshan can't tap Dilshan a 3. Also the Dilshan row doesn't have anymore of 1's left. Hence, Eshan has to tap Dilshan a 2. Look at Eshan's column now, Eshan can't tap Clive a 3. Because, the Clive row can't accomodate one more 3. Hence Eshan taps Badal 3 and Clive 1.
From the only possibilities Clive must tap Badal 1 and Badal must tap Clive 2.

Dilshan can't be tapped a 3 by Badal. So he has to be tapped a 3 by Clive and 2 by Badal.
Badal taps Eshan 1, and Clive taps Eshan 2.

Received	Tapped
	Alia	Badal	Clive	Dilshan	Eshan	Total
Alia	x	1	2	3	3	9 (1, 2, 3, 3)
Badal	2	x	1	2	3	8 (1,2,3,2)
Clive	1	2	x	3	1	7 (1,2,3,1)
Dilshan	1	2	3	x	2	8 (1,2,3,2)
Eshan	2	1	2	3	x	8 (1,2,3,2)
Total	6 (1,1,2,2)	6 (1,1,2,2)	8 (1,2,2,3)	11 (3,3,3,2)	9 (1,2,3,3)	40

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The question is " How many taps did Clive receive for his question? "

Hence, the answer is '7'

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