Comprehension
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: 1

How many taps did Clive receive for his question?

Show Hint

When total responses are fixed, sum of taps received across people must match total taps. Solving such puzzles often reduces to finding integer solutions satisfying minimum-per-question constraints.
Updated On: Jul 4, 2026
Show Solution

Correct Answer: 10

Solution and Explanation

Step 1: Build the 5x4 grid (rows = responder, columns = whose question). Fill in the given facts: Alia answers Yes to Clive and Dilshan, and since her total is \(6\) with at most two Yeses allowed, her replies to Badal and Ehsaan must both be No. Dilshan answers No to Badal.
Step 2: Dilshan's total is \(11\), only reachable as three Maybes and one No; since his No is already fixed at Badal, his replies to Alia, Clive and Ehsaan are all Maybe.
Step 3: Working through the remaining rows the same way (Badal's total forces two Yeses and two Nos; Ehsaan's total of \(9\) and the Alia/Ehsaan mirror-rule fix the rest) completes the grid, including the column for Clive's question reading \(1,2,3,1\) down its four entries.
Step 4: Add that column: \(1+2+3+1=7\).
\[ \boxed{7} \]
Was this answer helpful?
0
Question: 2

Which two people tapped an equal number of times in total?

Show Hint

In puzzles where both row and column totals matter, solve received-tap constraints first, then fit outgoing-tap patterns while enforcing logical rules. Often the identity of “equal totals” becomes uniquely determined.
Updated On: Jul 2, 2026
  • Badal and Dilshan
  • Clive and Ehsaan
  • Dilshan and Clive
  • Alia and Badal
Show Solution

The Correct Option is D

Solution and Explanation

Approach: Rule out the wrong pairings by checking the arithmetic floor and the running total, so the surviving pair is forced rather than guessed.

Step 1: Known tapped totals: Alia $= 6$, Dilshan $= 11$, Ehsaan $= 9$. These three already differ, so any equal pair must involve Badal or Clive. The remaining two satisfy
\[ \text{Badal} + \text{Clive} = 40 - 6 - 11 - 9 = 14. \]

Step 2: Nobody taps Yes more than twice, so over 4 answers the minimum tap-total is two Yes plus two No $= 1+1+2+2 = 6$. Thus Badal $\ge 6$ and Clive $\ge 6$.

Step 3: Of the splits of 14 into two parts each $\ge 6$ — namely $(6,8)$ and $(7,7)$ — clue 6 says Clive $>$ Badal, eliminating $(7,7)$. So Badal $= 6$, Clive $= 8$.

Step 4: Now match totals: Alia $6$, Badal $6$, Clive $8$, Dilshan $11$, Ehsaan $9$. Only Alia and Badal coincide, both at $6$.

Answer: Alia and Badal
Was this answer helpful?
0
Question: 3

What was Clive’s response to Ehsaan’s question?

Show Hint

When row sums, column sums, and logical rules do not uniquely fix an entry of the response matrix, the correct answer is “Cannot be determined.” Always check whether multiple consistent configurations can exist.
Updated On: Jul 2, 2026
  • No
  • Maybe
  • Cannot be determined
  • Yes
Show Solution

The Correct Option is C

Solution and Explanation

Approach: Instead of grinding the whole grid, test the target cell directly \(-\) if you can exhibit two fully valid completions that disagree on Clive\(\to\)Ehsaan, the answer is settled as undetermined.


Rules recap: Five players each ask one question; the other four tap Yes $=1$, No $=2$, Maybe $=3$. Every question gets at least one of each, and total taps $=40$. Given: Alia received 9; Badal, Dilshan, Ehsaan each received 8; Clive received 7. Players gave: Alia 6, Badal 6, Clive 8, Dilshan 11, Ehsaan 9. Alia tapped Yes to Clive and Dilshan.


Witness 1. Take Clive's four taps as $A:3,\,B:2,\,D:2,\,E:1$ (sum 8). Pair this with Ehsaan giving $A:3,B:1,C:2,D:3$ and the other rows chosen so each column hits its target (A:9, B:8, C:7, D:8, E:8) and every question has a Yes, a No and a Maybe. This is consistent, and here Clive answered Ehsaan with $1$ \(=\) Yes.


Witness 2. Now shift Clive's taps to $A:3,\,B:2,\,D:1,\,E:2$ (still sum 8) and rebalance the Badal/Ehsaan rows so all column totals stay 8 and the per-question rule still holds. This is equally consistent, but now Clive answered Ehsaan with $2$ \(=\) No.


Conclusion. Two legal grids give two different answers for the same cell, so no single reply is forced.


\[ \boxed{\textbf{Cannot be determined}} \]

Was this answer helpful?
0
Question: 4

How many “Yes” responses were received across all the questions?

Show Hint

When both row and column sums are fixed, the number of “Yes’’ responses becomes a global constraint. Checking all feasible matrices consistent with the puzzle often reveals a uniquely possible total even when individual answers remain undetermined.
Updated On: Jul 4, 2026
Show Solution

Correct Answer: 7

Solution and Explanation

Step 1: With the grid fully worked out, Alia's row reads No, Yes, Yes, No (to Badal, Clive, Dilshan, Ehsaan); Badal's row reads Yes, No, No, Yes (to Alia, Clive, Dilshan, Ehsaan); Clive's row reads No, Yes, Maybe, No (to Alia, Badal, Dilshan, Ehsaan); Dilshan's row reads Maybe, No, Maybe, Maybe (to Alia, Badal, Clive, Ehsaan); Ehsaan's row reads Maybe, Maybe, Yes, No (to Alia, Badal, Clive, Dilshan).
Step 2: Mark every Yes: Alia has 2, Badal has 2, Clive has 1, Dilshan has 0, Ehsaan has 1.
Step 3: Sum across all five people: \(2+2+1+0+1=6\).
\[ \boxed{6} \]
Was this answer helpful?
0

Top Questions on Logical Reasoning

Questions Asked in CAT exam