Comprehension
DIRECTIONS for the following three questions: These questions are based on the situation given below: Ten coins are distributed among four people P, Q, R, S such that one of them gets one coin, another gets two coins, the third gets three coins and the fourth gets four coins. It is known that Q gets more coins than P, and S gets fewer coins than R.
Question: 1
If the number of coins distributed to Q is twice the number distributed to P then which one of the following is necessarily true?
If the number of coins distributed to Q is twice the number distributed to P then which one of the following is necessarily true?
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The four people get 1, 2, 3, 4 coins in some order. List the pairs (P, Q) with Q = 2P and then fill in R and S using S less than R.
Updated On: Nov 4, 2026
- S gets an odd number of coins.
- R gets an odd number of coins.
- S gets an even number of coins.
- R gets an even number of coins.
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The Correct Option is A
Solution and Explanation
Step 1: Find (P, Q):
The values are 1, 2, 3, 4. With Q = 2P, the possible pairs are (P, Q) = (1, 2) or (2, 4).
Step 2: Fill in R and S (S < R):
If (P, Q) = (1, 2), the remaining coins 3 and 4 go to R and S with S < R: R = 4, S = 3.
If (P, Q) = (2, 4), the remaining coins 1 and 3 go to R and S: R = 3, S = 1.
Step 3: Check the options:
R is 4 in one case and 3 in the other, so R is not always even or always odd. S is 3 or 1, and in both cases it is odd.
Final Answer:
The correct option is (1): S gets an odd number of coins.
The values are 1, 2, 3, 4. With Q = 2P, the possible pairs are (P, Q) = (1, 2) or (2, 4).
Step 2: Fill in R and S (S < R):
If (P, Q) = (1, 2), the remaining coins 3 and 4 go to R and S with S < R: R = 4, S = 3.
If (P, Q) = (2, 4), the remaining coins 1 and 3 go to R and S: R = 3, S = 1.
Step 3: Check the options:
R is 4 in one case and 3 in the other, so R is not always even or always odd. S is 3 or 1, and in both cases it is odd.
Final Answer:
The correct option is (1): S gets an odd number of coins.
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Question: 2
If R gets at least two more coins than S, then which one of the following is necessarily true?
If R gets at least two more coins than S, then which one of the following is necessarily true?
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In coin distribution, consider the relationships between the players to determine the exact distribution satisfying all conditions.
Updated On: Sep 21, 2026
- Q gets at least two coins more than S.
- Q gets more number of coins than P.
- P gets more coins than S.
- P and Q together get at least five coins.
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The Correct Option is B
Solution and Explanation
Given that R gets at least two more coins than S, we know that the total number of coins for R and S is fixed. Therefore, Q must get more coins than P to satisfy the condition of having more coins than both. The answer is option (2).
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Question: 3
If Q gets fewer coins than R, then which one of the following is not necessarily true?
If Q gets fewer coins than R, then which one of the following is not necessarily true?
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List all distributions with Q > P, S < R and now also Q < R, then test each statement in every case.
Updated On: Nov 4, 2026
- P and R together get at least five coins.
- Q and S together get at least four coins.
- R and S together get at least five coins.
- P and Q together get at least four coins.
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The Correct Option is D
Solution and Explanation
Step 1: List the allowed distributions (P, Q, R, S):
Q > P, S < R and Q < R. So R must be 4 (R is larger than both Q and S, and P < Q < R). Checking all cases gives exactly three: (1, 2, 4, 3), (1, 3, 4, 2) and (2, 3, 4, 1).
Step 2: Test each statement:
(4) P + Q = 3, 4, 5: it is only 3 in the first case, so "at least four" fails.
(2) Q + S = 5, 5, 4: always at least 4. True.
(3) R + S = 7, 6, 5: always at least 5. True.
(1) P + R = 5, 5, 6: always at least 5. True.
Step 3: Conclusion:
Only statement (4) is not necessarily true.
Final Answer:
The correct option is (4): P and Q together get at least four coins.
Q > P, S < R and Q < R. So R must be 4 (R is larger than both Q and S, and P < Q < R). Checking all cases gives exactly three: (1, 2, 4, 3), (1, 3, 4, 2) and (2, 3, 4, 1).
Step 2: Test each statement:
(4) P + Q = 3, 4, 5: it is only 3 in the first case, so "at least four" fails.
(2) Q + S = 5, 5, 4: always at least 4. True.
(3) R + S = 7, 6, 5: always at least 5. True.
(1) P + R = 5, 5, 6: always at least 5. True.
Step 3: Conclusion:
Only statement (4) is not necessarily true.
Final Answer:
The correct option is (4): P and Q together get at least four coins.
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