Which one of the following statements is correct ?
- (a) Weight of Mohan is greatest
- (b) Weight of Sohan is greatest
- (c) Weight of Rohan is greatest
- (d) 'Whose weight is greatest' cannot be determined ✓ UPSC's answer
Why the answer is (d)
• Let S, M, and R represent the weights of Sohan, Mohan, and Rohan respectively.
• Statement S1 states that 2S < M or 2S < R, meaning Sohan's weight is less than half of either Mohan's or Rohan's weight.
• Statement S2 states that 2R > M or 2R > S, meaning Rohan's weight is greater than half of either Mohan's or Sohan's weight.
• Consider Case 1: If M = 100, R = 60, and S = 40, then 2S (80) < M (100) satisfies S1, and 2R (120) > M (100) satisfies S2. Here, Mohan is the heaviest.
• Consider Case 2: If R = 100, M = 60, and S = 40, then 2S (80) < R (100) satisfies S1, and 2R (200) > M (60) satisfies S2. Here, Rohan is the heaviest.
• Since both Mohan and Rohan can be the heaviest depending on the specific values, the greatest weight cannot be uniquely determined.
Why the other options are wrong
- (a) Weight of Mohan is greatest
- Mohan is not necessarily the greatest, as Rohan can be heavier in valid scenarios satisfying both statements.
- (b) Weight of Sohan is greatest
- Sohan cannot be the greatest because S1 requires his weight to be less than half of either Mohan's or Rohan's weight.
- (c) Weight of Rohan is greatest
- Rohan is not necessarily the greatest, as Mohan can be heavier in valid scenarios satisfying both statements.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2019, held on 2 June 2019. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.