UPSC Prelims 2019 CSAT Paper II · Q80 of 79 Comprehension medium

Passage

Directions for the following 2 (two) items : Read the following statements S1 and S2 and answer the two items that follow : S1 : Twice the weight of Sohan is less than the weight of Mohan or that of Rohan. S2 : Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.

Which one of the following statements is correct ?

  1. (a) Weight of Mohan is least
  2. (b) Weight of Sohan is least ✓ UPSC's answer
  3. (c) Weight of Rohan is least
  4. (d) 'Whose weight is least' cannot be determined

Why the answer is (b)

• Let S, M, and R represent the weights of Sohan, Mohan, and Rohan respectively.

• Statement S1 states that 2S < M or 2S < R, implying S is less than half of M or half of R.

• Statement S2 states that 2R > M or 2R > S, implying R is greater than half of M or half of S.

• Combining these, if 2S < M, then S < M/2. If 2R > S, then R > S/2. This does not immediately rank all three.

• However, consider the case where 2S < R. Then S < R/2. From S2, if 2R > M, then R > M/2. This still leaves ambiguity between M and R relative to S.

• Let's test specific values: If S=10, M=25 (2S=20 < 25), R=15 (2R=30 > 25). Here S(10) < R(15) < M(25). S is least.

• If S=10, M=15 (2S=20 > 15, so this part of S1 fails, but S1 says 'or', so we need 2S < R). Let R=25 (2S=20 < 25). S2: 2R=50 > M(15) or S(10). True. Here S(10) < M(15) < R(25). S is least.

• In all valid scenarios satisfying the 'or' conditions, Sohan's weight is consistently the smallest because his weight is bounded by being less than half of another person's weight, while the others are bounded by being greater than half of another's, allowing them to be larger.

Why the other options are wrong

(a) Weight of Mohan is least
Mohan's weight is not necessarily the least; in valid scenarios, Mohan can be the heaviest or intermediate.
(c) Weight of Rohan is least
Rohan's weight is not necessarily the least; in valid scenarios, Rohan can be the heaviest or intermediate.
(d) 'Whose weight is least' cannot be determined
The weight of Sohan can be definitively determined to be the least based on the logical constraints provided.

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.

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