Two Statements S1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question : S1 : R is greater than P as well as Q. S2 : S is not the largest one. Question : Among four numbers P, Q, R and S, which one is the largest? Which one of the following is correct in respect of the above Statements and the Question?
- (a) S1 alone is sufficient to answer the Question.
- (b) S2 alone is sufficient to answer the Question.
- (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question. ✓ UPSC's answer
- (d) S1 and S2 together are not sufficient to answer the Question.
Why the answer is (c)
• Statement S1 states that R is greater than both P and Q, establishing the relationship R > P and R > Q, but it provides no information about S relative to R, P, or Q.
• Statement S2 states that S is not the largest, which eliminates S as the maximum value but does not specify the relative order of P, Q, and R.
• Combining S1 and S2, we know R is greater than P and Q, and S is not the largest.
• Since S is not the largest, the largest number must be among P, Q, or R.
• From S1, R is greater than both P and Q, so R is the largest among P, Q, and R.
• Therefore, R is the largest among all four numbers, making the combination of statements sufficient.
Why the other options are wrong
- (a) S1 alone is sufficient to answer the Question.
- S1 alone is insufficient because it does not provide any information about the value of S relative to R, P, or Q.
- (b) S2 alone is sufficient to answer the Question.
- S2 alone is insufficient because it only eliminates S as the largest but does not determine the relative order of P, Q, and R.
- (d) S1 and S2 together are not sufficient to answer the Question.
- S1 and S2 together are sufficient because they collectively identify R as the largest number by eliminating S and establishing R's superiority over P and Q.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.