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?

The correct answer is (C) (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question..

Explanation:

We are given four numbers P, Q, R, and S. Statement S1: R is greater than P as well as Q (R > P and R > Q). Statement S2: S is not the largest one (S is not max{P, Q, R, S}). We need to find the largest number. Combining S1 and S2: S1 tells us R is greater than P and Q. S2 tells us S is not the largest. However, we still do not know the exact relationship between R and S. R could be larger than S, or S could be larger than R (as long as S is not the absolute largest, but here S could be smaller than R, making R the largest, but we lack direct comparison between R and S if S is smaller than R but larger than P and Q). Wait, let's re-verify: S1 says R > P and R > Q. S2 says S is not the largest. This means the largest must be either R or S (since P and Q are smaller than R). If S is not the largest, then R must be the largest! Let us check: candidates for largest are among R and S (since R > P, Q). Since S is NOT the largest, by elimination, R MUST be the largest. Therefore, S1 and S2 together are sufficient. Wait, let's check if S1 alone is sufficient: S1 only gives R > P and R > Q, but S could be larger than R. So S1 alone is insufficient. S2 alone is insufficient. Together, S1 establishes R > P, Q, and S2 eliminates S from being the largest, leaving R as the definite largest number. Thus, both statements together are sufficient.