Two Statements S1 and S2 are given below with regard to two numbers followed by a Question:
S1: Their product is 21.
S2: Their sum is 10.

Question: What are the two numbers?

Which one of the following is correct in respect of the above Statements and the Question?

Correct Option: (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

Let the two numbers be x and y. Statement S1: Their product is 21 (x × y = 21). Statement S2: Their sum is 10 (x + y = 10). We need to find the two numbers. S1 alone gives pairs like (1, 21) or (3, 7) (also negative integers, but assuming natural/whole numbers usually). S2 alone gives pairs summing to 10 like (1, 9), (2, 8), (3, 7), etc. Combining S1 and S2: We have a system of equations: x + y = 10 and x × y = 21. By substitution or quadratic equation, t^2 - 10t + 21 = 0, which factors as (t - 3)(t - 7) = 0. Thus, the two numbers are 3 and 7. Therefore, S1 and S2 together are sufficient to answer the Question, but neither alone is sufficient.