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?

S1 alone gives you a × b = 21 (where a and b are two numbers) which have multiple possibilities like 3×7 = 21, 1.5×14 = 21 or 6 × 3.5 = 21. (it is not mentioned that numbers are integers)

So S1 alone is not sufficient.

S2 alone will also not sufficient as it will give you a + b = 10, and again multiple possibilities of a and b like (1, 9); (2, 8); (3, 7)… etc.

By combining bothwe have a + b = 10 or b = 10 – a …(1) and a × b = 21 …(2)

Putting the value of b in equation 2, we have a × (10 – a) = 21 =>a2 – 10a +21 = 0

=> a2 – 7a – 3a +21 = 0 => a(a – 7) – 3 (a – 7) = 0 =>a – 7) (a – 3) = 0

=> If a = 7, b = 3 and If a = 3, b = 7.

So both S1 and S2 are required to find the numbers. Option (c) is correct.