Two Statements S1 and S2 are given below with regard to two numbers followed by a Question: S1: Their…
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 is sufficient to answer the Question.
S2 alone is sufficient to answer the Question.
S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
S1 and S2 together are not sufficient to answer the Question.
Solution
S1 alone: product 21 has many possible pairs — not sufficient. S2 alone: sum 10 has infinitely many pairs — not sufficient. Together: numbers with product 21 and sum 10 satisfy $x^2 - 10x + 21 = 0$, giving $x = 3$ or $x = 7$. The two numbers are uniquely 3 and 7. Hence both together are sufficient but neither alone.