Q. 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?
(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.
(d) S1 and S2 together are not sufficient to answer the Question.
Correct Answer: (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
Question from UPSC Prelims 2020 CSAT Paper
Explanation :
Product is 21 and Sum is 10
Statement S1: xy = 21
Statement S2: x + y = 10
Solution Steps:
1. From S1: y = 21/x
2. Substitute this in S2:
x + 21/x = 10
3. Solve for x:
Multiply both sides by x: x² + 21 = 10x
Rearrange: x² – 10x + 21 = 0
Factor: (x – 7)(x – 3) = 0
Therefore: x = 7 or x = 3
4. Find corresponding y values:
When x = 7: y = 21/7 = 3
When x = 3: y = 21/3 = 7
5. The two numbers are 3 and 7
Conclusion:
Neither statement alone is sufficient, but together they give us the unique solution. Therefore, answer is (c): S1 and S2 together are sufficient to answer the Question.
