2020 CSAT, all questions
UPSC Prelims 2020 · CSAT
Question 30: Data Interpretation
Two Statements S1 and S2 are given below with regard to two numbers followed by a Question :
- S1Their product is 21.
- S2Their sum is 10.
- QuestionWhat are the two numbers?
Which one of the following is correct in respect of the above Statements and the Question?
aS1 alone is sufficient to answer the Question.
bS2 alone is sufficient to answer the Question.
cS1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
dS1 and S2 together are not sufficient to answer the Question.
AnswerUPSC’s answer is (c).
S1 alone: a product of 21 comes from 3 and 7 or 1 and 21, so it is not enough. S2 alone: a sum of 10 fits many pairs, such as 4 and 6 or 3 and 7. Together: x + y = 10 and xy = 21 give x² - 10x + 21 = 0, so (x - 3)(x - 7) = 0 and the numbers are 3 and 7. Both statements are needed.
Why each option is right or wrong
- (a) S1 alone allows 3 and 7, 1 and 21, and non-integers.
- (b) S2 alone allows many pairs with sum 10.
- (c) Right: together they give x² - 10x + 21 = 0, so 3 and 7.
- (d) Together they fix the pair uniquely.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.