UPSC Prelims 2019 · CSAT

Question 58: Data Interpretation

Consider two statements S1 and S2 followed by a question :

S1p and q both are prime numbers.
S2p + q is an odd integer.
QuestionIs pq an odd integer?

Which one of the following is correct ?

aS1 alone is sufficient to answer the question

bS2 alone is sufficient to answer the question

cBoth S1 and S2 taken together are not sufficient to answer the question

dBoth S1 and S2 are necessary to answer the question

AnswerUPSC’s answer is (b).

S2 says p + q is odd, so exactly one of p and q is even; the only even prime is 2, so one of them is 2 and pq is even. The answer to the question is therefore a definite no, so S2 alone suffices. S1 alone is not enough: 3 and 5 give an odd product, while 2 and 3 give an even one. S1 adds nothing once S2 is known.

S1. Not sufficient alone: two primes can give an odd product (3, 5) or an even one (2, 3).
S2. Sufficient alone: an odd sum means one number is even, hence 2, so pq is even.

Why each option is right or wrong

(a) Wrong: S1 allows both odd and even products.
(b) Right: an odd sum forces one number to be 2, so pq is even.
(c) Wrong: S2 is sufficient on its own.
(d) Wrong: S1 is not needed.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.