2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 55: Basic Numeracy
Let p and q be positive integers satisfying p < q and p + q = k. What is the smallest value of k that does not determine p and q uniquely?
a3
b4
c5
d6
AnswerUPSC’s answer is (c).
p < q with p + q = k. List the pairs for each k. k = 3: only (1, 2). k = 4: (1, 3) only, because (2, 2) breaks p < q. k = 5: (1, 4) and (2, 3), two pairs, so p and q are no longer fixed. The smallest such k is 5. Remember to check the small cases in order when the question asks for the smallest value.
Why each option is right or wrong
- (a) Wrong. k = 3 gives only (1, 2).
- (b) Wrong. k = 4 gives only (1, 3), since (2, 2) has p = q.
- (c) Right. k = 5 gives both (1, 4) and (2, 3).
- (d) Wrong. k = 6 also has more than one pair, but 5 comes earlier.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.