UPSC Prelims 2024 · CSAT

Question 64: Data Interpretation

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

QuestionWhat are the unique values of x and y, where x, y are distinct natural numbers?
Statement–Ix / y is odd.
Statement–IIxy = 12

Which one of the following is correct in respect of the above Question and the Statements?

aThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

bThe Question can be answered by using either Statement alone

cThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

dThe Question cannot be answered even by using both the Statements together

AnswerUPSC’s answer is (c).

Statement I: x/y odd means x is an odd multiple of y, which has many solutions such as (3, 1) and (9, 3). Statement II: xy = 12 gives pairs such as (1, 12), (2, 6), (3, 4) and their reverses. Together, x = ky with k odd and greater than 1 (x and y are distinct), so y²k = 12: y = 2 and k = 3 works, while y = 1 needs k = 12, which is even. The unique answer is x = 6, y = 2.

Why each option is right or wrong

(a) Wrong. Neither statement alone gives a unique pair.
(b) Wrong. Each alone leaves several pairs.
(c) Right. Combining the two gives only (6, 2).
(d) Wrong. Together they give (6, 2).

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

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Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.