UPSC Prelims 2024 · CSAT

Question 68: Data Interpretation

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

QuestionIs (x + y) an integer?
Statement–I(2x + y) is an integer.
Statement–II(x + 2y) is an integer.

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 (d).

Statement I alone: 2x + y being an integer does not fix x + y; the same holds for statement II. Together, adding them gives 3x + 3y, an integer, so x + y is a multiple of 1/3, not necessarily a whole number. Check: x = y = 1/3 gives 2x + y = 1 and x + 2y = 1, yet x + y = 2/3; x = y = 0 gives an integer. So the answer varies.

Why each option is right or wrong

(a) Wrong. Neither statement alone settles it.
(b) Wrong. Neither statement alone is enough.
(c) Wrong. Even together, x + y can be 2/3 or 0.
(d) Right. Together they give only that 3(x + y) is an integer.

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.