UPSC Prelims 2022 · CSAT

Question 19: Data Interpretation

Consider the Question and two Statements given below :

QuestionIs x an integer?
Statement–1x / 3 is not an integer.
Statement–23x is an integer.

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

aStatement–1 alone is sufficient to answer the Question

bStatement–2 alone is sufficient to answer the Question

cBoth Statement–1 and Statement–2 are sufficient to answer the Question

dBoth Statement–1 and Statement–2 are not sufficient to answer the Question

AnswerUPSC’s answer is (d).

Statement 1 says x/3 is not an integer: x could be 1 (an integer) or 1/2 (not), so it is not enough. Statement 2 says 3x is an integer: x could be 1 or 1/3, so it is not enough. Together, x = 1 satisfies both and is an integer, while x = 1/3 also satisfies both (x/3 = 1/9, 3x = 1) and is not. Even together the answer varies, so the statements are not sufficient.

Why each option is right or wrong

(a) Fails: x = 1 and x = 1/2 both satisfy statement 1 and give different answers.
(b) Fails: x = 1 and x = 1/3 both satisfy statement 2.
(c) Fails: x = 1 and x = 1/3 both satisfy the two statements together.
(d) Correct: even together, x may or may not be an integer.

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

Practise this paper timedPrevious question Next question

Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.