UPSC Prelims 2026 · CSAT

Question 5: Data Interpretation

If x, y and z are integers, each greater than 1, then is x a prime number?

Statement Ixy^2 = 116
Statement IIxz = 261

Each item in this section contains a question followed by two statements. Answer each item using the following instructions and mark your response on the Answer Sheet accordingly.

aSelect this option if the question can be answered using one of these statements alone, but cannot be answered using other statement

bSelect this option if the question can be answered using either statement alone

cSelect this option if the question can be answered using both the statements together, but cannot be answered using either statement alone

dSelect this option if the question cannot be answered even using any of the statements

AnswerUPSC’s answer is (a).

Statement I: 116 = 2² × 29. With y at least 2, y² must be 4, so y = 2 and x = 29, which is prime. Sufficient. Statement II: 261 = 3² × 29, so x can be 3, 9, 29 or 87 (with z = 87, 29, 9, 3, all above 1), and 9 is not prime. Not sufficient. So Statement I alone answers the question and Statement II alone does not.

Why each option is right or wrong

(a) Right: I fixes x = 29 (prime); II allows x = 9 as well as primes.
(b) Wrong: Statement II alone is not enough because x could be 9.
(c) Wrong: Statement I alone is already sufficient.
(d) Wrong: Statement I answers the question.

Only the provisional key (27 May 2026) was found; the final key replaces it when found.

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 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.