2026 CSAT, all questions

UPSC Prelims 2026 · CSAT

Question 4: Data Interpretation

X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y?

  1. Statement IThe sum of any two numbers belonging to T is even.
  2. Statement IIIf both p and q are picked from T, then (p − 1)q is even.

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 (d).

Statement I says any two numbers in T share a parity, so T is all odd or all even. Statement II only rules out an even p paired with an odd q, since that product would be odd; again T must be one parity throughout. Both say the same thing. An all-odd T such as {3, 5} satisfies both, and an all-even T does too. So even together they cannot show that every number comes from Y.

Why each option is right or wrong
  • (a) Wrong: Statement I alone leaves both all-odd and all-even sets possible.
  • (b) Wrong: neither statement alone is sufficient.
  • (c) Wrong: combining adds nothing, as both only force a single parity.
  • (d) Right: T = {3, 5} and an all-even T both fit every statement.

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 questionNext question

Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.