2024 CSAT, all questions

UPSC Prelims 2024 · CSAT

Question 67: Data Interpretation

A Question is given followed by two Statements I and II. Consider the Question and the Statements. There are three distinct prime numbers whose sum is a prime number.

  1. QuestionWhat are those three numbers?
  2. Statement–ITheir sum is less than 23.
  3. Statement–IIOne of the numbers is 5.

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 (a).

Three distinct primes with a prime sum cannot include 2 (2 plus two odd primes gives an even sum above 2), so all three are odd. Statement I: a prime sum below 23 occurs only for 3 + 5 + 11 = 19; the other triples give 15 or 21 (not prime) or 23 and above, so the triple is 3, 5, 11. Statement II: one number is 5; 3, 5, 11 (sum 19) and 5, 7, 11 (sum 23) both work, so it is not unique.

Why each option is right or wrong
  • (a) Right. Statement I alone gives (3, 5, 11); statement II alone does not.
  • (b) Wrong. Statement II alone gives more than one triple.
  • (c) Wrong. Statement I alone is enough.
  • (d) Wrong. Statement I alone settles the question.

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.