2024 CSAT, all questions

UPSC Prelims 2024 · CSAT

Question 73: Data Interpretation

A Question is given followed by two Statements I and II. Consider the Question and the Statements. Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.

  1. QuestionWhat is the difference of their ages?
  2. Statement–IThe age of P is greater than the age of Q.
  3. Statement–IIThe sum of their ages is 11/6 times their difference.

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).

Let P = 10a + b and Q = 10b + a, so the difference is 9(a − b) and the sum is 11(a + b). Statement I only says a > b, so the difference could be 9, 18 and so on: not fixed. Statement II: 11(a + b) = (11/6) × 9|a − b| gives 2(a + b) = 3|a − b|, so one digit is 5 times the other: the ages are 51 and 15, difference 36. Statement II alone suffices.

Why each option is right or wrong
  • (a) Right. Statement II alone gives 36; statement I alone does not.
  • (b) Wrong. Statement I alone leaves many possible differences.
  • (c) Wrong. Statement II alone is enough.
  • (d) Wrong. Statement II settles it.

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.