2023 CSAT, all questions

UPSC Prelims 2023 · CSAT

Question 26: Basic Numeracy

If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r + s) ?

a230
b225
c224
d221

AnswerUPSC’s answer is (b).

The sum of four distinct single digits is at most 9 + 8 + 7 + 6 = 30. For a fixed total, the product (p + q)(r + s) is largest when the two sums are equal. Split 9, 8, 7, 6 as 9 + 6 = 15 and 8 + 7 = 15. The greatest value is 15 x 15 = 225.

Why each option is right or wrong
  • (a) Wrong: exceeds the maximum, since the two sums total at most 30.
  • (b) Right: 15 x 15 = 225.
  • (c) Wrong: 14 x 16 = 224 is smaller than 15 x 15.
  • (d) Wrong: 13 x 17 = 221 is smaller than 15 x 15.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.