UPSC Prelims 2025 CSAT Paper II · Q48 of 78 Basic Numeracy easy

The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r ?

  1. (a) k ✓ UPSC's answer
  2. (b) k - 1
  3. (c) k + 1
  4. (d) k/2

Why the answer is (a)

• The average of p, q, and r is k, so their sum is p + q + r = 3k.

• The condition 'p is as much more than the average as q is less than the average' means p - k = k - q.

• Rearranging this equation gives p + q = 2k.

• Substituting p + q = 2k into the sum equation yields 2k + r = 3k.

• Solving for r gives r = 3k - 2k = k.

• Therefore, the value of r is k, which corresponds to option (a).

Why the other options are wrong

(b) k - 1
Option (b) is incorrect because the algebraic derivation shows r equals k, not k - 1.
(c) k + 1
Option (c) is incorrect because the algebraic derivation shows r equals k, not k + 1.
(d) k/2
Option (d) is incorrect because the algebraic derivation shows r equals k, not k/2.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

Reading the answer is not the same as getting it right under a clock. Practise this question with UPSC's negative marking, and anything you miss goes into an error notebook until you get it right twice.

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