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UPSC PYQPrelims 2025

Civil Services Examination · Question 7

How many possible values of (p + q + r) are there satisfying 1/p + 1/q + 1/r = 1, where p, q and r are natural numbers (not necessarily distinct)?

  1. None
  2. One
  3. Three
  4. More than three
Show answer & explanation

Answer: (C) Three

Explanation

The solutions are (3, 3, 3), (2, 4, 4) and (2, 3, 6), giving sums 9, 10 and 11: three values. (Answer as per the official UPSC answer key.)