UPSC PYQPrelims 2025

Civil Services Examination · Question 76

Let p + q = 10, where p, q are integers. Value-I = Maximum value of p × q when p, q are positive integers. Value-II = Maximum value of p × q when p ≥ -6, q ≥ -4. Which one of the following is correct?

  1. Value-I < Value-II
  2. Value-II < Value-I
  3. Value-I = Value-II
  4. Cannot be determined due to insufficient data
Show answer & explanation

Answer: (C) Value-I = Value-II

Explanation

In both cases the maximum is at p = q = 5, giving 25. (Answer as per the official UPSC answer key.)