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

(UPSC CSAT – 2023)

  1. 230
  2. 225
  3. 224
  4. 221

Solution: Ans.(2)

To be (p+q)(r+s) greatest, (p+q) and (r+s) both should be greatest

So p, q, r and s must be 9, 8, 7 and 6 not necessary in same order.

As we know the sum of all 4 numbers remain constant, so to make product maximum the two number’s difference should be minimum

So (9+6)(8+7) would be greatest

(9+6)(8+7) = 15×15 = 225

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