Multiple choice general knowledge math & puzzles

Find the smallest number in GP whose sum is 38 and whose product is 1728

  1. 12

  2. 20

  3. 8

  4. none of these

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C Correct answer
Explanation

Let the three terms of the GP be a/r, a, ar. Their product is a^3 = 1728, which means a = 12. Their sum is (12/r) + 12 + 12r = 38, leading to 12/r + 12r = 26, or 6r^2 - 13r + 6 = 0. Solving this gives r = 3/2 or r = 2/3. The terms are 8, 12, 18, and the smallest number is 8.