Multiple choice

A teacher gave a sum to his class to find the average of 'n' number wiz 1, 2, 3, ... n. But when the teacher checked the solution, he found that during calculation, a student just missed a number for addition and thus his average of 'n' numbers was 15. The least value of n is

  1. n = 29

  2. n = 30

  3. n = 31

  4. n = 32
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B Correct answer
Explanation

The sum of 1 to n is n(n+1)/2. The average is (n+1)/2. If one number x (where 1 <= x <= n) is missed, the new average is (n(n+1)/2 - x) / (n-1) = 15. For n=30, sum is 465. (465-x)/29 = 15 implies 465-x = 435, so x = 30. Since 30 is a valid number in the set, n=30 is correct.

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