Multiple choice

If each of the five numbers: 23, 16, 19, 21, 31, was decreased by K, the average of the resulting set of 5 numbers would be 18. The value of K is

  1. 1

  2. 2

  3. 3

  4. 4

  5. 5
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D Correct answer
Explanation

Original sum = 23 + 16 + 19 + 21 + 31 = 110. New sum = 110 - 5K. New average = (110 - 5K) / 5 = 18. 22 - K = 18, so K = 4.

AI explanation

The original average is calculated by dividing the sum of the numbers by 5, so (23 + 16 + 19 + 21 + 31) / 5 = 110 / 5 = 22. If decreasing each number by K results in an average of 18, the new average is the original average minus K. Solving 22 - K = 18 gives K = 4.

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