Multiple choice

The average of four numbers is 27. If the first number is increased by K, the second by (K + 7), the third by (2K + 3) and the fourth is decreased by 2, then the new average of the four numbers will become 32. Find the value of K.

  1. 2

  2. 3

  3. 4

  4. 5

  5. 7
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B Correct answer
Explanation

Original sum = 4 * 27 = 108. New sum = 108 + K + (K+7) + (2K+3) - 2 = 108 + 4K + 8 = 116 + 4K. New average = (116 + 4K) / 4 = 29 + K. Given new average = 32, so 29 + K = 32, K = 3.

AI explanation

The new average increases from 27 to 32, so the total increase in the sum is 4 times 5, which equals 20. The net increase in the numbers is K plus K plus 7 plus 2K plus 3 minus 2, simplifying to 4K plus 8. Setting this equal to the total increase gives 4K plus 8 equals 20, and solving this yields K equals 3.

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