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21, 22, 23, … , and (20+n) are n consecutive integers. One

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by Max@Math Revolution » Mon Jul 15, 2019 11:56 pm

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[GMAT math practice question]

21, 22, 23, ... , and (20+n) are n consecutive integers. One integer is excluded, and the average (arithmetic mean) of the remaining integers is calculated. The minimum possible value of this average is 60. What is the maximum possible value of this average?

A. 60
B. 61
C. 62
D. 63
E. 64
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by Max@Math Revolution » Thu Jul 18, 2019 2:08 am
=>

The minimum value of the average after excluding one of the numbers occurs when the largest integer, (20+n) is excluded. The average of the remaining numbers is then n/2 (21 + (20+n-1))/n = (n + 40) /2 = 60. So, n = 80.

The maximum value of the average after excluding one of the numbers occurs when the smallest integer, 21 is excluded. The average of the remaining numbers is then n/2 (22 + (20+n))/n = 122 / 2 = 61.

Therefore, B is the answer.
Answer: B
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