[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
21, 22, 23, … , and (20+n) are n consecutive integers. One
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- Max@Math Revolution
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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
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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