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Arithmetic Mean

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Arithmetic Mean

by wingsoffire » Sun Oct 09, 2011 8:16 am
If eleven consecutive integers are listed from least to greatest, what is the
average (arithmetic mean) of the eleven integers?
(1) The average of the first nine integers is 7.
(2) The average of the last nine integers is 9.
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by GmatMathPro » Sun Oct 09, 2011 9:01 am
Use the property that the arithmetic mean of a set of consecutive integers is the same as the median. For example, average of 1,2,3 is 2 and average of 2,3,4,5 is 3.5. Finding the average of 11 consecutive integers is the same as finding the median, which would be the 6th number.

Statement 1: the average of the first 9 integers is 7 tells us that 7 is the median of these 9 integers, so the first 9 must be 3,4,5,6,7,8,9,10,11. This tells us that the 6th overall number is 8, so the average of the 11 consecutive integers is 8. SUFFICIENT.

Statement 2: Same idea. The average of the last 9 integers is 9, so the last 9 integers is 5,6,7,8,9,10,11,12,13. This means the 11th integer is 13. Counting backwards we again get that the 6th integer is 8. SUFFICIENT

Ans: D
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