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The average of the numbers 1, 2, 3, … , 98, 99 and x is 10

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The average of the numbers 1, 2, 3, … , 98, 99 and x is 10

by Max@Math Revolution » Mon Jul 01, 2019 11:49 pm

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[GMAT math practice question]

The average of the numbers 1, 2, 3, ... , 98, 99 and x is 100x. What is the value of x?

A. 1/10
B. 2/11
C. 5/51
D. 50/101
E. 50/201
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by Max@Math Revolution » Wed Jul 03, 2019 11:57 pm
=>

( 1 + 2 + 3 + ... + 98 + 99 + x ) / 100 = 100x.
So, 1 + 2 + 3 + ... + 98 + 99 + x = 10000x, and 1 + 2 + 3 + ... + 99 = 9999x.
It follows that 9999x = 99*100/2 = 4950, and x = 4950 / 9999 = 550 / 1111 = 50 / 101.

Therefore, the answer is D.
Answer: D
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