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If the sum of n consecutive positive integers is 42, which o

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If the sum of n consecutive positive integers is 42, which o

by Max@Math Revolution » Fri Apr 12, 2019 12:31 am

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[GMAT math practice question]

If the sum of n consecutive positive integers is 42, which of these could be the value of n?

A. 7
B. 8
C. 9
D. 10
E. 11
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by swerve » Fri Apr 12, 2019 10:50 am
mean\(=\)sum/n

If \(n\) is odd, mean 42/n must be an integer.

Only \(7\) divides into \(42\)

Therefore, __A__
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by Max@Math Revolution » Sun Apr 14, 2019 5:31 pm
=>

Recall that the sum of terms of an arithmetic sequence is {(a+l)/2}*n where a is the first term, l is the last term and n is the number of terms.

We are told that {(a+l)/2}*n = 42 or n(a+l) = 84.
Thus, n is a factor of 84.
7 is the unique factor of 84 among the choices.

Therefore, the answer is A.
Answer: A
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