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For which of the following values of n is 96+n/n

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Carcass
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For which of the following values of n is 96+n/n [#permalink] New post   05 Sep 2022, 07:54
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For which of the following values of n is \(\frac{96+n}{n}\) NOT an integer?

(A) 4
(B) 8
(C) 9
(D) 12
(E) 16



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C
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Re: For which of the following values of n is 96+n/n [#permalink] New post   05 Sep 2022, 08:04
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Carcass wrote:
For which of the following values of n is \(\frac{96+n}{n}\) NOT an integer?

(A) 4
(B) 8
(C) 9
(D) 12
(E) 16



Key (and often-tested) property: \(\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}\)

So, \(\frac{96+n}{n} = \frac{96}{n} + \frac{n}{n}= \frac{96}{n} + 1\)

Since 1 is an integer, the question boils down to finding a value of n so that \(\frac{96}{n}\) is NOT an integer

Since 96 is not the visible by 9, we know that \(\frac{96}{n}\) will not be an integer when n = 9

Answer: C
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gmatclubot
Re: For which of the following values of n is 96+n/n [#permalink]
05 Sep 2022, 08:04
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