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If n is an integer, is (29 - n)/n an integer?

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If n is an integer, is (29 - n)/n an integer?

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If n is an integer, is (29 - n)/n an integer?

(1) n is prime.
(2) n is an odd factor of 116.

The OA is B.

Why statement (1) is not sufficient? Can any expert help me? I would be thankful.

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M7MBA wrote:
If n is an integer, is (29 - n)/n an integer?

(1) n is prime.
(2) n is an odd factor of 116.
(29-n)/n = 29/n - n/n = 29/n - 1.
The expression in blue will be an integer if n is a FACTOR OF 29.
Since 29 has only two factors -- 1 and 29 -- the question stem can be rephrased as follows:
Does n=1 or n=29?

Statement 1:
If n=29, then the answer to the question stem is YES.
If n=2, then the answer to the question stem is NO.
INSUFFICIENT.

Statement 2:
Factor pairs of 116:
1*116
2*58
4*29.
Since n must be ODD factor of 116, n must be equal to one of the green factors above.
Thus, either n=1 or n=29, with the result that the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.

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Hi M7MBA,

We're told that N is an integer. We're asked if (29 - N)/(N) an integer. This is a YES/NO question. We can solve it by TESTing VALUES.

1) N is prime.

IF....
N = 2... 27/2 = 13.5 and the answer to the question is NO.
N = 29... 0/29 = 0 and the answer to the question is YES.
Fact 1 is INSUFFICIENT.

2) N is an ODD factor of 116.

The information in Fact 2 can be dealt with in a number of different ways. The fastest way to get through it though is to prime factor 116:

116 =
(2)(58) =
(2)(2)(29)

Thus, the only odd factors of 116 are 1 and 29:
N = 1... 28/1 = 28 and the answer to the question is YES.
N = 29... 0/29 = 0 and the answer to the question is YES.
The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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