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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If n is an integer, is (29 - n)/n an integer?
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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
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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(29-n)/n = 29/n - n/n = 29/n - 1.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.
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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