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If n is a positive integer and the greatest common divisor

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Senior Manager
Joined: 21 Oct 2013
Posts: 435
If n is a positive integer and the greatest common divisor [#permalink]

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24 Mar 2014, 03:19
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Difficulty:

25% (medium)

Question Stats:

73% (01:12) correct 27% (01:16) wrong based on 210 sessions

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If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 150?

A. 3
B. 6
C. 12
D. 15
E. 30

OE:
n is divisible by 4 & 3. Therefore, n is also divisible by 2 & 3. Therefore divisible by 6.
150 is also divisible by 6, and no greater answer choice holds a number that n is definitely divisible by.

Hi, is GCD of n & 16 not a 2?
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Joined: 02 Sep 2009
Posts: 46035
Re: If n is a positive integer and the greatest common divisor [#permalink]

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24 Mar 2014, 03:37
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4
goodyear2013 wrote:
If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 150?

A. 3
B. 6
C. 12
D. 15
E. 30

OE:
n is divisible by 4 & 3. Therefore, n is also divisible by 2 & 3. Therefore divisible by 6.
150 is also divisible by 6, and no greater answer choice holds a number that n is definitely divisible by.

Hi, is GCD of n & 16 not a 2?

The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5. Eliminate D and E.

150=2*3*5^2 is not divisible by 12, thus the greatest common divisor of n and 150 cannot be 12. Eliminate C.
Both n and 150 are divisible by 6, thus their greatest common divisor cannot be 3. Eliminate A.

As for your question: it's given that the greatest common divisor of n and 16 is 4, not 2.

Hope it's clear.
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Re: If n is a positive integer and the greatest common divisor [#permalink]

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27 Mar 2014, 20:56
LCM of 4 & 3 = 4 * 3 = 12

n = 12

GCD of 12 & 150 = 6

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Re: If n is a positive integer and the greatest common divisor [#permalink]

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24 Sep 2017, 07:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If n is a positive integer and the greatest common divisor   [#permalink] 24 Sep 2017, 07:22
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