GMAT Official Guide 2019 If n is an integer, what

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Jul 04, 2018 3:42 pm

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If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

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Source: Beat The GMAT — Data Sufficiency | Wed Jul 04, 2018 3:42 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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by GMATGuruNY » Thu Jul 05, 2018 1:55 am

BTGmoderatorDC wrote:If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

Statement 1:
12n = 432.
Since we can solve for n, the GCF of 12 and n can be determined.
SUFFICIENT.

Statement 2:
24 = 2*2*2*3.
Since the GCF of n and 24 is the blue product (12) without the red factor (2), n must be a multiple of 12 that does NOT include an additional factor of 2.
In other words:
n = 12a, where a is an ODD positive integer.
Options for n:
12*1, 12*3, 12*5, 12*7, 12*9...
In every case, the GCF of n and 12 is the value in green (12).
SUFFICIENT.

The correct answer is D.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Sat Jul 14, 2018 8:12 am

BTGmoderatorDC wrote:If n is an integer, what is the greatest common divisor of 12 and n ?

(1) The product of 12 and n is 432.
(2) The greatest common divisor of 24 and n is 12.

We need to determine the greatest common divisor or the greatest common factor (GCF) of 12 and n. If we can determine the value of n, then we can determine the GCF of 12 and n.

Statement One Alone:

The product of 12 and n is 432

Since 12n = 432, n = 432/12 = 36. So the GCF of 12 and 36 is 12.

Statement one alone is sufficient.

Statement Two Alone:

The greatest common divisor of 24 and n is 12.

Since the GCF of 24 and n is 12, that means n itself is a multiple of 12. Therefore, the GCF of 12 and n must be also 12.

Statement two is sufficient.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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