If x is the greatest common factor of 36 and 96, what is the

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

by BTGmoderatorDC » Sun Sep 30, 2018 1:30 am

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If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?

A. 2
B. 3
C. 4
D. 6
E. 9

OA B

Source: Veritas Prep

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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

by GMATGuruNY » Sun Sep 30, 2018 2:57 am

BTGmoderatorDC wrote:If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?

A. 2
B. 3
C. 4
D. 6
E. 9

36 = 2*2*3*3
96 = 2*2*2*2*2*3
GCF = the product of the factors in blue = 2*2*3 = 12.
Sum of the digits = 1+2 = 3.

The correct answer is B.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Sep 30, 2018 6:23 am

BTGmoderatorDC wrote:If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?

A. 2
B. 3
C. 4
D. 6
E. 9

OA B

Source: Veritas Prep

Mitch's solution is the approach I'd take, but another way to answer this question is to simply LIST the factors of each value and then find the GREATEST factor they have in common.
When listing factors, it's best to do so in pairs of values with a given product (either 36 or 96). Here's what I mean:

Factors of 36 = {1, 36}
= {1, 2, 18, 36}
= {1, 2, 3, 12, 18, 36}
= {1, 2, 3, 4, 9, 12, 18, 36}
= {1, 2, 3, 4, 6, 9, 12, 18, 36}

Following the same approach, we see that the factors of 96 are {1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96}

When we examine both sets of factors, we see that the greatest common factor is 12 (i.e., x = 12)

What is the sum of the digits of x?
1 + 2 = 3

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sat Oct 13, 2018 5:35 pm

BTGmoderatorDC wrote:If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?

A. 2
B. 3
C. 4
D. 6
E. 9

36 = 2^2 x 3^2

96 = 48 x 2 = 8 x 6 x 2 = 2^5 x 3^1

The GCF is the product of the prime factors that both numbers have in common. So the GCF of 36 and 96 is 2^2 x 3^1 = 12 and the sum of the digits of 12 is 1 + 2 = 3.

Answer: B

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