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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 80% (01:08) correct 20% (01:07) wrong based on 128 sessions

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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

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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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1

Solution

Given:
• In the question, x is defined as the greatest common factor of 36 and 96

To find:
• The sum of the digits of x

Approach and Working:
• Let’s factorise the numbers 36 and 96 first:
o 36 = $$2^2 * 3^2$$
o 96 = $$2^5 * 3$$
• Therefore, the greatest common factor of 36 and 96 = $$2^2 * 3$$ = 12
• Sum of the digits of 12 = 1 + 2 = 3

Hence, the correct answer is option B.

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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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Greatest common factor = 12

sum of digits of 12 = 1+2=3
Hence option B = 3 is the answer.
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GMAT 1: 560 Q42 V25 GMAT 2: 570 Q43 V27 GMAT 3: 710 Q49 V39 Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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A? How? Can we please have the OE?
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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urvashis09 wrote:
A? How? Can we please have the OE?

The OA is B. Edited. Thank you.
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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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Bunuel 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

Since 12 is the largest number that divides both 36 and 96, 12 is the GCF. The sum of the digits is 3.

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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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Top Contributor
Bunuel 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

Payal'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

Cheers,
Brent
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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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Another approach would be

36 96 both divided by 2

18 48 divided by 2 again

9 and 24 divided by 3
3 and 8 we stop here as we have nothing in common.

So 2 * 2 * 3 = 12

1 + 2 = 3

Posted from my mobile device Re: If x is the greatest common factor of 36 and 96, what is the sum of   [#permalink] 30 Sep 2018, 12:40
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