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Intern  Joined: 21 Nov 2013
Posts: 37
What is the greatest value of a positive integer n such that  [#permalink]

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Difficulty:   5% (low)

Question Stats: 95% (01:00) correct 5% (01:26) wrong based on 182 sessions

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What is the greatest value of a positive integer n such that $$3^n$$ is a factor of $$18^1^2$$?

A) 17
B) 24
C) 31
D) 33
E) 47
Math Expert V
Joined: 02 Sep 2009
Posts: 61549
Re: What is the greatest value of a positive integer n such that  [#permalink]

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BabySmurf wrote:
What is the greatest value of a positive integer n such that $$3^n$$ is a factor of $$18^1^2$$?

A) 17
B) 24
C) 31
D) 33
E) 47

$$18^{12}=(2*3^2)^{12}=2^{12}*3^{24}$$ --> the greatest value of n such that $$3^n$$ is a factor of $$18^{12}$$ is 24.

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Intern  Joined: 21 Nov 2013
Posts: 37
Re: What is the greatest value of a positive integer n such that  [#permalink]

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18 = 2*3*3 = 2*3^2 Therefore this term to the power of 12 equals: 2^12 * (3^2)^12

This equals 2^12 *3^24 since we can multiple the exponents of base 3.

The only possible answer is 24 which is also the greatest answer. Thus, the answer is B.

Note that if there were answers such as 6 and 12, but 24 (the greatest value) would not be among the answers, we would pick the greatest value. Thus, between 6 and 12 we would pick 12 since 3^12 would be one multiple of the overall term.

However, note that in the given case no other answer would match. None of the answers except B would even qualify as a lower possible value.
GMAT Tutor G
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Re: What is the greatest value of a positive integer n such that  [#permalink]

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BabySmurf wrote:
What is the greatest value of a positive integer n such that $$3^n$$ is a factor of $$18^1^2$$?

A) 17
B) 24
C) 31
D) 33
E) 47

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Director  S
Joined: 12 Nov 2016
Posts: 678
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: What is the greatest value of a positive integer n such that  [#permalink]

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BabySmurf wrote:
What is the greatest value of a positive integer n such that $$3^n$$ is a factor of $$18^1^2$$?

A) 17
B) 24
C) 31
D) 33
E) 47

Simple- the most practical way we can break down 18^12 is 9^12 x 2^12 = 3^24 x 2^12

Thus
"B" Re: What is the greatest value of a positive integer n such that   [#permalink] 27 Jun 2017, 15:34
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# What is the greatest value of a positive integer n such that  