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GRE Math Challenge #39-positive integer n such that 2^n
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09 Sep 2014, 01:29
09 Sep 2014, 01:29
Expert Reply
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Question Stats:
81% (00:20) correct
18% (00:28) wrong based on 16 sessions
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What is the greatest positive integer n such that \(2^n\) is a factor of \(12^{10}\)?
A. 10
B. 12
C. 16
D. 20
E. 60
A. 10
B. 12
C. 16
D. 20
E. 60
Re: GRE Math Challenge #39-positive integer n such that 2^n
[#permalink]
17 Jul 2018, 14:31
17 Jul 2018, 14:31
sandy wrote:
What is the greatest positive integer n such that \(2^n\) is a factor of \(12^{10}\)?
A. 10
B. 12
C. 16
D. 20
E. 60
A. 10
B. 12
C. 16
D. 20
E. 60
Given
\(12^{10}\)
= \((2*2*3)^{10}\)
= \(2^{10}\) \(2^{10}\) \(3^{10}\)
= \(2^{10+10}\) \(3^{10}\)
So , \(2^{20}\) and \(3^{10}\)
n has the maximum value of 20 as a power of 2.
The correct answer is D.
gmatclubot
Re: GRE Math Challenge #39-positive integer n such that 2^n [#permalink]
17 Jul 2018, 14:31
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