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# When 5^11 and 2^n7^2 have the same number of factors,

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4877
GPA: 3.82
When 5^11 and 2^n7^2 have the same number of factors, [#permalink]

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10 Apr 2017, 00:01
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Difficulty:

25% (medium)

Question Stats:

75% (00:38) correct 25% (01:35) wrong based on 59 sessions

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When $$5^{11}$$ and $$2^n7^2$$ have the same number of factors, what is the value of n?

A. 2
B. 3
C. 4
D. 5
E. 6
[Reveal] Spoiler: OA

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Joined: 09 Mar 2017
Posts: 83
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Re: When 5^11 and 2^n7^2 have the same number of factors, [#permalink]

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10 Apr 2017, 00:44
5^11 has (11+1) factors, ans should be (12/(2+1)-1 which is 3 or B

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Re: When 5^11 and 2^n7^2 have the same number of factors, [#permalink]

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10 Apr 2017, 08:06
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MathRevolution wrote:
When $$5^{11}$$ and $$2^n7^2$$ have the same number of factors, what is the value of n?

A. 2
B. 3
C. 4
D. 5
E. 6

$$5^{11}$$ has $$( 11 + 1 ) = 12$$ factors.

Now, $$12 = ( n + 1 ) ( 2 + 1 )$$

Or, $$n + 1 = 4$$

So, $$n = 3$$

Thus, the value of n = 3 , answer must be (B) 3
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4877
GPA: 3.82
Re: When 5^11 and 2^n7^2 have the same number of factors, [#permalink]

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12 Apr 2017, 00:14
==> From 11+1=(n+1)(2+1), you get 12=3(n+1), and n-3.

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Joined: 08 Sep 2015
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Re: When 5^11 and 2^n7^2 have the same number of factors, [#permalink]

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15 Apr 2017, 21:23
N=3
Easy, but a good question. Given the answer choices, It is very easy to commit a silly mistake
Re: When 5^11 and 2^n7^2 have the same number of factors,   [#permalink] 15 Apr 2017, 21:23
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