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# 700+ level question

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Intern
Joined: 06 Mar 2017
Posts: 5

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27 Mar 2017, 16:54
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:28) correct 0% (00:00) wrong based on 7 sessions

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If a and n are integers, and a3=360n, then n must be divisible by which of the following?

1) 2
2) 6
3) 25
4) 27
5) 60
Intern
Joined: 27 Mar 2017
Posts: 1

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27 Mar 2017, 17:00
6

Sent from my Nexus 5 using GMAT Club Forum mobile app
Intern
Joined: 06 Mar 2017
Posts: 5

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27 Mar 2017, 18:50
Could you explain how you reached the answer. I also got the same answer but unfortunately the OA is different.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7942
Location: Pune, India

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27 Mar 2017, 21:49
shagunnayyar wrote:
If a and n are integers, and a3=360n, then n must be divisible by which of the following?

1) 2
2) 6
3) 25
4) 27
5) 60

I am assuming you mean
$$a^3 = 360n$$

$$a^3 = 2*2*2*3*3*5*n$$

$$a^3 = 2^3 * 3^2 * 5 * n$$

Considering the cube of an integer, every prime factor will have an exponent that is a multiple of 3.
So n must have a 3 and two 5s at least so that you get $$2^3 * 3^3 * 5^3$$ (every prime will have an exponent that is a power of 3).
Note that n could be $$3*5^5$$ or $$3^4*5^2$$ etc (infinite possibilities)

So n must be divisible by 3*5*5.
Of the given options, n must be divisible by 5*5 = 25

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Manager
Joined: 17 May 2015
Posts: 210

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27 Mar 2017, 22:25
Quote:
If a and n are integers, and a3=360n, then n must be divisible by which of the following?

1) 2
2) 6
3) 25
4) 27
5) 60

Hi shagunnayyar
Please use math mode for writing equations. It should be $$a^{3} = 360n$$.

Solution:

$$360n = 2^{3}\times 3^{2} \times 5 \times n$$

To a perfect cube, the minimum value of $$n$$ should be 3*5*5.

=> $$n$$ must be divisible by 25.

Hope this helps.
Math Expert
Joined: 02 Sep 2009
Posts: 43828

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28 Mar 2017, 06:39
shagunnayyar wrote:
If a and n are integers, and a3=360n, then n must be divisible by which of the following?

1) 2
2) 6
3) 25
4) 27
5) 60

This question is discussed here: https://gmatclub.com/forum/if-a-and-n-a ... 27801.html

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Re: 700+ level question   [#permalink] 28 Mar 2017, 06:39
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