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# If the positive integer a is a multiple of 12 and the positive integer

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Math Expert
Joined: 02 Sep 2009
Posts: 59634
If the positive integer a is a multiple of 12 and the positive integer  [#permalink]

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25 Sep 2018, 05:36
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Difficulty:

65% (hard)

Question Stats:

59% (02:10) correct 41% (02:43) wrong based on 40 sessions

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If the positive integer a is a multiple of 12 and the positive integer b is a multiple of 14, is $$a^2b$$ a multiple of 216?

(1) a is a multiple of 16.
(2) b is a multiple of 12.

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Re: If the positive integer a is a multiple of 12 and the positive integer  [#permalink]

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25 Sep 2018, 08:33
Bunuel wrote:
If the positive integer a is a multiple of 12 and the positive integer b is a multiple of 14, is $$a^2b$$ a multiple of 216?

(1) a is a multiple of 16.
(2) b is a multiple of 12.

a has $$2^2*3$$ and b has $$2*7$$
i.e.$$a^2*b$$ will have $$2^3*3^2*7$$

$$216 = 2^3*3^3$$

i.e. all we need to know is whether b also has another prime factor 3 or not

[u]Question: is $$a^2b$$ a multiple of 216?[/u]

Statement 1: a is a multiple of 16.

NOT SUFFICIENT

Statement 2: b is a multiple of 12.
i.e. b is a multiple of 3 as well
SUFFICIENT

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Re: If the positive integer a is a multiple of 12 and the positive integer   [#permalink] 25 Sep 2018, 08:33
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