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If t is divisible by 12, what is the least possible integer

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GMAT Club Legend
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Joined: 07 Jun 2014
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If t is divisible by 12, what is the least possible integer [#permalink] New post 12 Aug 2018, 15:42
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Question Stats:

72% (01:12) correct 27% (00:32) wrong based on 11 sessions
If t is divisible by 12, what is the least possible integer value of a for which \(\frac{t^2}{2^a}\) might not be an integer?

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

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Re: If t is divisible by 12, what is the least possible integer [#permalink] New post 16 Aug 2018, 05:19
Since T is divisible by 12. Let's assume T to be 12. Then, \(T^2\) =144.
Then the minimum value for which \(T^2\) is not an integer when divided by 2^a is when a=5.
Hence D is the answer.
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GMAT Club Legend
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Re: If t is divisible by 12, what is the least possible integer [#permalink] New post 16 Aug 2018, 17:51
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Explanation

If t is divisible by 12, then \(t^2\) must be divisible by 144 or \(2 \times 2 \times 2 \times 2 \times 3 \times 3\). Therefore, \(t^2\) can be divided evenly by 2 at least four times, so a must be at least 5 before \(\frac{t^2}{2^a}\) might not be an integer.
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Re: If t is divisible by 12, what is the least possible integer   [#permalink] 16 Aug 2018, 17:51
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If t is divisible by 12, what is the least possible integer

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