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

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Retired Moderator
Joined: 07 Jun 2014
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If t is divisible by 12, what is the least possible integer [#permalink]  12 Aug 2018, 15:42
Expert's post
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Question Stats:

75% (01:04) correct 25% (00:45) wrong based on 32 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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Intern
Joined: 15 Aug 2018
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Kudos [?]: 5 [0], given: 0

Re: If t is divisible by 12, what is the least possible integer [#permalink]  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.
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3028 [2] , given: 394

Re: If t is divisible by 12, what is the least possible integer [#permalink]  16 Aug 2018, 17:51
2
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Expert's post
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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Sandy
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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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