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If t is divisible by 12, what is the least possible integer
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12 Aug 2018, 15:42
12 Aug 2018, 15:42
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Question Stats:
67% (01:10) correct
32% (01:00) wrong based on 88 sessions
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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
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Re: If t is divisible by 12, what is the least possible integer
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16 Aug 2018, 05:19
16 Aug 2018, 05:19
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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.
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.
Re: If t is divisible by 12, what is the least possible integer
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16 Aug 2018, 17:51
16 Aug 2018, 17:51
3
Expert Reply
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.
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.
