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
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Sandy
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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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