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Re: If t is divisible by 12, what is the least possible integer
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19 Sep 2022, 07:45
Given that t is divisible by 12 and we need to find what is the least possible integer value of a for which \(\frac{t^2}{2^a}\) might not be an integer
t is divisible by 12 => t is a multiple of 12 => t = 12x where x is an integer
\(\frac{t^2}{2^a}\) = \(\frac{(12x)^2}{2^a}\) = \(\frac{(2^2*3*x)^2}{2^a}\) = \(\frac{2^4*3^2*x^2}{2^a}\)
Now, in numerator 2 has a power of 4. So, a should be more than 4 for \(\frac{t^2}{2^a}\) to not be an integer
=> a = 5
So, Answer will be D.
Hope it helps!