If t is divisible by 12, what is the least possible integer value of a for

which (t^2)/ (2^a) might not be an integer?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

the answer is 5 but if t = 24, this would fail right? Moreover t could be any multiple of 12. For whatever value of ‘a’ there will a multiple of 12 for which it would fail. Please point the link im missing here.

Thanks in advance!

Hey there -

Well, I entered both cases in a calculator for both minimum cases (t=12 & t=24), and if you divide it by 2^5 (32), then we get integer values - which is the opposite of the condition of the question. In that case, you’re onto something.

Are you sure this is an ETS question…? I suggest trying out what you get for the other options, and if entering another value for a in the equation gives you a value for the expression which isn’t an integer.

Hey,

this question is from the 5lb book. edition 3, ch 13, q. no 21. My argument is we cannot really find a value for ‘a’ that will satisfy all the values for t. Option A,B,C fails directly for 12 itself. D and E would fail for t=24. Should we stress on the term ‘might not be an interger ?’

Well, that explains the vagueness of the question. I mean - *might not be an integer*…? It’s cool that you shared this to cross check, but I’d advise you to not worry to much about this question.