Hi lucas211,
This question is essentially about prime-factorization - the idea that any positive integer greater than 1 is either prime or the product of a bunch of primes.
Here, we're told that (AB)^5 = 96Y, and that A and B are integers, which means…
(AB)(AB)(AB)(AB)(AB) = 96Y
We can rewrite this as….
(A^5)(B^5) = (2^5)(3)(Y)
We're asked for what Y COULD equal. This means that Y could be MORE than one value…so we should start by looking for the smallest value that Y could equal.
Notice how 2^5 could "account for" either A or B, so we need to make sure that the "Y", when combined with the "3" that's already there, could account for the other variable….
If Y = 3^4, then 96Y would = (2^5)(3^5), which gives us two integers raised to the 5th power.
Y COULD = 3^4 = 81
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
