Can some help explain this problem?

Is k the square of an integer?

(1) k = t^2q^6r^10, where t, q, and r are integers
(2) k = t^2m^15, where t and m are integers

Thanks a bunch.

According to Statement (1)

k = t^2q^6r^10 if you take sqrt on both sides of the equation

sqrt(k) = sqrt(t^2q^6r^10)
since t, q and r are integers and raised to the even powers the sqrt of right hand side will be an integer.

Hence, sufficient

According to Statement (2)

k = t^2m^15, again take sqrt on both sides

sqrt(k) = sqrt(t^2m^15), in this case m is raised to the odd power, so the result may or may not be the perfect square.

Hence insufficient.

The answer should be (A)

GMAT 2007

Hi Guest,

Could you please post the source for this problem?

-Jad