DS Problem

[Guest]

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.

[GMAT 2007]

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

[JadranLee]

Hi Guest,

Could you please post the source for this problem?

-Jad