This one is best solved using some convenient counter-examples.sud21 wrote:m and n are integers, is m^n an integer?
1) n^m is positive
2) n^m is an integer
Statement 1:
There are several possible values for m and n that satisfy the condition that n^m is positive.
Here are two such cases:
Case a: m=1 and n=1, in which case m^n is an integer
Case b: m=2 and n=-1, in which case m^n is not an integer
Since statement 1 does not allow us to answer the target question with any certainty, it is NOT SUFFICIENT
Statement 2:
There are several possible values for m and n that satisfy the condition that n^m is an integer.
Here are two such cases:
Case a: m=1 and n=1, in which case m^n is an integer
Case b: m=2 and n=-1, in which case m^n is not an integer
Since statement 2 does not allow us to answer the target question with any certainty, it is NOT SUFFICIENT
Aside: Notice that I used the same values for m and n to show that each statement is NOT SUFFICIENT. As such, the statements combined are NOT SUFFICIENT, which means the answer is E
Cheers,
Brent
