We have to found whether m^3>1. If m^3>1 then we have a yes, if m^3<=1, then we have a no.
1. Put p=0 in the equation m= -p+(-2)^p, you get m=1, so m^3=1, so the answer is no.
Put p=2 in the equation m= -p+(-2)^p, you get m=2, so m^3=8, so the answer is yes.
Since we do not have a definite answer, statement 1 is not sufficient.
2. p^3<=-1 can be written as:
a. p^3=-1, so p=-1. Put p=-1 in the equation m= -p+(-2)^p, you get m=3/2, so m^3>1, so the answer is yes.
b. p^3<-1, so p<-1. Put p=-2 (since p could only be an integer) in the equation m= -p+(-2)^p, you get m=9/4, so m^3>1, so the answer is yes.
Since we have a definite yes, statement 2 is sufficient.
So, the answer is B .