5n= the square of a number

it is not difficult to see n=5.

75*n*p

=75*5*p

=3*5*5*5*p

=3*p*5^3=the cube of a number.

In order to get a cube, all the prime components (i.e. 3 and 5 here) have to be to the 3rd power. Therefore, the smallest number for p is 3^2 =9.

Therefore, n+p= 5 +9 =14 (A).

Originally Posted byinfinityzero