If n is a multiple of 5 and...

[Carlos]

...n=p^2 x q, where p and q are prime numbers, which of the following must be a multiple of 25?
a)p^2
b)q^2
c)pq
d)p^2 x q^2
e)p^3 x q

Correct answer is d), but I cannot find a way to solve it... can anyone help?
thanks!

[Caveman]

n= (p ^ 2) * q

now if n is a multiple of 5, then either p or q or both must be 5. let us look at the options:

a)p^2

not True if q is 5

b)q^2

not True if p is 5

c)pq

not true if only one of p or q is 5

d)p^2 x q^2

True. If anyone of p or q is 5, this is a multiple of 5 since both p and q are squared. If both are 5, it still is true.

e)p^3 x q

not True if q is 5

[esledge]

Great deductive reasoning, Caveman!