If n is a multiple of 5 and n = \(P^2Q\), where P and Q are prime number. Which of the following must be a multiple of 25?

A \(P^2\)

B \(Q^2\)

C \(PQ\)

D \(P^2*Q^2\)

E \(P^3Q\)

source: orbit test prep

I have made the modification it is the second one.

N is a multiple of 5 so either P or Q or both have to be 5.

We are looking for a multiple of 25 so,

Among the given option the right ans should be a multiple of 25 and not simply be 5, 10 or 15 or other multiples of 5 but not a multiple of 25.

Lets start with A:

It could be that P^2 = 2^2 and Q = 5. Since this would result in N becoming a multiple of 5 but not a multiple of 25 option A is wrong
For option B
we can reverse the scenario such that P = 5 and Q =2; Yet this will be a multiple of 5 but not a multiple of 25

For option C
If we take the same two value 5 and 2 we get PQ = 10 and yet this will not be a multiple of 25

For option D

If anyone of P and Q is 5 this will be a multiple of 5 because both P and Q are squared hence 5^2 = 25 and this will be divisible by 25.
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