Problem Solving

If n is a multiple of 5 and n = p^2q where p & q are prime numbers, which of the following must be a multiple of 25?

a. p^2
b. q^2
c. pq
d. p^2q^2
e. p^3q

Please provide an explanation. Thanks in advance!!

n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

25=5*5

Therefore, p^2q^2 will ensure that we have two 5's i.e. multiple of 25, irrespective of whether p is 5 or q is 5.

Hence D is the answer.

parallel_chase wrote:n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

Hence D is the answer.

here p should be 5 right...or else n can't be mulitple of 5...hope i'm not missing anything...

drizzle wrote:

parallel_chase wrote:n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

Hence D is the answer.

here p should be 5 right...or else n can't be mulitple of 5...hope i'm not missing anything...

q can also be 5. If q is 5 n would still be a multiple of 5

Agree with D)
p^2q^2 is p^2 * q^2

parallel_chase wrote:n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

25=5*5

Therefore, p^2q^2 will ensure that we have two 5's i.e. multiple of 25, irrespective of whether p is 5 or q is 5.

Hence D is the answer.

Thanks! I should have realized p or q had to be 5....

I am sorry I still don't get it - how can n be a multiple of 5 if p is not a multiple of 5?

The original question was not clear:
n=p^2q

Is it n=(p^2)*q, or n=p^(2q)?

n=(p^2)*q

pakaskwa wrote:The original question was not clear:
n=p^2q

Is it n=(p^2)*q, or n=p^(2q)?