Problem solving

[danjuma]

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

Note-The answer is psquare x q square, but how did you go about it.?

Thanks in advance.

[neerajkumar1_1]

given

n is a multiple of 5
and n=p^2 * q

now for the expression to be a multiple of 25...

u need (5^2 * any number)

if u know this... the problem gets very simple...

now n=p^2 * q
since n is a multiple of 5 and p & q are prime numbers, then either p is 5 or q is 5

and for the expression to be a multiple of 25, we have 2 conditions:
1) if p is 5 and q any prime, then n will be a multiple of 25 (since n has p^2)
2) if q is 5 and p any prime, then for n to be a multiple of 25, we need to square q

therefore, p^2 * q^2 will be a multiple of 25


Hope this helps!!!

[neerajkumar1_1]

Also next time try not to write the answer... I somewhat remember the question, so i was able to answer it.. If i am not wrong the source is MGMAT...

Just keep in mind to write only the question, and provide the original answers later...