Problem from the MBA.com practice test 1

[pranavc]

If n is a multiple of 5 and n=p^2*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^2q^2
(E) p^3q

Any input on the above will be highly appreciated. Thanks in advance.

[vishubn]

Is the answer C) if yes this is how i solved it /...


Plug in values , I considered two prime numbers,
case 1) p=3 ,q=5

n=45 and also multiple of 5

plug in the same value in the answer choices .
a)p^2=9- eliminate
b)q^2=25 = keep it
c)pq=15= keep it
d) p^2q^2 =3^100 { now we know the repeating pattern of powers of three the unit digit is 3 which is not multiple of 3 ) = eliminate
e)p^3q =( the unit digit is 7 which is again not multiple of 5 ) =eliminate

now u r left with two options b and c

case 2) p=5 q=3
n=5^2*3
n=75 which is multiple of 5

go ahead and plug in the two options left
b)q^2=9 elliminate

C is the answer

Please Confirm the OA

p.s. this took me more than 2min any other shortcut much appreiciated

[pranavc]

The OA is D. I'm really sleepy right now so I will probably mull over solution when I wake up. I appreciate the prompt response.

[vishubn]

I goofed it up totalluyyyyy I was lookg for mutilple of 5 rather for 25 will come back on this sooon


Vishu

[vishubn]

I goofed it up totalluyyyyy I was lookg for mutilple of 5 rather for 25 will come back on this sooon


Vishu

[Ian Stewart]

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

n is divisible by 5. n = p^2 * q, where p and q are primes. That is, n has only two distinct prime divisors, p and q, and one of them must be equal to 5. That is, either p = 5 or q = 5. Certainly p^2 * q^2 will be divisible by 5^2 = 25.

D.

[pranavc]

Thanks a lot for the explanation. My sincere apologies for not having acknowledged it earlier.