If n is multiple of 5, and n = p2q where p and q are prime, which of the following must be a multiple of 25?
a. p2
b. q2
c. pq
d. p2q2
e. p3q
* n2 = (n)^1/2
a. p2
b. q2
c. pq
d. p2q2
e. p3q
* n2 = (n)^1/2
IMO D.
n is a multiple of 5, we can take 5, and 2 as our counter examples.
5 must be squared to be a multiple of 25.
A) is out b/c if we take 2 = p and (2^2*5) = 20 which is multiple of 5 but not 25.
B) is out b/c if we take 2 = q this time and p = 5 = (2^2*5) = 20 which is multiple of 5 but not 25.
C) pq = 5*2 = 10
D) since both are squared, one of them is going to be 25, so it will be a multiple of 25
E) discounted for the same reason as A and B.
(D)
