srn wrote:If n is a multiple of 5 & n = p^2q where p and q are prime numbers which of the following is a multiple of 25?
a. p^2
b.q^2
c.pq
d.p^2.q^2
e.p^3.q
Please explain how you came to the conclusion.
I assume you meant n= q p^2. The other way around can be confusing as if q is in the exponent.
if q p^2 is a multiple of 5 then one of the following is true
I q is multiple of 5 but p is not
II P is a multiple of 5 but q is not
III both p and q are multiples of five.
The only multiple of 5 that is prime is 5 so see q and p which are both primes in terms of whether or not they are 5.
At least one of these must be true for n to be a multiple of five. Now you have to keep these in mind when evaluating the answers.
If I is true, eliminate a c and d from your answer choices, that leaves.
P^2 is not a multiple of 5 since by I p is prime number not equal to 5, (7, 3). For c, since p is different from 5, and q is 5, pq can never be a multiple of 25. imagine 7x5/25 or 11x5/ 25. YOu will never get an integer. Similar reasoning applies: p^3 fails and q being only 5 can only absorb one 5 from the denominator 2^3x 5/ 5x5 cannot be a multile of 25. Since this is a must question, the answer will pass all conditions and assumptions, so we can eliminate a c e. We can't elimate b and d under I since both are multiples of 25 under I. But we want to know who wins the Must Race.
Under II b falls leaving d and I probably wouldn't worry about reasoning d out at this point on the GMAT but just choose it.
For our purposes, You can check and see that only D meets all three conditions stated above, which it has to meet since it MUST be divisible by 25.
I. 2^2 x 5^2/25= Integer
II 5^2 x 2^2/25= Integer
III 5^2 x 5^2/25 = Integer
Hope this helps.
