If n is a multiple of 5, n=p^2q, where p and q are prime numbers. Which of the following must be a multiple of 25?
Choose the correct answer.
A) p^2	B) q^2	C) pq	D) p^2q^2	E) p^3q
You are given that n = p^2 * q, which is a multiple of 5. Therefore p^2 * q is a multiple of 5. Since 5 is a prime number, p OR q must be a multiple of 5. Therefore, in order to be a multiple of 25, you must have a MINIMUM of p^2 * q^2 in the answer, since you don't know whether p or q is the multiple of 5. The only answer which satisfies this condition is D. The answer is p^2q^2: p^2*q^2.
<result>D</result>
If n is a multiple of 5, n=p^2q, where p and q are prime numbers. Which of the following must be a multiple of 25?