PP1-PS 57

[妃沁樂炘]

57. 7044-!-item-!-187;#058&005427
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^2)(q^2)
(E) (p^3)q

嗚~我果然是問白痴題，這題都沒有人發問...

為什麼不是A？謝謝！

我的想法：25=5^2=(p^2)q
那，q不就是1了嗎？有沒有q都沒差了嘛~請指正！

[vantreal]

let n=5a=p^2 *q
in order to get a multiple of 25, times 5 on both sides
25a=5(p^2 *q)

look at the right hand side,
we still need a 5 in order to get a multiple of 25.
so q=5
then 25a=5(p^2 *q)=5(p^2 *5)=(p^2)(q^2)

Ans: (D)