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# If n is a multiple of 5, n=p^2q, where p and q are prime num

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If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]

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28 Sep 2009, 00:34
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57% (02:04) correct 43% (01:18) wrong based on 310 sessions

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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?

A. p^2
B. q^2
C. pq
D. p^2q^2
E. p^3q

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-is-n-is-multiple-of-5-and-n-p-2-q-where-p-and-q-are-prim-92383.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 25 Aug 2014, 04:33, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]

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28 Sep 2009, 00:50
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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.
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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]

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02 May 2011, 20:32
n = 5k = 20,45 etc.

20 = 2^2 * 5; 45 = 3^2 * 5

hence min solution possible is p^2 * q^2.
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Manager
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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]

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02 May 2011, 22:29
It is given that
$$n = p^2 (q)$$
$$n = 5(...)$$

We do not know whether p = 5 OR q = 5. There are 2 possibilities.

$$n = 5^2 (q)$$
OR
$$n = p^2 (5)$$

Since, we do not know whether p or q is 5 then. (A) and (B) could be eliminated.

(D) on the other hand raises both p and q to a power of 2. This guarantees 5 to be raised to 2 which is equivalent to 25.

Hence, D.
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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]

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24 Aug 2014, 16:54
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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]

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25 Aug 2014, 04:34
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If $$n$$ is multiple of $$5$$, and $$n = p^2q$$ where $$p$$ and $$q$$ are prime, which of the following must be a multiple of $$25$$?

A $$p^2$$
B. $$q^2$$
C. $$pq$$
D. $$p^2q^2$$
E. $$p^3q$$

$$n=5k$$ and $$n=p^2p$$, ($$p$$ and $$q$$ are primes).
Q: $$25m=?$$

Well obviously either $$p$$ or $$q$$ is $$5$$. As we are asked to determine which choice MUST be multiple of $$25$$, right answer choice must have BOTH, $$p$$ and $$q$$ in power of 2 or higher to guarantee the divisibility by $$25$$. Only D offers this.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-is-n-is-multiple-of-5-and-n-p-2-q-where-p-and-q-are-prim-92383.html
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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]

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14 Aug 2015, 14:31
DenisSh wrote:
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?

A. p^2
B. q^2
C. pq
D. p^2q^2
E. p^3q

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-is-n-is-multiple-of-5-and-n-p-2-q-where-p-and-q-are-prim-92383.html

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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num   [#permalink] 14 Aug 2015, 14:31
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