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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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13 Aug 2009, 21:06
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57% (01:00) correct 43% (01:21) wrong based on 234 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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13 Aug 2009, 23:26
[quote="joyseychow"]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

n = p^2q = 5x thus either p or q is a multiple of 5

to insure a multiple of 25

then at least we need a the square of each ( we cant be sure otherwise) p^2q^2 is the answer
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14 Aug 2009, 03:44
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OA must be D. Heres how :

n = Multiple of 5.
Also, n = p^2q. which means either p = 5 or q = 5. We cannot assume either of it. Option D squares off both the variables, hence leaving no room. We can safely say that D will be definitely a multiple of 25.
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26 Aug 2009, 04:27
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
or both.

Please explain the above..i dnt understand the logic.
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26 Aug 2009, 13:36
Lets plugin numbers: n = 20 , 50

If n = 20 then, p = 2 and q = 5

if n = 50 then, p = 5 and q = 2

Plug in these numbers and you will find that only D satisfies the condition.

if n has to be a multiple of 5, and p and q are prime numbers ( prime numbers are not divisible by any other number except 1 and themselves) then, p or q must contain 5 as a factor).

We can not say that only p or q will have 5 as a factor.
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26 Aug 2009, 14:21
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I like D

Here's why.

N= is a factor of 5 Therefore we know that either P or Q must have 5 as prime factor.

We know want to know which equation is a multiple of 25. Which means when broken into it's primes there must be 5x5.

A. p^2 - doesn't guarantee as Q could have contained the 5
B. q^2 - doesn't guarantee as P could have contained the 5
C. pq - doesn't guarantee as 1 and not both might have contained the 5
D. p^2q^2 - with n equation we know 1 variable contained a 5 now we can guarantee one contains 2 5's
E. p^3q - doesn't guarantee as Q could have contain the 5
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26 Aug 2009, 14:49
If n is a multiple of 5 and n = p^2q, then obviously p should be a multiple of 5, as p and q are prime numbers. So p^2 and p^2q^2 will both be multiples of 25. What is the source for this question?
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26 Aug 2009, 16:06
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Aleehsgonji wrote:
If n is a multiple of 5 and n = p^2q, then obviously p should be a multiple of 5, as p and q are prime numbers. So p^2 and p^2q^2 will both be multiples of 25. What is the source for this question?

Based on the answer choices, it is not $$n=p^{2q}$$ but $$n={p^2} \times q$$.
If it was $$n=p^{2q}$$, then like you said both choices must be multiples of 25. By the way, that what I thought too. But then I screened the answer choices and figured out there must be something wrong with my reading of the formula
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27 Aug 2009, 06:36
Thanks for clarifying Lena
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06 Apr 2014, 10:27
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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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06 Apr 2014, 10:49
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Expert's post
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] 06 Apr 2014, 10:49
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