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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] New post 13 Aug 2009, 20:06
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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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Re: Multiples [#permalink] New post 13 Aug 2009, 22:26
[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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Re: Multiples [#permalink] New post 14 Aug 2009, 02:44
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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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Re: Multiples [#permalink] New post 26 Aug 2009, 03:27
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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Re: Multiples [#permalink] New post 26 Aug 2009, 12:36
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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Re: Multiples [#permalink] New post 26 Aug 2009, 13:21
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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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Re: Multiples [#permalink] New post 26 Aug 2009, 13:49
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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Re: Multiples [#permalink] New post 26 Aug 2009, 15:06
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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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Re: Multiples [#permalink] New post 27 Aug 2009, 05:36
Thanks for clarifying Lena
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Re: Multiples [#permalink] New post 06 Apr 2014, 09:27
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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink] New post 06 Apr 2014, 09:49
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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.

Answer: D.

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, 09:49
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