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# If n=6p, where p is a prime number greater than 2, how many

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Intern
Joined: 13 Jul 2009
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If n=6p, where p is a prime number greater than 2, how many [#permalink]

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15 Aug 2009, 06:59
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If n=6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A. 2
B. 3
C. 4
D. 6
E. 8

Please explain the ans in detail.

Last edited by Bunuel on 28 Feb 2012, 14:23, edited 1 time in total.
Topic is locked

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15 Aug 2009, 07:48
[quote="hariharakarthi"]If n=6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A.2
B.3
C.4
D.6
E.8

any prime>2 is odd

all devis = (1,2,3,6,p,2p,3p,6p ) however (1,3,p,3p are odd) thus answer is 4..C

Kudos [?]: 431 [0], given: 49

Manager
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15 Aug 2009, 08:23
If n=6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A.2
B.3
C.4
D.6
E.8

Just use substitution:

Use p = 5

n=6(5)
n=30

Divisors of 30: 1, 2, 3, 5, 6, 10, 15, 30

4 divisors are even.

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GMAT Tutor
Joined: 24 Jun 2008
Posts: 1339

Kudos [?]: 1955 [1], given: 6

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15 Aug 2009, 19:08
1
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Expert's post
hariharakarthi wrote:
If n=6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A.2
B.3
C.4
D.6
E.8

Please explain the ans in detail.

Is that really the question, or does it say that p is greater than 3? If p > 3, then 6p = 2*3*p, which has 8 divisors, half of which are even: 2, 2*3, 2*p and 2*3*p. If p = 3, however, then 6p = 2*3^2, which has only six divisors, three of which are even: 2, 2*3 and 2*3^2. As written, the question has two possible correct answers, three or four, depending on the value of p.
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Kudos [?]: 1955 [1], given: 6

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16 Aug 2009, 08:45
Thanx Ian & sam.

But, the actual question stated as given in the problem. I too had the same doubt. Hence I posted the question to find out if I miss anything.

I have a quick qn here, can you let me know how find out 8 divisors for 6p, where as I could find only the following,
1,2,3,p,2p,3p,2*3*p out of which 2,2p,2*3*p only are even divisors. what I am missing here? can you kindly explain.

regards,
hhk

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16 Aug 2009, 09:03
hariharakarthi wrote:
Thanx Ian & sam.

But, the actual question stated as given in the problem. I too had the same doubt. Hence I posted the question to find out if I miss anything.

I have a quick qn here, can you let me know how find out 8 divisors for 6p, where as I could find only the following,
1,2,3,p,2p,3p,2*3*p out of which 2,2p,2*3*p only are even divisors. what I am missing here? can you kindly explain.

regards,
hhk

If the original question is phrased as in the original post, there's a problem with the question. Where is it from?

If p is a prime greater than 3, the divisors of 6p = 2*3*p are:

1, 2, 3, p, 2*3, 2p, 3p, 2*3*p

(you're missing 2*3 = 6 in your list).
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Kudos [?]: 1955 [0], given: 6

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16 Aug 2009, 09:31
Thx Ian. I got it, I did silly mistake in finding divisors.

As per the qn is concerned, I think p should be greater than 3 not 2. Source of the qn is unknown.
I got it in net...

regards,
hhk

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17 Aug 2009, 02:56
1
KUDOS
gmac25 wrote:
will substition work in all questions like these??

personally , i wont generalize any approach in GMAT, that said and after a while of practice you will develope an eye for different problems that will guide you to the most suitable approach. regards

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13 Sep 2009, 19:00
yezz wrote:
hariharakarthi wrote:
If n=6p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
A.2
B.3
C.4
D.6
E.8

any prime>2 is odd

all devis = (1,2,3,6,p,2p,3p,6p ) however (1,3,p,3p are odd) thus answer is 4..C

Must be p is a prime number greater than 3
When p is 3, n = 18, which is divisible by 1, 2, 3, 6, 9, and 18. Only three even divisors.

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28 Feb 2012, 13:49
n = 6p and 2 < p.
possible divisors are: 2, 6, 6p, n. so, a total of 4 divisors.

ans: c
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28 Feb 2012, 14:22
MBAhereIcome wrote:
n = 6p and 2 < p.
possible divisors are: 2, 6, 6p, n. so, a total of 4 divisors.

ans: c

As noted above the question has TWO possible correct answers
4 in case p>3, for example if p=5, 6p=30 and 30 has 4 positive even divisors: 2, 6, 10, and 30;
3 in case p=3. In this case 6p=18 and 18 has 3 positive even divisors: 2, 6 and 18.

The question is flawed.

Topic locked.
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Re: Factors   [#permalink] 28 Feb 2012, 14:22
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