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If integer N has p factors; how many factors will 2N have ?

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If integer N has p factors; how many factors will 2N have ?  [#permalink]

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New post Updated on: 07 Aug 2016, 20:55
2
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

59% (01:08) correct 41% (00:57) wrong based on 68 sessions

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Originally posted by stonecold on 07 Aug 2016, 20:06.
Last edited by stonecold on 07 Aug 2016, 20:55, edited 2 times in total.
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Re: If integer N has p factors; how many factors will 2N have ?  [#permalink]

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New post 07 Aug 2016, 20:48
stonecold wrote:
if integer N has p factors ; how many factors will 2N have ?
A) p
B) 2p
C) P+1
D) 2p+1
E) Cannot be determined


How is the OA C? shouldn't it be E

Case 1:
Let N = 6 => 2 x 3 (prime factorization) => p = 4;

2N = 12 => 2^2 x 3 (prime factorization) => no. of factors = 6; (p+2)

Case 2:
Let N = 9 => 3^2 (prime factorization) => p = 3;

2N = 18 => 3^2 x 2 (prime factorization) => no of factors = 6; (2p)

For different N different results are observed. So, shouldn't E be the right answer?
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Re: If integer N has p factors; how many factors will 2N have ?  [#permalink]

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New post 07 Aug 2016, 20:56
chnarjun wrote:
stonecold wrote:
if integer N has p factors ; how many factors will 2N have ?
A) p
B) 2p
C) P+1
D) 2p+1
E) Cannot be determined


How is the OA C? shouldn't it be E

Case 1:
Let N = 6 => 2 x 3 (prime factorization) => p = 4;

2N = 12 => 2^2 x 3 (prime factorization) => no. of factors = 6; (p+2)

Case 2:
Let N = 9 => 3^2 (prime factorization) => p = 3;

2N = 18 => 3^2 x 2 (prime factorization) => no of factors = 6; (2p)

For different N different results are observed. So, shouldn't E be the right answer?


Hi Its indeed E
Thanks
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Re: If integer N has p factors; how many factors will 2N have ?  [#permalink]

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New post 15 Dec 2016, 02:48
1
Our number is \(N=2^a*q^b*r^c*s^d …\)

Number of factors of N: \((a + 1)*(b + 1)*(c + 1)*(d + 1) … = p\)

\(2N = 2*2^a*q^b*r^c*s^d … = 2^{(a+1)} *q^b*r^c*s^d …\)

Total # of factors of \(2N = (a + 2)*(b + 1)*(c + 1)*(d + 1) …\)

For simplicity sake we denote \((b + 1)*(c + 1)*(d + 1) … = X\)

\((a + 2)*X = (a + 1 + 1)*X = (a + 1)*X + X = p + (b + 1)*(c + 1)*(d + 1) …\)

In order to find our total # of factors of 2N we need to know number of odd factors of N and this is not given in the question.

Answer E.
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Re: If integer N has p factors; how many factors will 2N have ?  [#permalink]

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New post 04 Feb 2019, 18:33
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If integer N has p factors; how many factors will 2N have ?   [#permalink] 04 Feb 2019, 18:33
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