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

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stonecold
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If integer N has p factors; how many factors will 2N have ? [#permalink] New post   Updated on: 07 Aug 2016, 21:55
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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
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Official Answer
E

Originally posted by stonecold on 07 Aug 2016, 21:06.
Last edited by stonecold on 07 Aug 2016, 21:55, edited 2 times in total.
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Re: If integer N has p factors; how many factors will 2N have ? [#permalink] New post   07 Aug 2016, 21:48
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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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stonecold
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Re: If integer N has p factors; how many factors will 2N have ? [#permalink] New post   07 Aug 2016, 21:56
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] New post   15 Dec 2016, 03:48
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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] New post   26 Sep 2023, 21:51
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Re: If integer N has p factors; how many factors will 2N have ? [#permalink]
26 Sep 2023, 21:51
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