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If a positive odd integer N has p positive factors, how many positive

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If a positive odd integer N has p positive factors, how many positive [#permalink]

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New post 07 Aug 2016, 20:08
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If a positive odd integer N has p positive factors, how many positive factors will 2N have ?

A) p
B) 2p
C) p + 1
D) 2p + 1
E) Cannot be determined
[Reveal] Spoiler: OA

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Last edited by stonecold on 09 Aug 2016, 07:21, edited 1 time in total.

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Re: If a positive odd integer N has p positive factors, how many positive [#permalink]

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no of factor of a=b^m * c^n * d^o * e^q.... = (m+1)*(n+1)*(o+1)*(q+1)...

Given that N is an odd integer. So N can be b^m * c^n * d^o * e^q, where b,c,d,e are odd numbers.
The number of factors of N = (m+1)*(n+1)*(o+1)*(q+1) = p

For a number 2N = 2^1 * b^m * c^n * d^o * e^p, number of factors will be (1+1)*(m+1)*(n+1)*(o+1)*(q+1) = 2*p

So, number of factors of 2N = 2*p

Hence, answer will be B.
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Re: If a positive odd integer N has p positive factors, how many positive [#permalink]

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I have added some extra text to make this question more GMAT-like:

stonecold wrote:
if positive odd integer N has p positive factors, how many positive factors will 2N have ?
A) p
B) 2p
C) P+1
D) 2p+1
E) Cannot be determined


Let's TEST some values of N
Try N = 3
The factors of 3 are {1, 3}. Here, p = 2
So, 2N = (2)(3) = 6
The factors of 6 are {1, 2, 3, 6}. So, we have a total of 4

Now check the answer choices:
A) p = 2 No good. We want an output of 4. ELIMINATE
B) 2p = (2)(2) = 4. PERFECT! KEEP B
C) P+1 = 2 + 1 = 3 No good. We want an output of 4. ELIMINATE
D) 2p+1 = (2)(2) + 1 = 5 No good. We want an output of 4. ELIMINATE
E) Cannot be determined. POSSIBLE. KEEP E


Let's TEST another value of N
Try N = 7
The factors of 7 are {1, 7}. Here, p = 2
So, 2N = (2)(7) = 14
The factors of 14 are {1, 2, 7, 14}. So, we have a total of 4

Now check the REMAINING answer choices:
B) 2p = (2)(2) = 4. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E


Let's TEST one more (non-prime) value of N
Try N = 9
The factors of 9 are {1, 3, 9}. Here, p = 3
So, 2N = (2)(9) = 18
The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of 6

Now check the REMAINING answer choices:
B) 2p = (2)(3) = 6. PERFECT! KEEP B
E) Cannot be determined. POSSIBLE. KEEP E

At this point, it SEEMS LIKELY that the correct answer is B
NOTE: This strategy of testing values, while not perfect, can still help you eliminate answer choices to give yourself a better chance of correctly guessing the right answer.

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Re: If a positive odd integer N has p positive factors, how many positive [#permalink]

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New post 15 Dec 2016, 04:49
Here dismay understanding of this Question=>

Firstly,Any odd integer can never have any even divisor.
Now N is an odd integer with => P factors.
Each of these P factors is odd.

For 2N => Each Odd factor will have its own even Divisor counterpart.
E.g => 9 has 3 divisors =>
1
3
9

2N=18 => Divisors will be =>
1
1*2=2
3
3*2=6
9
9*2=18

Hence 2N will have 2p factors in total.

Hence B
A few Takeaways from this Question=>
If N is odd and has P factors => 2N will have 2P Factors.
One must be a factor of every number ,so if the Question says that the difference between any of its factors is even => All factors must be odd.So, the number must be odd
.


NOTE => If n is even we cannot say that 2N will have 2p factors.
E.g =>
2 => 2 factors
4 => 3 factors

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Re: If a positive odd integer N has p positive factors, how many positive [#permalink]

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Re: If a positive odd integer N has p positive factors, how many positive   [#permalink] 22 Dec 2017, 06:26
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