Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

07 Aug 2016, 23:41

3

This post received KUDOS

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

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.

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

Show Tags

15 Dec 2016, 05:49

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 _________________

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

Show Tags

22 Dec 2017, 07:26

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________