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Re: If a positive odd integer N has p positive factors, how many positive
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07 Aug 2016, 22:41

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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

Re: If a positive odd integer N has p positive factors, how many positive
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09 Aug 2016, 07:16

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Top Contributor

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
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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 _________________

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

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