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If N is a positive integer, not including N, how many factors does N

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If N is a positive integer, not including N, how many factors does N  [#permalink]

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New post 03 Jul 2018, 10:58
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If N is a positive integer, not including N, how many factors does N have?

(1) Not including N^2, N^2 has 4 factors.

(2) Not including 2N, 2N has 3 factors.

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If N is a positive integer, not including N, how many factors does N  [#permalink]

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New post 03 Jul 2018, 11:15
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If N is a positive integer, not including N, how many factors does N have?

(1) Not including N^2, N^2 has 4 factors.
so \(N^2\) has 5 factors including itself.. ODD factors means square number
what is 5 = 1*5..
as the number of factors of a number in simplest form \(x^ay^b\) is (a+1)(b+1)
so 1*5 means (0+1)(4+1).....
so \(N^2= (x^2)^2\), where x is prime
so x is a prime number and \(x^2\) has (2+1) or 3 factors
suff

(2) Not including 2N, 2N has 3 factors.
2N has total 4 factors...
2*2 means (1+1)(1+1)
N can be any other prime such that 2N = 2*3 or 2*5
then factors of 2*3 = 1,2,3,6 ....4
so N will be a prime number and there will be TWO factors
4 is also 1*4=(3+1)..
so N can be 2^2 such that 2*2^2=2^3..
then N = 2^2 means (2+1) = 3 factors
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If N is a positive integer, not including N, how many factors does N  [#permalink]

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New post 05 Jul 2018, 13:55
Bunuel wrote:
If N is a positive integer, not including N, how many factors does N have?

(1) Not including N^2, N^2 has 4 factors.

(2) Not including 2N, 2N has 3 factors.


St1:-
Re-phrasing:-\(N^2\) has 5 factors. Or, N is the square of a prime number.
No of factors of N excluding N is 2 . (1,\(\sqrt{N}\))
Sufficient.
St2:-
Re-phrasing:-2N has 4 factors.
This hold true when 2N=\(2^1*3^1\)or \(2^1*5^1\) or \(2^2\) or \(2*(2^2)\) etc.
So, we have N=\(\frac{2N}{2}\)=3 or 5 or 2 or \(2^2\)
So, no of factors of N :- 1 or 1 or 1 or 2 (excluding N)
Since no of factors have more than one value.
hence insufficient.
Ans. (A)
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Re: If N is a positive integer, not including N, how many factors does N &nbs [#permalink] 05 Jul 2018, 13:55
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