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Is the integer n odd? (1) n is divisible by 3 (2) 2n is

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SVP
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Is the integer n odd? (1) n is divisible by 3 (2) 2n is [#permalink]

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New post 02 Aug 2008, 04:26
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Is the integer n odd?

(1) n is divisible by 3

(2) 2n is divisible by twice as many positive integers as n.








guys, the OA here is B, but I honestly don't understand what statement 2 is really saying. can someone explain? because i feel that both even and odd integers can fulfill statement 2.
thanks

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Director
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Re: DS: Divisibility [#permalink]

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New post 02 Aug 2008, 06:25
tarek99 wrote:
Is the integer n odd?

(1) n is divisible by 3

(2) 2n is divisible by twice as many positive integers as n.

guys, the OA here is B, but I honestly don't understand what statement 2 is really saying. can someone explain? because i feel that both even and odd integers can fulfill statement 2.
thanks


if number of positive factors for n is k
then number of positive factors for 2n is 2k

lets plug in numbers
n = 2 factors : 1,2 k=2, 2n=4, factors : 1,2,4 = 3 not equal to 2k
n = 3, factors : 1,3 k=2, 2n=6, factors : 1,2,3,6 = 4 = 2k
n = 4, factors : 1,2,4 k=3, 2n=8, factors : 1,2,4,8 = 4 not equal to 2k
lets see one non prime odd also
n=9, factors : 1,3,9 k=3, 2n=18, factors : 1,3,6,9,18 = 6 = 2k

Suff

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Re: DS: Divisibility [#permalink]

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New post 02 Aug 2008, 23:01
durgesh79 wrote:
tarek99 wrote:
Is the integer n odd?

(1) n is divisible by 3

(2) 2n is divisible by twice as many positive integers as n.

guys, the OA here is B, but I honestly don't understand what statement 2 is really saying. can someone explain? because i feel that both even and odd integers can fulfill statement 2.
thanks


if number of positive factors for n is k
then number of positive factors for 2n is 2k

lets plug in numbers
n = 2 factors : 1,2 k=2, 2n=4, factors : 1,2,4 = 3 not equal to 2k
n = 3, factors : 1,3 k=2, 2n=6, factors : 1,2,3,6 = 4 = 2k
n = 4, factors : 1,2,4 k=3, 2n=8, factors : 1,2,4,8 = 4 not equal to 2k
lets see one non prime odd also
n=9, factors : 1,3,9 k=3, 2n=18, factors : 1,3,6,9,18 = 6 = 2k

Suff


Is there any easy method to solve this since this kind of substituion will call for different combinations of numbers
_________________

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Re: DS: Divisibility   [#permalink] 02 Aug 2008, 23:01
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Is the integer n odd? (1) n is divisible by 3 (2) 2n is

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