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

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VP
Joined: 21 Jul 2006
Posts: 1491
Is the integer n odd? (1) n is divisible by 3 (2) 2n is [#permalink]

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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
Director
Joined: 27 May 2008
Posts: 539

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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
VP
Joined: 17 Jun 2008
Posts: 1325

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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
_________________

cheers
Its Now Or Never

Re: DS: Divisibility   [#permalink] 02 Aug 2008, 23:01
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