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# Solution on this

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Joined: 12 Nov 2009
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Solution on this [#permalink]  08 Dec 2009, 01:45
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0% (00:00) correct 100% (01:08) wrong based on 2 sessions
Hi,

Is the integer n odd?
(1) n is divisible by 3
(2) 2n is divisible by twice as many positive integers as n.

Thanks!
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Ques.doc [68 KiB]

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Joined: 29 Oct 2009
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Re: Solution on this [#permalink]  08 Dec 2009, 04:10
Question Stem : Is 'n' odd?
Answer will be in the form of Yes/No.

St.(1) : 'n' is divisible by 3
If n = 9, answer to question stem is Yes.
If n = 12, answer to question stem is No.

St.(2) : '2n' is divisible by twice as many positive integers as n.
'2n' can be divisible by twice as many positive integers ONLY IF every factor of 'n' when multiplied by 2 gives a new factor. This can only happen when 'n' is odd. Why? Because when 'n' is even, it will have definitely have at least '1' and '2' as its factors. To find factors of '2n', if we multiply '1' by 2, we get '2' which does not give us any new factor.

Thus for any even number 'n', '2n' will always have less than two times the factors of 'n'. (Try it out with examples!)

Since St.(2) gives us enough information to conclude that 'n' is odd, it is sufficient.

_________________

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Re: Solution on this   [#permalink] 08 Dec 2009, 04:10
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