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

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Manager
Joined: 15 Aug 2006
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Is the integer n odd? 1. n is divisible by 3 2. 2n is [#permalink]  25 Nov 2006, 18:41
Is the integer n odd?

1. n is divisible by 3
2. 2n is divisible by twice as many positive integers as n
VP
Joined: 28 Mar 2006
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I think its B

take numbers

25 1,5,25 are the factors
50 has 1,2,5,10,25,50 as factors

take a number divisible by 3 like 9

9 has 1,3,9 as factors
18 has 1,2,3,6,9,18 as factors

So n neednt be divisible by 3 for and ofcourse n is odd

take any even number and multipley by 2 then this test fails for even number

try 12 and 24
Manager
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correct! B is the answer. But I was not able to understand the 2nd question. Can you explain the 2nd question.
Senior Manager
Joined: 01 Sep 2006
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Location: Phoenix, AZ, USA
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Re: Is the integer n odd? [#permalink]  25 Nov 2006, 21:08
Is the integer n odd?

1. n is divisible by 3
2. 2n is divisible by twice as many positive integers as n

Using 1

assume n=3 odd
assume n=24 even

insuff

assume n=8 even 2*2*2*2 total 5devisors
2n=16 even 2*2*2*2*2 total 6 devisors

assume n=27 odd 27 is divisible by 3*3*3 = 3^3 which means total 4 devisors
2n=54 is divisible by 2*3*3*3 = 2^1*3^3 emans total 4*2=8 devisors

suff
VP
Joined: 25 Jun 2006
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B 2.

if n is even, then n has a factor of 1 and 2.
and 2n cannot double the factor because 1*2 = 2 is already included n's factor. contradiction. -> n is odd.
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