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Manager
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Is the integer n odd? 1. n is divisible by 3 2. 2n is [#permalink]
 25 Nov 2006, 19:41
Is the integer n odd?
1. n is divisible by 3
2. 2n is divisible by twice as many positive integers as n
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VP
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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
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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.
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Senior Manager
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Re: Is the integer n odd? [#permalink]
25 Nov 2006, 22:08
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
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VP
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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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close
