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Even-Odd

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Even-Odd

by gmattester » Thu Aug 21, 2008 8:50 pm
IS the integer n odd?
1) n is divisible by 3.
2) 2n is divisible by twice as many positive integers as n

First stmt is clear to me, Can someone explain the 2nd one.
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by P_mashru » Thu Aug 21, 2008 9:49 pm
to understand B clearly, assure two different value sets for n and then arrive on 2n

let me try;
Assume n as Odd - let's say 5, divisible by 2 different integers (factors); 1 & 5
so 2n is 10 - having 4 factors; 1,2,5,10

Now Assure even - let's say 6 - 4 factors; 1,2,3,6
so 2n is 12 - 6 factors; 1,2,3,4,6,12

Tried with couple of other odd and even nos and found the same result.

IMO B

What is OA?
I am I
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by robust » Thu Aug 21, 2008 10:36 pm
i think this is B because to have twice the number of factors if multiplied by 2, n has to have factors which are distinct and prime (not including 2)


meaning that it will be odd since all prime numbers other than 2 are odd.
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by gmattester » Thu Aug 21, 2008 10:48 pm
robust wrote:i think this is B because to have twice the number of factors if multiplied by 2, n has to have factors which are distinct and prime (not including 2)


meaning that it will be odd since all prime numbers other than 2 are odd.
OA is B but can you explain.
I am not clear how you proved that n has to have factors which are distinct and prime
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by Ian Stewart » Fri Aug 22, 2008 5:14 am
Ron Purewal posted a good explanation of the reason here:

www.beatthegmat.com/few-quetions-which- ... 10004.html
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by vish150783 » Fri Aug 22, 2008 7:21 am
I tried using a table for the second seems to help gather my ideas quite clearly..

n 2n nf 2nf
3 6 2 4
4 8 3 4
5 10 2 4
9 18 3 6

here nf = factors of n
2nf - factors of 2n

you see a pattern emerges. only for odd numbers it seems true.[/list]
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by gmattester » Fri Aug 22, 2008 10:32 am
vish150783 wrote:I tried using a table for the second seems to help gather my ideas quite clearly..

n 2n nf 2nf
3 6 2 4
4 8 3 4
5 10 2 4
9 18 3 6

here nf = factors of n
2nf - factors of 2n

you see a pattern emerges. only for odd numbers it seems true.[/list]
I am not clear how you have calculated nf and 2nf and what pattern emerges
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