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Is the integer n odd?

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Is the integer n odd?

by gmat25 » Sun Jul 24, 2011 5:36 am
Is the integer n odd?

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

OA is B...well by putting values for some no's i find the solution but still if someone can explain the proper solution that will be really helpful.
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Source: — Data Sufficiency |
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by Frankenstein » Sun Jul 24, 2011 8:24 am
Hi,
if n has p factors, 2n has 2p factors..
if n = (a^i).(b^j).(c^k)... where a,b,c are all distinct primes.
So, p = (i+1)(j+1)..
Now 2n = 2^1.(a^i).(b^j).(c^k)...
Number of factors of 2n will be (1+1).(i+1)(j+1)... For this to happen, a,b,c... should be distinct from 2. So, n is product of powers of primes other than 2 i.e. product of odd numbers. So, n is odd number.
Sufficient

Hence, B

You can even follow this link:
https://www.beatthegmat.com/n-odd-t84998.html
Cheers!

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