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GMAT prep integer question

Expert replies
by Baldini » Sat Mar 14, 2009 12:32 am
If the integer n is greater than 1, is n equal to 2?

(1) n has exactly two positive factors
(2) The difference of any two positive factors of n is odd

Can someone please explain why the OA is B?

Thanks
GMAX
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Source: — Data Sufficiency |

by DanaJ » Sat Mar 14, 2009 2:24 am
This question has been discussed before. One link would be:

https://www.beatthegmat.com/ds-div-prime ... 15987.html
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Re: GMAT prep integer question

by Vemuri » Sat Mar 14, 2009 2:24 am
Hey Baldini, please try to use the spoiler to mask the OA. This will allow others to first take a go at the question & see if they are getting the same answer as the OA :wink:

The question is asking if n=2?

Stmt 1: Does not help. All prime numbers have exactly 2 positive integers. One itself & the other 1. Since cannot narrow down to one answer, this statement is not sufficient.

Stmt 2: Hmm...at first glance it is tempting to rule this option out (especially if you are running against time). Take any number greater than 1, the factors are:
2 = 1X2 (difference 2-1=1 is odd)
3 = 1X3 (difference 3-1=2 is even)
4 = 1X2X4 (difference 2-1=1 (odd), but 4-2=2 (even)) This is not good enough because the difference of any 2 factors should be odd. The same thing will happen with all other numbers.

The only number that has the difference of any of its factors as an odd number is 2. So, statement B is sufficient to answer the question.
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