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25 Aug 2007, 12:30
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If Integer n >1, is n = 2?
1. n has exactly 2 +ve factors.
2. difference of any two distinct +ve factors of n is odd.
OA says 2 alone is sufficient. can somebody give reasoning for 2 being sufficient?
1. n has exactly 2 +ve factors.
2. difference of any two distinct +ve factors of n is odd.
OA says 2 alone is sufficient. can somebody give reasoning for 2 being sufficient?
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Updated on: 25 Aug 2007, 15:17
Originally posted by KillerSquirrel on 25 Aug 2007, 12:46.
Last edited by KillerSquirrel on 25 Aug 2007, 15:17, edited 5 times in total.
Last edited by KillerSquirrel on 25 Aug 2007, 15:17, edited 5 times in total.
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somethingbetter
statement 1
Every prime number has exactly two positive factor (by definition) so n can be 2,3,5,7 etc.
insufficient
statement 2
This statement is not true for any odd number (i.e 15) factoring 15 will yiled 5-3 = 2 ---> hence n is not odd.
If you take any even number (i.e 10) then the factors are (1,2,5) and you need that the difference of all of them to be odd ! the only even number that upholds this is 2.
The source of your confusion is in the words any two distinct. meaning all !
so the answer is indeed (B)
see more here:
https://www.gmatclub.com/phpbb/viewtopic.php?t=48718
https://www.gmatclub.com/phpbb/viewtopic.php?t=38274
25 Aug 2007, 12:48
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somethingbetter
1) n can be any prime. if n = 3, then it has two positive factors. If n=2, it also have two positive factors. INSUFFICIENT.
2) Factor1 - Factor2 = odd
This can only be when one of them is odd, one of them is even.
Other than 2, you can take out all the primes here since the difference between factor of prime other than 2 is odd-odd. In fact, all odd numbers are out since it has a factor of itself and 1.
Now, for all even number except 2, you are always going to have 2 as a factor and itself, which makes the difference even. So all even numbers other than 2 is out. This only leave with n=2.
SUFFICIENT
