If the integer is greater than 1,is n equal to 2? 1. n has

Question

If the integer is greater than 1,is n equal to 2?
1. n has exactly 2 positive factors
2 The difference of any two distinct factors of n is odd

With explanation please

crackgmat3 · Answer

C

statement 1- the n can any prime number

statement 2- 
Lets assume n as 1,2,3,4,5,6,7,8
1- 1 - diff -0
2- 1,2 - diff - 1
3-1,3 - diff - 2
4-1,2,4 -diff - 1,2
5-1,5 - diff - 4
6-1,2,3,6 - diff - 1,1,3
7-1,7 - diff - 6
8-1,2,4,8 - diff - 1,2,4

From the above example difference of positive factors which yields odd numbers are 2 and 6.

If we combine the two we should get only one answer for n.

anuramm · Answer

I will go with B on this one.
1 - we can have any prime no as n .
2 - The difference of any two distinct factors of n is odd.
The diff of any two nos is odd implies that one factor is even and the other factor is odd.
If we take any even composite no. then 2 is defintely a factor and the no itself is also a factor. Therefore, we will surely have atleast 2 even factors and hence their diff will be even.
If we take any odd composite no. then 3 and the number itself will be factors of the no. Therefore, we will surely have atleast 2 odd factors and hence their diff will be even.
The last case is prime nos - 2 is the only even prime no. and hence only 2 qualifies for the stem2. even other prime no is odd and hence every other prime no- 1 is even.
hence 2 is sufficient.

neelam · Answer

what if n=4 ,factors of 4 will be 1,2,4 then 2-1 is 1 or 4-1=3 (odd) 

my guess is C .

anuramm · Answer

neelam,
the stem 2 says that the diff of any two factors of n is odd.
so if n=4, factors of n are 1,2,4.
its truw that 2-1 and 4-1 are odd.
but when we consider 4-2, the diff is even. i think we need to consider all the combinations and the diff shd be odd for any two combination.

dushver · Answer

Anuramm,
You should also be considering 6 (as in the earlier explaination given by crackgmat).

The choice is clearly C.

ian7777 · Answer

The answer to this one is B.

The statement says that the diff between any two factors is odd. That doesn't mean that some of them make odd numbers, that means ALL of them do. The only number this is true about is 2. the number 6, as given in the examples above, has the factors 2 and 6 in it, and their diff is 4, so that doesn't work.

All odd numbers will have an even diff, because odd - odd is even. All even numbers have at least 2 and the number itself, and even - even is even. Only 2 has only one odd and one even factor, and even - odd is odd.

If the integer is greater than 1,is n equal to 2? 1. n has

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