value of X OG-10 question

[taneja.niks]

Q-> 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 distinct factors of n is odd

[selango]

stmt1,


All prime numbers have exactly 2 factors.

So n can be 2,3,5,7.....

Insuff

stmt2,

Only for 2 the differnce bw 2 distinct factors(ie) 1 and 2 is odd.For remaining prime numbers the difference is even.

n=2

Suff

Pick B

[taneja.niks]

for the second statement why dou consider only the prime numbers thts wrong the question no where says tht the number is prime the st-1 may infer tht the numbers r prime..............

where as statement 2 or the question stem no where states tht the number r prime......... there r other number like 10 whose prime factors being 2,5 and the difference is 3 ->odd

[Fractal]

good point, but i think you are wrong!

because:

2. The difference of any two distinct factors of n is odd

--> of any two distinct factors of n, not just of some!

ok?

[John@Knewton]

I just wanted to add one extra point here. Selango has the right approach here. Here are the steps spelled out a just a bit more:

Looking at Statement 2 alone, we can't assume that n is prime. The only things we know for sure is that it is an positive integer greater than 1, and that the difference between any of n's factors is odd. Since the difference between two even numbers is even, and the difference between two odd numbers is even, that means that n must have even and odd factors. But the real key here is that that also means n must have ONLY one even factor and ONLY one odd factor. If it had more than one of either, than there would be a difference of 2 factors which was either even - even or odd - odd.

And with that realization, that n can only have one even factor and one odd factor, we know that n must be prime, since it has only two factors. And since one of the factors is even, n must be 2, since 2 is the only even factor. So, Statement 2 alone is sufficient.

Since Statement 1 is insufficient, for the reason Selango pointed out, answer choice B is correct.