Data Sufficiency

I didn't particularly catch the explanation given in the OG....Please help!

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

1) n has exactly 2 positive factors

2) The difference of any 2 distinct positive factors of n is odd


OA here is B....However, consider an example where n=4....Factors = 4,2,1 ......Now 4-1 =3 (Odd)....So how is B sufficient....I think I am not understanding the Statement too well!

1,2 and 4 are the factors of 4. In this case 4-2 is even.

Question says that difference of "any" two positive factors is odd.

So B alone is suuficient

[quote="f2001290"]1,2 and 4 are the factors of 4. In this case 4-2 is even.

Question says that difference of "any" two positive factors is odd.

So B alone is suuficient[/quote]

Hi, f2001290---

Can you pls explain a little more RE: "any"?

I thought that 4 would be a val for n that satisfied statement (2). I saw from the MGMAT forum that we are supposed to take it that "any" means "all", but I interpreted "any distinct positive factors" to mean all "eligible" factors of n.

4's factors:
1 and 4,
2 and 2

I thought that 2 and 2 should be tossed out since they are not distinct factors of 4, leaving only 4 and 1 to be considered.

Can you please help me understand where I'm going wrong?

Thanks!

kansonne, when you have to take factors of a number you consider all factors together. In this example 4 has 1,2 and 4 as factors.

Stmt 2 says that diff of any 2 factors is odd... for this case diff of 4 and 1 is 3. However, diff of 4 and 2 is even. So 4 does not satisfy stmt 2.