Data Sufficiency

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

1. N has exactly 2 positive factors

2. The difference between any 2 distinct factors of N is odd.

I solved and found ans as C but OG tells ans as B.

Please clarify [/img]

Why did you think that (2) alone was insufficient? Did you find examples of two different answers?

If n is an integer greater than 1, it is either equal to 2 or greater than 2.

Case I
If n is an even integer greater than 2, it has factors that include 2 and n, and n - 2 is even.

Case II

If n is an odd integer greater than 2, it has factors that include 1 and n, and n - 1 is even.

Since (2) tells us that no matter which two factors of n that we choose, their difference is odd. Thus neither case I nor case II are valid (i.e. n is not greater than 2). We can conclude that n is equal to 2.

SUFF

ankurmit wrote:If the integer N is greater than 1, is n equal than 2?

1. N has exactly 2 positive factors

2. The difference between any 2 distinct factors of N is odd.

I solved and found ans as C but OG tells ans as B.

Please clarify [/img]

1/ insuff

2/ only when diffenrence between 2 factors is 2 và others factors


ex: 11 - 2 = 9 , 11 - 3 = 8.... suff

If I take N=6 it will have factors 1,2,3, and 6.

As per your ans you are taking differnce b/w 2 and 6 which is not doubt even but why are you not taking difference b/w 3 and 6 as they are also 2 distinct factors of 6?

Will distinct mean only first and last factors of a number??

ankurmit wrote:Will distinct mean only first and last factors of a number??

No

option 1
number factors
2 1 2
3 1 3
5 1 5
7 1 7

not possible


option 2
number factors
2 1 2

hence b is the answer

ankurmit wrote:If the integer N is greater than 1, is n equal than 2?

1. N has exactly 2 positive factors

2. The difference between any 2 distinct factors of N is odd.

I solved and found ans as C but OG tells ans as B.

Please clarify [/img]

Instructor..than please clear my doubt

Reread my post: I have bolded the key words. The difference between two distinct factors of n is odd no matter which two factors we consider.

i am sorry..i may be thinking in wrong way but can u please clear this :


If I take N=6 it will have factors 1,2,3, and 6.

As per your ans you are taking differnce b/w 2 and 6 which is not doubt even but why are you not taking difference b/w 3 and 6 as they are also 2 distinct factors of 6?