OG 11 #132

[bk136587]

N is an integer greater than 1, does n=2?

(1) n has exactly 2 positive factors
(2) The difference of any two distinct positive factors of n is odd.

I understand that (1) is wrong bc this defines any positive prime #

I also think that (2) is in not sufficient:
if n=2, 2-1 the difference is odd
if n=4, 4-1 the difference is odd
if n=6, 6-1 the difference is odd

Together, know Odd-Odd = Even, and Even-Odd = Odd, since 2 is the only even prime Number then together they should be sufficient...

HOWEVER - OG states that (B) is the answer.

Can someone please help me on this. Thanks.

[relic]

I think I can help.

Statement two says "any two positive distinct factors", so when you test n = 4, you must test all of 4's factors {1,2,4}. 4-2=2. The only number that will result in only odd differences is 2.

[iamcste]

N is an integer greater than 1, does n=2?

(1) n has exactly 2 positive factors
(2) The difference of any two distinct positive factors of n is odd.

I understand that (1) is wrong bc this defines any positive prime #

I also think that (2) is in not sufficient:
if n=2, 2-1 the difference is odd
if n=4, 4-1 the difference is odd
if n=6, 6-1 the difference is odd

Together, know Odd-Odd = Even, and Even-Odd = Odd, since 2 is the only even prime Number then together they should be sufficient...

HOWEVER - OG states that (B) is the answer.

Can someone please help me on this. Thanks.

For statement 2

If difference is odd, nos which are subtracted have to be different, I mean one has to be odd, other has to be even or vice-versa

when you take 4 , 4 and 2 both are even hence their result can be never odd.

Also as pointed by reloc, "any" factor was the key