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OG 11 #132

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OG 11 #132

by bk136587 » Fri Apr 17, 2009 7:03 am
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.
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by relic » Fri Apr 17, 2009 7:09 am
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.
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Re: OG 11 #132

by iamcste » Fri Apr 17, 2009 7:26 am
bk136587 wrote: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
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