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# If the integer n>1, is n=2? (1) n has exactly two

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If the integer n>1, is n=2? (1) n has exactly two [#permalink]  12 Jul 2007, 15:39
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If the integer n>1, is n=2?

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

I'm thinking the OA is wrong, but I'm probably just missing something. I'll let a few people post and then give the OA.
Manager
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Yes, it's B. But for B, couldn't n=2 or n=6?
Manager
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No! factors of 6 are 6, 3, 2, 1

6-2=4 -->> even!
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Re: DS 132 - OG - Incorrect OA? [#permalink]  12 Jul 2007, 15:58
mavery wrote:
If the integer n>1, is n=2?

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

I'm thinking the OA is wrong, but I'm probably just missing something. I'll let a few people post and then give the OA.

B. only 2 has factors whose difference is odd.
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I'm feeling really stupid here, but what am I missing? 3 & 2 are factors of 6 and 3-2 is odd. Just as 2-1 is odd.
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mavery wrote:
What about 6-3, 6-1, and 3-2?

The difference between any two positive distinct factors!

for 6 I pick 6 and 2. 6-2=4 -->> doesn't work

for 2 I can only pick 2 and 1. 2-1=1 -->> odd
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Quote:
The difference between any two positive distinct factors!

for 6 I pick 6 and 2. 6-2=4 -->> doesn't work

for 2 I can only pick 2 and 1. 2-1=1 -->> odd

I'm really not trying to be argumentative here, I'm just trying to get this. Are 3 and 2 not distinct positive factors of 6? And isn't the difference between the two odd?

6 and 2 are distinct even positive factors of 6, but the question in my book only says they need to be distinct positive factors.
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mavery wrote:
Quote:
The difference between any two positive distinct factors!

for 6 I pick 6 and 2. 6-2=4 -->> doesn't work

for 2 I can only pick 2 and 1. 2-1=1 -->> odd

I'm really not trying to be argumentative here, I'm just trying to get this. Are 3 and 2 not distinct positive factors of 6? And isn't the difference between the two odd?

6 and 2 are distinct even positive factors of 6, but the question in my book only says they need to be distinct positive factors.

"ANY DISTINCT" - meaning any distinct )

You pick 3 and 2, but I pick 6 and 2. In both cases we pick any.

I guess the wording is a little confusing. They should say "all"....I guess.
We are getting into a game of words, which reminds me - I gotta work on my verbal. I suck at it )
Manager
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Ahhh...ding, ding...I think I got it now...thanks for your help...
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Quote:
If the integer n>1, is n=2?

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

I'm thinking the OA is wrong, but I'm probably just missing something. I'll let a few people post and then give the OA.

I say C.

(1) 3s factors are 3 and 1, 2s factors are 2 and 1 - insufficient

(2) 3 and 1 are distinct. the difference b/w 3 and 1 is 2 (not what we're looking for). 2 and 1 are distinct. the diff b/w 2 and 1 is 1.

Last edited by ggarr on 12 Jul 2007, 20:07, edited 1 time in total.
Manager
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2 is not an odd number.....I think
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