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# ds 243 OG 10 TH

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ds 243 OG 10 TH [#permalink]  24 Nov 2005, 12:53
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if INTEGer n is greater than 1? IS N EQUAL TO to 2 ?

st1 N has exactely 2positive factors
st 2 The difference of any 2 distinct positive factors of n is odd

Thanks
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Re: ds 243 OG 10 TH [#permalink]  24 Nov 2005, 13:01
mand-y wrote:
:) if INTEGer n is greater than 1? IS N EQUAL TO to 2 ?

st1 N has exactely 2positive factors
st 2 The difference of any 2 distinct positive factors of n is odd

Thanks

(1) N has exactly 2 positive factors so N is a prime number. Insufficient.
(2) Take 6 as an example. Factors of 6 are 1, 2 3, 6. 3-2 = 1
Take 2 as an example. Factors of 2 are 1 and 2. 2-1 = 1

(1) + (2) N has to be the prime number 2. Sufficient.
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Re: ds 243 OG 10 TH [#permalink]  24 Nov 2005, 13:16
TeHCM wrote:
mand-y wrote:
:) if INTEGer n is greater than 1? IS N EQUAL TO to 2 ?

st1 N has exactely 2positive factors
st 2 The difference of any 2 distinct positive factors of n is odd

Thanks

(1) N has exactly 2 positive factors so N is a prime number. Insufficient.
(2) Take 6 as an example. Factors of 6 are 1, 2 3, 6. 3-2 = 1
Take 2 as an example. Factors of 2 are 1 and 2. 2-1 = 1

(1) + (2) N has to be the prime number 2. Sufficient.

Quote:
any 2 distinct positive factors of n is odd

B)...only 2
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VP
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2 and 3 are not distinct positive factors of 6?
VP
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TeHCM wrote:
2 and 3 are not distinct positive factors of 6?

yes they are. 3 and 1 are distinct factors of 6 as well. diff of 3 and 1 is even. thats why i mentioned "any". the diff of any 2 dist factors.
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Last edited by christoph on 24 Nov 2005, 13:55, edited 1 time in total.
VP
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4 is a factor of 6? You meant 6..

I see what you mean now. The wording is tricky. Hopefully I won't make similar mistakes on the real deal!

Thanks
VP
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TeHCM wrote:
4 is a factor of 6? You meant 6..

I see what you mean now. The wording is tricky. Hopefully I won't make similar mistakes on the real deal!

Thanks

edited it
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If INTEGer n is greater than 1? IS N EQUAL TO to 2 ?

1) N has exactely 2positive factors
2) The difference of any 2 distinct positive factors of n is odd

***************************************************

1) All the prime numbers have exactly 2 positive factors. Insufficient.

2) N and 1 are always distinct positive factors of N, and N-1 should be odd.

Thus, N should be an even number.

However, if N is bigger than 2 and contains 2 (like 4, 6, 8 ...), N - 2 is even! Therefore, only 2 is possible. Sufficient.

(B) should be it.
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