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# If the integer n is greater than 1, is n equal to 2? 1. n

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Director
Joined: 25 Jan 2004
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If the integer n is greater than 1, is n equal to 2? 1. n [#permalink]  05 Jun 2004, 11:41
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If the integer n is greater than 1, is n equal to 2?

1. n has exactly 2 positive factors

2. the difference of any two distict positive factors of n is odd
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Praveen

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Joined: 30 Oct 2003
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a) Any prime number has exactly two divisors ( Insufficient )
b) Sufficient
2 has divisors 2 and 1 and the difference between them is 1
Director
Joined: 25 Jan 2004
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Anand,

what about 10 which as 2 & 5 as factors and still has difference (5-2 =3) as odd?

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Praveen

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difference between any two of the distincive fators is odd
10 has factors 1 and 5 and difference is 4 which is not odd
Intern
Joined: 26 Jan 2003
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Re: try this DS question [#permalink]  06 Jun 2004, 05:05
praveen_rao7 wrote:
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If the integer n is greater than 1, is n equal to 2?

1. n has exactly 2 positive factors

2. the difference of any two distict positive factors of n is odd

(1) => n is prime. Insufficient.
(2) => it should have one even factor, which is 2, and one more which should be only 1, because other ways we will not have the difference of ANY two factors odd. (statement 1 can be derived from 2). So the only integer is 2. Sufficient.

Director
Joined: 25 Jan 2004
Posts: 728
Location: Milwaukee
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Thanks guys,

I mis-interpreted word "Any" in second choice. B is right . You guys rock.
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Praveen

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