q#132 OG 11th edition page 331

[ifthyder]

Q132) if the integer n is greater than 1 is n equal to 2?

1)n has exactly two positive factors.
2)the difference of any two distinct positibe factores of n is odd.

answer is B
explaination
2) note tha if n>2 and n is odd then 1 and n are factors of n , and their difference is even. also if n >2 and n is even,
then 2 and n are factors of n and their difference is even.

Now according to me if we take even value of n >2 for example 6 as n value and take two factors of 6 in such a way that one factor of n be even i.e 2 and other factor of 6 be odd i.e 3 then , difference of factors will be 3-2 =1 (odd).Isn't that answer insufficient

6 could be value of n isn't it?

[Stuart@KaplanGMAT]

Q132) if the integer n is greater than 1 is n equal to 2?

2)the difference of any two distinct positibe factores of n is odd.

Now according to me if we take even value of n >2 for example 6 as n value and take two factors of 6 in such a way that one factor of n be even i.e 2 and other factor of 6 be odd i.e 3 then , difference of factors will be 3-2 =1 (odd).Isn't that answer insufficient

6 could be value of n isn't it?

You're misinterpreting statement (2). You need to interpret "any two factors" as "every pair of factors".

So, even though some pairs of factors of 6 have an odd difference, it's not true that every pair of factors of 6 have an odd difference. For example, the difference between 1 and 3 is even.

The only way for the difference between every pair of factors to be odd is if the number has exactly 2 factors: 1 even and 1 odd. Only "2" fits that description, so statement (2) gives us a definite "yes" answer to the question.

[olpre4]

Factors for 6

3x2 --> 3-2 = 1 odd

6x1 --> 6-1 = 5 odd

Could n be 6 as well?

[olpre4]

How is 3x1 a factor pair of 6?

Unless I am thinking about things the wrong way, I can only identify 3x2 and 6x1 as factors of 6.

[Ian Stewart]

How is 3x1 a factor pair of 6?

Unless I am thinking about things the wrong way, I can only identify 3x2 and 6x1 as factors of 6.

While you're right that those are the only pairs of positive integers with a product of six, the question does not mention 'factor pairs'. Factors are divisors. The positive factors of 6 are 1, 2, 3 and 6.