Error in OG Data Sufficiency Book - check my math

[MaleInNC2007]

I have issues with the following Data Sufficiency problem in
the OG 11 edition. I also have a question at the bottom.

Problem 132 (answer on page 331)

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 positive distinct factors of n is odd.

n can be any prime number.

(2)I say not sufficient. n could be 6 or 2.

The factors of 6 are 1, 2, and 3.

3-2 = 1; 2-1 = 1; both 3-2 and
2-1 are the difference of any two positive factors of n and both are odd
satisfying the requirements of (2); n could also be 2; the factors of
2 are 1 and 2; 2-1 = 1 which is odd

Thus, n could be 2 or 6; not
sufficient

Using both (1) and (2) it would leave the only number possible as 2 thus the answer is C

The OG says (2) is sufficient. I disagree for the
aforementioned reasons.

The answer in the book is subtracting n with the distinct factor. It states that if n is greater than 2 and n is odd, then 1 and n are factors of n,
and their difference is even. Also, if n
is greater than 2 and n is even, then 2 and n are factors, and the difference is even. Even using this logic, using 6 = n can still
result in satisfying (2) For example,
6-3 = 3; 3 is odd thus giving 6 and 2 as possible answers.

(2) asks for the difference of any two positive distinct factors though, not the difference between n and the factors. I believe the answer to this
problem in the OG is wrong.

Also, another question:

is zero an integer?

I say yes. I cannot remember the problem but it required an integer, and when zero was used, the answer I obtained was different than the answer in the OG. I am curious if the GMAT doesn’t consider zero to be an integer. I’m reviewing for the GMAT next Monday and if I can find the problem I will post it.

[beatthegmat]

With regard to your second question--whether zero is an integer--please see my GMAT Flashcards: I believe you can find the answer there.

https://www.beatthegmat.com/viewtopic.php?t=32

[MaleInNC2007]

With regard to your second question--whether zero is an integer--please see my GMAT Flashcards: I believe you can find the answer there.

https://www.beatthegmat.com/viewtopic.php?t=32

Thanks!

[colinbendell]

The factors of 6 are 1, 2, and 3.

The Factors of 6 are actually 1, 2, 3 and 6.

Notice that the statement does not imply only prime factors - all factors are valid. Therefore if you take any two factors you could come up with 6 - 2 which of course is a positive and therefore does not qualify for statement #2.

The answer in the OG is correct.

[coachy]

You are right. I was confused about this question. And it suddenly dawned on me that I have to consider the statement 2 as true and evaluate if n can be 2. I was trying to prove the statement 2 as wrong but I guess that is what DS practice is about. I have to keep on reminding myself that the statement 1 and 2 are universal truths.

[Tame the CAT]

3-1 is even. So it cannot be 6.