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.
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.
