enigma123
If |r| is not equal to 1, is integer r even?
(1) r is not positive
(2) 2r > -5
This is my approach:
Considering statement 1
r is a negative integer and is not equal to 1. But it can be any other integer. Therefore insufficient.
Considering statement 2
2r>-5
For this to happen r has to be -2, -1, 0,1,2,...n. Therefore r can be either ODD or EVEN. Insufficient.
Combining the two:Yes. How? from Statement 1-> r is negative and not equal to 1 and from statement 2 we can tell r can only be -2 and therefore negative.
The question is again the same - is my approach correct?
Guys - My sincere apologies to everyone on this forum by asking about the approach. As I said before, GMAT did bite me 3 times previously and this time I am not taking any chances as most of you guys said its always best to work on basics first. Therefore, I want to be sure that my concepts are getting better.
If |r| is not equal to 1, is integer r even?\(|r|\neq{1}\) --> \(r\neq{1}\) and \(r\neq{-1}\).
(1) \(r\) is not positive --> Clearly insufficient, \(r\) can be any non-positive integer (except -1) even or odd (0, -2, -3, -4, ...).
(2) \(2r>-5\) --> \(r>-\frac{5}{2}=-2.5\) --> again \(r\) can be even or odd (except -1 and 1): -2, 0, 2, 3, 4, 5, ... Not sufficient.
(1)+(2) \(r\) is not positive and \(r>-2.5\) --> \(r\) can be -2, -1, or 0. But as given that \(r\neq{-1}\) then only valid solutions for \(r\) are -2 and 0, both are even. Sufficient.
Answer: C.