If |r| is not equal to 1, is integer r even?

Question

(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.

Bunuel · Accepted Answer

If |r| is not equal to 1, is integer r even?

|r|
eq{1}  -->  r
eq{1}  and  r
eq{-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
eq{-1}  then only valid solutions for  r  are -2 and 0, both are even. Sufficient.

Answer: C.

ankushjain · Answer

Its C and I solved exactly as you did.

nikhilsamuel89 · Answer

When 2r>-5, and r is NOT positive.
=> r can be -2 OR 0.
But since both are even, we don't need to bother.

navami · Answer

combining both cases r = -2

nikhilsamuel89 · Answer

Combining both cases, we get -2 and 0.
0 is also not positive, is even ans is >-2.5

Spidy001 · Answer

r != (+-)1

1. Not sufficient
r<=0

......-3,-2,0

=> r can be even or odd

2. Not sufficient

r>-2.5

-2,0,2,3,....

=> r can be even or odd

together
Sufficient
r>-2.5 & r<=0
=> r can be -2,0
=> r can only be even

Answer is C.

GyanOne · Answer

enigma123,

Your approach to solve this problem is correct. The only correction needed is that when you combine both statements, you take the possible value of r to be only -2, but the value of r can also be 0 (as zero is a non-negative integer. As an aside, it is also non-positive).

Some points to remember: 
(1) Negative integers too can be even
(2) 0 is the only integer that is both non-negative as well as non-positive. If ever you come across a question that asks you to work with non-negative integers, don't just take positive integers as the valid set. Remember to include the zero. Similarly, non-positive integers also include zero

jimwild · Answer

Where it is mentionned r is an integer ?

Bowtye · Answer

last part of the question stem. If |r| is not equal to 1,  is integer r  even? Kind of tricky because most of the time it will state that it is an integer near the beginning.

bumpbot · Answer

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If |r| is not equal to 1, is integer r even?

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If |r| is not equal to 1, is integer r even?

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