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# Is Integer r even?

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Director
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Is Integer r even? [#permalink]  06 Jul 2011, 06:51
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Difficulty:

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Question Stats:

50% (01:55) correct 50% (00:37) wrong based on 16 sessions
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.
[Reveal] Spoiler: OA

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Intern
Joined: 11 Sep 2010
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Kudos [?]: 5 [0], given: 0

Re: Is Integer r even? [#permalink]  06 Jul 2011, 07:05
enigma123 wrote:
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.

Its C and I solved exactly as you did.
Manager
Joined: 25 Sep 2010
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Schools: HBS, LBS, Wharton, Kelloggs, Booth
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Kudos [?]: 4 [0], given: 15

Re: Is Integer r even? [#permalink]  02 Aug 2011, 23:24
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.
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Re: Is Integer r even? [#permalink]  03 Aug 2011, 07:30
combining both cases r = -2
Manager
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Re: Is Integer r even? [#permalink]  03 Aug 2011, 07:58
Combining both cases, we get -2 and 0.
0 is also not positive, is even ans is >-2.5
Intern
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Re: Is Integer r even? [#permalink]  03 Aug 2011, 12:06
enigma123 wrote:

The question is again the same - is my approach correct?

+1
Director
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Re: Is Integer r even? [#permalink]  03 Aug 2011, 13:41
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

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Re: Is Integer r even? [#permalink]  03 Aug 2011, 20:26
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
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Re: Is Integer r even?   [#permalink] 03 Aug 2011, 20:26
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