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

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Director
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If |r| is not equal to 1, is integer r even? [#permalink]

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06 Jul 2011, 07:51
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Question Stats:

55% (02:01) correct 45% (00:50) wrong based on 56 sessions

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

(1) r is not positive
(2) 2r > -5

[Reveal] Spoiler:
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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MGMAT 2--> 640
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GMAT ==> 730

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Re: If |r| is not equal to 1, is integer r even? [#permalink]

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06 Jul 2011, 08:05
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.
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Re: If |r| is not equal to 1, is integer r even? [#permalink]

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03 Aug 2011, 00:24
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: If |r| is not equal to 1, is integer r even? [#permalink]

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03 Aug 2011, 08:30
combining both cases r = -2
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Re: If |r| is not equal to 1, is integer r even? [#permalink]

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03 Aug 2011, 08:58
Combining both cases, we get -2 and 0.
0 is also not positive, is even ans is >-2.5
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Re: If |r| is not equal to 1, is integer r even? [#permalink]

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03 Aug 2011, 13:06
enigma123 wrote:

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

+1
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Re: If |r| is not equal to 1, is integer r even? [#permalink]

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03 Aug 2011, 14:41
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: If |r| is not equal to 1, is integer r even? [#permalink]

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03 Aug 2011, 21:26
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: If |r| is not equal to 1, is integer r even? [#permalink]

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08 Oct 2015, 01:54
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.

Where it is mentionned r is an integer ?
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Re: If |r| is not equal to 1, is integer r even? [#permalink]

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08 Oct 2015, 05:59
jimwild wrote:
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.

Where it is mentionned r is an integer ?

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.
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Re: If |r| is not equal to 1, is integer r even? [#permalink]

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08 Oct 2015, 07:30
Expert's post
enigma123 wrote:
If |r| is not equal to 1, is integer r even?

(1) r is not positive
(2) 2r > -5

[Reveal] Spoiler:
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.

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Re: If |r| is not equal to 1, is integer r even?   [#permalink] 08 Oct 2015, 07:30
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