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# DS - POSITIVE INTEGER (m04q17)

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DS - POSITIVE INTEGER (m04q17) [#permalink]

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03 Sep 2008, 14:34
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Is integer $$R$$ positive?

1. $$R^3 = R$$
2. $$|R| = R$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 14:36
B

from 1 : two possibilities -1,1

from 2 : has to be +ve else not possible
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 14:38
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Again E.
1) R=0 or R=+-1
2) R=0 or Any positive #, including 1

1+2) still R=0 or R=1 So E.
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 14:52
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IMO E.

At 1st I thought it will be B, but ya if R=0, that screws up evrything..
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 17:15
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Hmm I am getting B for this. This is Yes/No DS and a No answer is sufficient

We all agree on A is insuff. R ^ 3 - R = 0, which means R =0, 1 ,-1 ( No, Yes, No for the Q Is R +ve? ) hence Insuff

B is saying

R = R and -R = R (R is integer)

Lets say R =1 -R = -1 which is not equal to R same thing for any -ve integer

The only number I can think of satisfying the above two equations is 0

Is 0 positive? No ( neither positive nor negative) . Hence B.

Do you agree? Did I go wrong any where?
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 18:00
|R|=R means R=R when ris +ve and R=-R, when R is -ve

so, option gives you all the +ve integers + 0
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 19:16
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I'm getting E for this problem as well.

(1) R could be negative, zero, or even positive.

(2) R could be positive or zero.

(1&2) R could still be positive or Zero

So our answer is E.
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 20:16
Yeap E is the answer!

Thanks for discussion.

I chose B making another stupid mistake..
considered "zero" as +ve..

RULE IS "ZERO is neither positive nor negative"
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 21:04
K! Seriously I need some enlightenment as I am totally lost here.

When I see a absolute variable I create 2 equations and we are given that R is integer and | R | = R

I read it as Can you find integer(s) such that R = R and -R = R

For all integers positive and negative I can say R is not equal to -R except for 0

0 is the integer that satisfies both R = R and -R = R

0 is neither +ve nor -ve. Going back to the Q Is R positive? NO

I felt that its sufficient and chose B.

Can some one explain where I am going wrong?
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 21:11
icandy wrote:
K! Seriously I need some enlightenment as I am totally lost here.

When I see a absolute variable I create 2 equations and we are given that R is integer and | R | = R

I read it as Can you find integer(s) such that R = R and -R = R

For all integers positive and negative I can say R is not equal to -R except for 0

0 is the integer that satisfies both R = R and -R = R

0 is neither +ve nor -ve. Going back to the Q Is R positive? NO

I felt that its sufficient and chose B.

Can some one explain where I am going wrong?

|R|=R

one solution for this is R=0
other solutions
when R>0 R=R So R is +ve
when R<0 R=-R --> invalid so R can't be -ve

So all together two solutions R=0 or R is +ve

Is R Positive? No when R=0
Is R Positive? Yes when R is +ve

insuffcient.
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 21:33
x2suresh wrote:
icandy wrote:
K! Seriously I need some enlightenment as I am totally lost here.

When I see a absolute variable I create 2 equations and we are given that R is integer and | R | = R

I read it as Can you find integer(s) such that R = R and -R = R

For all integers positive and negative I can say R is not equal to -R except for 0

0 is the integer that satisfies both R = R and -R = R

0 is neither +ve nor -ve. Going back to the Q Is R positive? NO

I felt that its sufficient and chose B.

Can some one explain where I am going wrong?

|R|=R

one solution for this is R=0
other solutions
when R>0 R=R So R is +ve
when R<0 R=-R --> invalid so R can't be -ve

So all together two solutions R=0 or R is +ve

Is R Positive? No when R=0
Is R Positive? Yes when R is +ve

insuffcient.

Now I see what I am doing differently. When I look at |R| = R and consider the two equations I am considering that both the cases of R = R and R = -R needs to be satisfied. What needs to be checked is whether I arrive at same answer in all three cases.

Thanks.
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Re: DS - POSITIVE INTEGER [#permalink]

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03 Sep 2008, 21:44
x2suresh wrote:
Is integer R positive?

1.R^3=R
2.|R|= R

1: r could be 0 or 1.
2: r could be 0 or any +ve.

1&2: o or 1. nsf.

E.
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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24 Jul 2010, 05:25
Yep. Answer is E. The rule tested here is: 0 is neither +ve nor -ve

Cheers!
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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28 Jul 2011, 06:32
Simply test +1, -1, and 0 here to get answer. E
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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31 Jul 2012, 12:06
Seemed really easy to lead to B. I made the silly mistake and did not consider 0 for the statement (ii). Realized my mistake and learnt from it.
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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31 Jul 2012, 21:48
is it something like /0/ does not exist or the value of /0/ is again a zero which is neither positive nor negative???
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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02 Aug 2012, 00:53
Expert's post
mohan514 wrote:
is it something like /0/ does not exist or the value of /0/ is again a zero which is neither positive nor negative???

$$|0|=0$$ and yes, zero is nether positive nor negative.

Check Absolute Value and Number Theory chapters of Math Book for more:
math-absolute-value-modulus-86462.html
math-number-theory-88376.html

Hope it helps.
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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31 Jul 2013, 10:52
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x2suresh wrote:
Is integer $$R$$ positive?

1. $$R^3 = R$$
2. $$|R| = R$$

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Is integer R positive?

(1) R^3=R --> $$r^3-r=0$$ --> $$r(r^2-1)=0$$ --> $$r(r-1)(r+1)=0$$ --> $$r=0$$, $$r=1$$, or $$r=-1$$. Not sufficient.

(2) |R|=R --> $$r$$ is some non-negative integer, so $$r$$ can be 0 or any positive integer. Not sufficient.

(1)+(2) $$r$$ can be 0, so not a positive integer or 1, a positive integer, two different answers, hence not sufficient.

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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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26 Oct 2013, 03:23
Hello Bunuel,

Can you please tell me if "0" is a positive even integer or not.

The notes of GMAT Club Math book does say that 0 is an even positive integer, but in this question, we again differ with it.

Can you please clarify this doubt of mine. Appreciate it
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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26 Oct 2013, 03:42
Expert's post
amkabdul wrote:
Hello Bunuel,

Can you please tell me if "0" is a positive even integer or not.

The notes of GMAT Club Math book does say that 0 is an even positive integer, but in this question, we again differ with it.

Can you please clarify this doubt of mine. Appreciate it

Where does Math Book say that?

Zero is nether positive nor negative even integer.
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Re: DS - POSITIVE INTEGER (m04q17)   [#permalink] 26 Oct 2013, 03:42

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# DS - POSITIVE INTEGER (m04q17)

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