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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. \(|R| = R\)

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! Ravi

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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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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. \(|R| = R\)

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.

Answer: E.

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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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