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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

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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, 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 (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 [#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, 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

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

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26 Oct 2013, 03:53
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Under Integers topic:

Even and Odd Numbers
An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.
An even number is an integer of the form , where is an integer.
An odd number is an integer that is not evenly divisible by 2.
An odd number is an integer of the form , where is an integer.

Zero is an even number.

Can u please correct me on these:
1) Zero is not a positive nor a negative number
2) Zero is an Integer
3) Zero is an even Integer
4) Zero is not an odd integer

Are any of the above statements wrong ?

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

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26 Oct 2013, 03:58
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amkabdul wrote:
Under Integers topic:

Even and Odd Numbers
An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.
An even number is an integer of the form , where is an integer.
An odd number is an integer that is not evenly divisible by 2.
An odd number is an integer of the form , where is an integer.

Zero is an even number.

Can u please correct me on these:
1) Zero is not a positive nor a negative number
2) Zero is an Integer
3) Zero is an even Integer
4) Zero is not an odd integer

Are any of the above statements wrong ?

You wrote:
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

Nowhere it's said that 0 is positive!

Again: zero is nether positive nor negative even integer.

As for point 4: 0 it's even, thus naturally it's not odd.
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Re: DS - POSITIVE INTEGER (m04q17) [#permalink]

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26 Oct 2013, 04:01
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Thanks alot Bunuel... U are really helpful... Dont mind my silly doubts..guess the pressure is building up for the G Day; messing up with basics

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

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17 Jul 2014, 12:03
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Riles479 wrote:
This is my first QOTD and I'm a total noob. Why are the answer choices for A, B, C, D & E not posted with each Quant question?

Hi, and welcome to GMAT Club.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following post ALL YOU NEED FOR QUANT.

Hope this helps.
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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, 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, 20:16

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] 31 Jul 2012, 12:06

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# DS - POSITIVE INTEGER (m04q17)

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