Is x a negative number? : GMAT Data Sufficiency (DS)
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# Is x a negative number?

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Is x a negative number? [#permalink]

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06 Aug 2012, 02:11
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Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

Practice Questions
Question: 13
Page: 276
Difficulty: 550
[Reveal] Spoiler: OA

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Re: Is x a negative number? [#permalink]

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06 Aug 2012, 02:11
SOLUTION

Is x a negative number?

(1) 9x > 10x --> rearrange: $$0>10x-9x$$ --> $$0>x.$$ Sufficient.
(2) x + 3 is positive --> $$x+3>0$$ --> $$x>-3$$. Not sufficient.

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Re: Is x a negative number? [#permalink]

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06 Aug 2012, 06:45
From Statement -1 : 9 X > 10 X
Case -1 :Assuming X > 0
Dividing by X , 9>10 - Which is no true - So X <0 - Sufficient

Case-2 : X+3 >0
i.e X> -3 ....X can be any number greater than -3 -Not sufficient

[Reveal] Spoiler:
A
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Re: Is x a negative number? [#permalink]

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06 Aug 2012, 06:57
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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

Practice Questions
Question: 13
Page: 276
Difficulty: 550

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Now let us take it down fat and very fast, cos this is a very wussy question where we have to save time for the other tough problems we should not take more than 10 seconds to solve it .
9x>10x implies x < 0 9 (Awesome )
x+3 > 0 implies x > -3 ( not good )
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Re: Is x a negative number? [#permalink]

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06 Aug 2012, 07:35
IMO A

st 1: sufficient x is -ve
st 2: not sufficient x can be +ve, -ve or zero
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Re: Is x a negative number? [#permalink]

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10 Aug 2012, 03:58
SOLUTION

Is x a negative number?

(1) 9x > 10x --> rearrange: $$0>10x-9x$$ --> $$0>x.$$ Sufficient.
(2) x + 3 is positive --> $$x+3>0$$ --> $$x>-3$$. Not sufficient.

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Is x a negative number? [#permalink]

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22 Sep 2012, 16:08
Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

i would like to know if my process is correct

1) 9x - 10x >0 ----> x (9-10) > 0 -----> x > 0 suff

2) x + 3 = pos x can be a positive value 4 + 3 = 7 or negative -1 + 3 = 2 always positive insuff

In particular I wish to know about the first stat.

Thanks
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Re: Is x a negative number? [#permalink]

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22 Sep 2012, 21:52
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Expert's post
carcass wrote:
Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

i would like to know if my process is correct

1) 9x - 10x >0 ----> x (9-10) > 0 -----> x > 0 suff

2) x + 3 = pos x can be a positive value 4 + 3 = 7 or negative -1 + 3 = 2 always positive insuff

In particular I wish to know about the first stat.

Thanks

Merging similar topics. Please refer to the solutions above and ask if anything remains unclear.
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Re: Is x a negative number? [#permalink]

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22 Sep 2012, 22:24
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9x>10X only if x is -ve it cant be greater when x is + ve
hence 1 is sufficient
but statement 2 is insufficient as x can hav the value as 0 and any + ve num
zero is neither +ve nor - ve
hence insufficient
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Re: Is x a negative number? [#permalink]

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23 Sep 2012, 04:00
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Bunuel wrote:
SOLUTION

Is x a negative number?

(1) 9x > 10x --> rearrange: $$0>10x-9x$$ --> $$0>x.$$ Sufficient.
(2) x + 3 is positive --> $$x+3>0$$ --> $$x>-3$$. Not sufficient.

Hi Bunuel.

What is unclear for me is not the probelm by itself (I picked the right answer but the first statement

1) 0 > of something then X must be negative. The answer is definitevely YES.

Instead, I have obtained YES too but X is definetevely positive. In this scenario is the same, the most imprtant thing is to have a definitive answer, or is wrong thinking in this way??

Thanks
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Re: Is x a negative number? [#permalink]

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24 Sep 2012, 03:04
carcass wrote:
Bunuel wrote:
SOLUTION

Is x a negative number?

(1) 9x > 10x --> rearrange: $$0>10x-9x$$ --> $$0>x.$$ Sufficient.
(2) x + 3 is positive --> $$x+3>0$$ --> $$x>-3$$. Not sufficient.

Hi Bunuel.

What is unclear for me is not the probelm by itself (I picked the right answer but the first statement

1) 0 > of something then X must be negative. The answer is definitevely YES.

Instead, I have obtained YES too but X is definetevely positive. In this scenario is the same, the most imprtant thing is to have a definitive answer, or is wrong thinking in this way??

Thanks

Well, from (1) we have that x<0, so x is negative not positive.

As for your question: in a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

Hope it's clear.
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Re: Is x a negative number? [#permalink]

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10 Jan 2014, 06:57
Bunuel wrote:
Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

Practice Questions
Question: 13
Page: 276
Difficulty: 550

1) tells us that 0 > 10x - 9x ---> 0 > x , so 1 is sufficient
2) x could be 1 or -1, for instance.. So insufficient..

We go with A
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Re: Is x a negative number? [#permalink]

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27 Feb 2015, 22:24
Hi....in this why cant the value of x lie between 0 or 1? like a fraction 1/3?

Bunuel wrote:
Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

Practice Questions
Question: 13
Page: 276
Difficulty: 550
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Re: Is x a negative number? [#permalink]

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27 Feb 2015, 22:41
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Hi mandakini,

Fact 1 tells us that 9X > 10X. That is a specific "restriction" that eliminates certain possible values of X.

ANY POSITIVE value for X (even a positive fraction), won't "fit" with that inequality. Neither will the value 0.

IF....X = 1/3
9(1/3) = 3
10(1/3) = 3.3333
3 is NOT > than 3.3333, so X CANNOT be 1/3.

9(0) is NOT > than 10(0), so X CANNOT be 0.

You can also do algebra to simplify the inequality....

9X > 10X
-9X -9X
0 > X

In either approach, you can prove that X CANNOT be positive and CANNOT be 0. Negative values are all that are left, so the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Intern Joined: 10 Sep 2015 Posts: 18 Followers: 0 Kudos [?]: 1 [0], given: 19 Re: Is x a negative number? [#permalink] ### Show Tags 11 Sep 2015, 01:47 statement 1) 9x > 10x: only true if X is negative (2) x + 3 is positive. x can be from -2 to +infinity , insufficient hence A EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8287 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 380 Kudos [?]: 2459 [0], given: 163 Re: Is x a negative number? [#permalink] ### Show Tags 24 Sep 2015, 08:58 HI mrslee, With 9X > 10X... If you use X = 2/90, then you will end up with.... 9(2/90) > 10(2/90) 2/10 > 2/9 1/5 > 2/9 .2 > .222222 This is NOT true, so X CANNOT be 2/90. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: Is x a negative number? [#permalink]

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30 Jul 2016, 07:32
Bunuel wrote:
Is x a negative number?

(1) 9x > 10x
(2) x + 3 is positive.

Solution:

We need to determine whether x is a negative number.

Statement One Alone:

9x > 10x

We can subtract 9x from both sides of the inequality:

9x – 9x > 10x – 9x

0 > x

Since 0 is greater than x, x is less than 0. In other words, x must be negative.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C and E.

Statement Two Alone:

x + 3 is positive.

From statement two we see that x itself could be either positive or negative. Let’s use a few convenient values to illustrate.

If x is positive

Let x = 1:

1 + 3 = 4, which is positive.

If x is negative

Let x = -1:

-1 + 3 = 2, which is also positive.

Statement two alone is not sufficient to answer the question.

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Re: Is x a negative number?   [#permalink] 30 Jul 2016, 07:32
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