GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 May 2020, 07:56 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x=-|x|, then which one of the following statements

Author Message
TAGS:

### Hide Tags

Manager  Joined: 25 Dec 2009
Posts: 67
If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

6
10 00:00

Difficulty:   5% (low)

Question Stats: 74% (00:42) correct 26% (00:56) wrong based on 690 sessions

### HideShow timer Statistics

If x = - |x| , then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

Originally posted by GMATMadeeasy on 24 Feb 2010, 05:21.
Last edited by Bunuel on 05 Jul 2013, 01:51, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 64243
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

6
1
If x = ± |x| , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0

(A) None (B) I only (C) III only (D) I and II (E) II and III

I've never seen real GMAT question using the sign "±". Moreover as the OA believed to be D, then the question should be:

If x=-|x|, then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

In this case, D would be correct answer as x can be zero as well as any negative number.
_________________
##### General Discussion
SVP  Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2449
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

1
B- I only

this equality will hold true only when x =0
as if you take x>0 then x cannot be - |x|
and if you take x<0 then x cannot be |x|
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
Manager  Joined: 09 Dec 2009
Posts: 111
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

gurpreetsingh wrote:
B- I only

this equality will hold true only when x =0
as if you take x>0 then x cannot be - |x|
and if you take x<0 then x cannot be |x|

Yes, but with statement 1 if x=0, the absolute value of x will be 0 .. and that can't have a negative or positive value.
I agree statements II and III are impossible but am weary of statment I.

I would vote for A none of the above. Am I overthinking this problem?

Whats the OA?
CEO  B
Joined: 17 Nov 2007
Posts: 2926
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

What does x =+-|x| exatly mean? Not sure that it is GMAT question

_________________
HOT! GMAT Club Forum 2020 | GMAT ToolKit 2 (iOS) - The OFFICIAL GMAT CLUB PREP APPs, must-have apps especially if you aim at 700+
Intern  Joined: 27 Jan 2010
Posts: 28
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

1
Only 0(zero) will satisfy the condition because you cannot have +0 or -0.

Manager  Joined: 25 Dec 2009
Posts: 67
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

For me the answer is 0, I agree with all of you.

This question is from Nova guide, I will post explanation as given in the nova tomorrow.
The OA is 0 and x < 0 though but I do not agree with it.That's why wanted to know the opinion of others.
Manager  Joined: 09 Dec 2009
Posts: 111
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

For me the answer is 0, I agree with all of you.

...but we have competing opinions, and 0 isn't an answer choice. Post the OA when you get a chance.

I'm with walker, GMAT problems can be hard but this question seems illogical and atypical of what you might see on the real deal.
Manager  Joined: 22 Dec 2009
Posts: 225
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

If x = ± |x| , then which one of the following statements could be true?
I.

x = 0
II.

x < 0
III.

x > 0
(A) None (B) I only (C) III only (D) I and II (E) II and III

Not too sure... but if the question was y = ± |x| - x, I would have gone with D as Answer.

If you plot y = ± |x| - x , we get y <= 0....
Senior Manager  Joined: 21 Jul 2009
Posts: 262
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

One way of solving modulus questions, square on both sides.

x = +- |x|, implies x^2 = x^2, you can't cancel both sides because you can't divide with 0.
So, x^2 - x^2 = 0, this is of the form a^2 - b^2.
so, (x - x)(x + x) = 0.
2x(x - x)=0.

X can be 0 or x can be any number in the whole wide universe. There's no option specifying all three statements together, so go with the safer bet, since we have definitely proved one possibility that x can be 0. So B should be the answer.
Manager  Joined: 09 Dec 2009
Posts: 111
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

BarneyStinson wrote:
If , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

In this case, D would be correct answer as x can be zero as well as any negative number.

God this guy is good...
Manager  Joined: 25 Dec 2009
Posts: 67
Re: Inequality - Interesting one (Pay attention)  [#permalink]

### Show Tags

Statement I could be true because ± 0 = −(+0) = −(0) = 0 .
Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal.
Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:
Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.

Hence, x cannot be positive. The answer is (D).
Intern  Joined: 22 Feb 2010
Posts: 2
If x= +or- │x│which of the statments could be true?  [#permalink]

### Show Tags

hey guys, I got this Problem even with the solution but I do not get it at all, can u guys help?

If x= +or- │x│which of the statments could be true? (better seen in the attachment)

I x = 0
II x < 0
III x > 0

Attachments Bildschirmfoto 2013-07-03 um 18.33.15.png [ 29.37 KiB | Viewed 8002 times ]

Math Expert V
Joined: 02 Sep 2009
Posts: 64243
Re: If x= +or- │x│which of the statments could be true?  [#permalink]

### Show Tags

natsche wrote:
hey guys, I got this Problem even with the solution but I do not get it at all, can u guys help?

If x= +or- │x│which of the statments could be true? (better seen in the attachment)

I x = 0
II x < 0
III x > 0

Merging topics. Please refer to the solutions above.
_________________
Senior Manager  Joined: 13 May 2013
Posts: 389
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

If x = - |x| , then which one of the following statements could be true?

x = - |x|
0 = - |0|
0 = - 0
0 = 0
VALID

x = - |x|
-1 = - |-1|
-1 = -(1)
-1=-1
VALID

x = - |x|
1 = - |1|
1 = -(1)
1 = -1
INVALID

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

(D)
Manager  Joined: 12 Jan 2013
Posts: 137
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

I understand clearly that x = - !x! would mean x is negative since an absolute value always is positive.. But why is 0 even a valid answer? x = -0? What does -0 even mean? Zero is zero regardless, there is no "negative" zero. Now, in this case I picked the right answer since I couldn't pick II alone. But HAD I been able to do so, I cannot say I would have picked "I and II".

So if someone has a good, intuitive explanation, feel free to explain (preferbly Bunuel)
Math Expert V
Joined: 02 Sep 2009
Posts: 64243
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

1
aeglorre wrote:
I understand clearly that x = - !x! would mean x is negative since an absolute value always is positive.. But why is 0 even a valid answer? x = -0? What does -0 even mean? Zero is zero regardless, there is no "negative" zero. Now, in this case I picked the right answer since I couldn't pick II alone. But HAD I been able to do so, I cannot say I would have picked "I and II".

So if someone has a good, intuitive explanation, feel free to explain (preferbly Bunuel)

0=-0.

$$x=-|x|$$ means that $$x\leq{0}$$. If $$x=0$$, then we'd have $$0=-|0|$$ --> $$0=-0$$.
_________________
Manager  S
Joined: 25 Mar 2013
Posts: 217
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

1
ans D equation is x = - /x/
1, x =0
0 = - /0/ ,
0 = -0
0 = 0

2, x< 0 = - numbers
-1 = - / -1/
-1 = - 1

3, x > 0
5 = - /5/
5 = - 5 is not equal
Director  B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 516
GPA: 2.81
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

Only D(I & II) fits the condition if I pick any number of X.So,the Correct Answer is D
Manager  Joined: 10 Jun 2015
Posts: 110
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

If x = - |x| , then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

x is not positive; C and E are eliminated
when x is negative it is true.
So, II has to be in the answer.
You have only one option, that is, D Re: If x=-|x|, then which one of the following statements   [#permalink] 23 Aug 2015, 04:16

Go to page    1   2    Next  [ 31 posts ]

# If x=-|x|, then which one of the following statements  