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

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Manager
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If x=-|x|, then which one of the following statements [#permalink]

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24 Feb 2010, 06:21
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Question Stats:

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Jul 2013, 02:51, edited 1 time in total.
Edited the question.
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 06:37
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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|
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 07:56
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?
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 09:30
What does x =+-|x| exatly mean? Not sure that it is GMAT question

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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 09:39
Only 0(zero) will satisfy the condition because you cannot have +0 or -0.

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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 13:48
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.
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 14:06
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.
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 14:11
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....
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 16:29
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.
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 17:26
3
KUDOS
Expert's post
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.
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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24 Feb 2010, 19:07
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...
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Re: Inequality - Interesting one (Pay attention) [#permalink]

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25 Feb 2010, 03:44

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).
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If x= +or- │x│which of the statments could be true? [#permalink]

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05 Jul 2013, 02:27
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 4346 times ]

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Re: If x= +or- │x│which of the statments could be true? [#permalink]

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05 Jul 2013, 02:53
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.
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Re: If x=-|x|, then which one of the following statements [#permalink]

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09 Jul 2013, 16:02
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)
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Re: If x=-|x|, then which one of the following statements [#permalink]

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16 Dec 2013, 11:36
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)
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Re: If x=-|x|, then which one of the following statements [#permalink]

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17 Dec 2013, 01:24
1
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Expert's post
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 $$0=-|0|$$ --> $$0=-0$$.
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Re: If x=-|x|, then which one of the following statements [#permalink]

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09 Jan 2014, 05:49
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
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Re: If x=-|x|, then which one of the following statements [#permalink]

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Re: If x=-|x|, then which one of the following statements [#permalink]

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23 Aug 2015, 02:49
Only D(I & II) fits the condition if I pick any number of X.So,the Correct Answer is D
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Re: If x=-|x|, then which one of the following statements   [#permalink] 23 Aug 2015, 02:49

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