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

Question

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

Bunuel · Accepted Answer

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.

gurpreetsingh · Answer

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|

TheSituation · Answer

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?

walker · Answer

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

https://gmatclub.com/static/posted_from.png    Posted from    GMAT ToolKit

theYogi · Answer

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

So answer is   B

GMATMadeeasy · Answer

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.

TheSituation · Answer

...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.

jeeteshsingh · Answer

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....

BarneyStinson · Answer

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.

TheSituation · Answer

God this guy is good...

GMATMadeeasy · Answer

Answer copied from NOVA guide

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  . 
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).

natsche · Answer

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

thank you in advanced!

Bunuel · Answer

Merging topics. Please refer to the solutions above.

WholeLottaLove · Answer

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)

aeglorre · Answer

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)

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

Bunuel · Answer

0=-0.

x=-|x|  means that  x\leq{0} . If  x=0 , then we'd have  0=-|0|  -->  0=-0 .

kanusha · Answer

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

AbdurRakib · Answer

Only D(I & II) fits the condition if I pick any number of X.So,the  Correct Answer is D

mathivanan · Answer

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

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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