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

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

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23 Aug 2015, 04:16
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

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

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25 Jun 2017, 23:07
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Re: If x=-|x|, then which one of the following statements [#permalink]

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26 Jun 2017, 00:58
If x = - |x| , then which one of the following statements could be true?

$$x = - |x|$$

The above equation means:

1. x can be ZERO
2. x can be any negative number

Now lets go the options.

I. x = 0 ===> Holds true based on point (1) above =====> TRUE
II. x < 0 ===> Holds true based on point (2) above =====> TRUE
III. x > 0 ===> Not True as value should either be ZERO or Less than ZERO =====> FALSE

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

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13 Jul 2017, 07:54
Bunuel wrote:
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.

Thanx Bunuel very well explained just tell me if it is x=|x| then what the answer should be
TIA

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

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13 Jul 2017, 09:07
Bunuel wrote:
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.

Thanx Bunuel very well explained just tell me if it is x=|x| then what the answer should be
TIA

x = |x| means that x >= 0. So, I and III could be true.
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Re: If x=-|x|, then which one of the following statements [#permalink]

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13 Jul 2017, 23:36
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 = -|x|
Now |x|>=0
-|x|<=0
so x<=0

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

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16 Jul 2017, 16:38
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

Since x = -|x|, x must be negative or zero. Thus, I and II are true.

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

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13 Sep 2017, 05:24

1) If x<0, then x=-|x|=0

2) If x<0 i.e. negative, then x= -(-x) [Here -x is positive because x is less than 0. -ve*-ve= +ve]
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Help me make my explanation better by providing a logical feedback.

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Last edited by Shiv2016 on 01 Oct 2017, 22:10, edited 1 time in total.

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

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01 Oct 2017, 08:34
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[/quote]

x=-|x|
I. 0=-|0| =0 YES.
II. -1=-|1|
-1=-1 YES.
III. 2=-|2|
2 = -2 NO.
HENCE ANS IS D.

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

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01 Oct 2017, 11:10
1
KUDOS
Shiv2016 wrote:
It would be great if for once someone clear this doubt. I am not able to move to something new in absolute values because of this same doubt. Every time I try to clear it, it becomes worse.

1) If x>=0
then |x|= x

2) If x<0
then |x|= -(-x)= x (in this x is negative now or positive?)

Then in this question, how is II correct?

x<0

x=-|x|

Shiv2016 , in case you are still wondering . . .

On a different question, about a week after you posted this (sorry, I didn't see your post until just now), someone asked exactly what I think you are asking.

I answered, because, as I wrote, that rule can feel very counterintuitive to me.

I wrote down a few ways to think about what you asked and I highlighted, above. Bunuel then added another important way to think about it. So . . . three posts that address what I think you are asking.

Please, take a look at Bunuel 's post starting HERE

Then go to my post (same thread) here: WAYS TO THINK ABOUT x = -|x|

Finally, right below mine, Bunuel here: FINISHES THE DISCUSSION

All of them come from this question

I hope they help.

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

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01 Oct 2017, 22:22
genxer123 wrote:
Shiv2016 wrote:
It would be great if for once someone clear this doubt. I am not able to move to something new in absolute values because of this same doubt. Every time I try to clear it, it becomes worse.

1) If x>=0
then |x|= x

2) If x<0
then |x|= -(-x)= x (in this x is negative now or positive?)

Then in this question, how is II correct?

x<0

x=-|x|

Shiv2016 , in case you are still wondering . . .

On a different question, about a week after you posted this (sorry, I didn't see your post until just now), someone asked exactly what I think you are asking.

I answered, because, as I wrote, that rule can feel very counterintuitive to me.

I wrote down a few ways to think about what you asked and I highlighted, above. Bunuel then added another important way to think about it. So . . . three posts that address what I think you are asking.

Please, take a look at Bunuel 's post starting HERE

Then go to my post (same thread) here: WAYS TO THINK ABOUT x = -|x|

Finally, right below mine, Bunuel here: FINISHES THE DISCUSSION

All of them come from this question

I hope they help.

Thank you so much for your reply. Your posts and Bunuel's posts are to the point and cleared all my doubts related to negative sign.
I again solved the question. I hope the reasoning makes sense now

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

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13 Oct 2017, 07:32
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 always positive. Putting a negative sign infront of a positive sign makes the value a negative. So, the value of x is negative. X CANNOT be greater than zero, because this would make x a positive, which would make - |x| a negative, which contradicts the given equation. X could be zero, because the absolute value of zero is zero, and the negative sign does not change the value of zero; therefore, 0 = - |0| holds true.

Therefore, the answer is (D) I and II

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Re: If x=-|x|, then which one of the following statements   [#permalink] 13 Oct 2017, 07:32

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