If x = -|w|, which of the following MUST be true
A. x=-w
B. x=w
C. x^2=w
D. x^2=w^2
E. x^3=w^3
Why option (a) is not the correct answer? the question clearly says x=-|w|
which means
|w|=-x
and by definition, w=-x
regards

Relevant page
<a href="https://gmatclub.com/forum/if-x-w-which-of-the-following-must-be-true-218960.html">If x = -|w|, which of the following must be true : GMAT Problem Solving (PS) </a>
What I've done so far
x=-|w|
=> |w|=-x
=> w=-x
or
w^2=x^2
i am stuck between A or D

@Mansoor: Sorry - I must have missed your question when it first came in.

With this kind of question, proceed as follows. Try some actual examples.

(i) `w` is positive

Try `w = 3.`

Which ones of A, B, C, D, E are correct?

(ii) `w` is negative

Try `w = -5`

Which ones of A, B, C, D, E are correct?

What's your conclusion?

X

@Mansoor: Sorry - I must have missed your question when it first came in.
With this kind of question, proceed as follows. Try some actual examples.
(i) `w` is positive
Try `w = 3.`
Which ones of A, B, C, D, E are correct?
(ii) `w` is negative
Try `w = -5`
Which ones of A, B, C, D, E are correct?
What's your conclusion?

So the answer can't be Choice A (since it doesn't allow for my second answer), nor Choice B (which doesn't allow for my first answer).

Choice C will only work is `x = w = 0`.

Choice D looks most promising.

If `w=-x`, square both sides gives `x^2 = x^2.`

If `w=x`, square both sides also gives `x^2 = x^2.`

Choice E is not OK because cube root of a negative is negative.

Using the example numbers Murray gave:

If `w=3`, then `x = -|3| = -3.`

A. `x=-w=-3` works
B. `x=w=3` is not true
C. `x^2=9` does not equal `w=3`
D. `x^2=9=w^2` is true
E. `x^3=-27` does not equal `w^3=27`

If `w=-5`, then `x = -|-5| = -5.`

A. `x=-5` does not equal `-w=-(-5)=5`
B. `x=-5` does equal `w=-5`
C. `x^2=25` does not equal `w=-5`
D. `x^2=25=w^2` is true
E. `x^3=-125` does equal `w^3=-125`

The only option that works for negative, zero or positive `w` is Choice D.

X

I agree that if `x = -|w|,`
`|w|=-x,` but not
"and by definition, w=-x"
When we have say `|a| = 5`, then "by definition",
`a = 5` or `a = -5.`
So in this case, it will be:
`w=-x` or `w=-(-x)=x`
So the answer can't be Choice A (since it doesn't allow for my second answer), nor Choice B (which doesn't allow for my first answer).
Choice C will only work is `x = w = 0`.
Choice D looks most promising.
If `w=-x`, square both sides gives `x^2 = x^2.`
If `w=x`, square both sides also gives `x^2 = x^2.`
Choice E is not OK because cube root of a negative is negative.
Using the example numbers Murray gave:
If `w=3`, then `x = -|3| = -3.`
A. `x=-w=-3` works
B. `x=w=3` is not true
C. `x^2=9` does not equal `w=3`
D. `x^2=9=w^2` is true
E. `x^3=-27` does not equal `w^3=27`
If `w=-5`, then `x = -|-5| = -5.`
A. `x=-5` does not equal `-w=-(-5)=5`
B. `x=-5` does equal `w=-5`
C. `x^2=25` does not equal `w=-5`
D. `x^2=25=w^2` is true
E. `x^3=-125` does equal `w^3=-125`
The only option that works for negative, zero or positive `w` is Choice D.