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Absolute value [Solved!]

My question

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

If x = -|w|, which of the following must be true : GMAT Problem Solving (PS)

What I've done so far

x=-|w|
=> |w|=-x
=> w=-x

or

w^2=x^2

i am stuck between A or D

X

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

Re: Absolute value

i also think te correct anwser sould be A-(x=-w)

X

i also think te correct anwser sould be A-(x=-w)

Re: Absolute value

@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?

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?

Re: Absolute value

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.

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.

Re: Absolute value

Good, thorough answer, Opera. Well done!

X

Good, thorough answer, Opera. Well done!