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If x = -|w|, which of the following must be true

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If x = -|w|, which of the following must be true [#permalink]

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New post 22 May 2016, 21:21
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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. \(x^3 = w^3\)
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 22 May 2016, 22:55
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nalinnair wrote:
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. \(x^3 = w^3\)


Given, \(x = –|w|\)
On squaring both the sides, we get
\(x^2 = (-1)^2*|w|^2\)
\(x^2 = w^2\)

Correct Option: D
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 23 May 2016, 10:08
|w| = w when w>0 OR |w| = -(w) when w<0

According to question, there are two possible cases

x = (w) or x = (-w). These two options can be eliminated as the question asks "Which of the following MUST be true?". IN this case, one is not, when the other is.

The only other option that is for sure in all cases imaginable is when both x and w are same in magnitude as well as quantity. Possible only in Option D
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Re: OG question Absolute Value [#permalink]

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New post 30 Jun 2016, 05:13
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DevS93 wrote:
6. (Book Question: 90)

If x = –|w|, which of the following must be true?

A. x = –w
B. x = w
C. x2 = w
D. x^2 = w^2
E. x3 = w3

I picked A.

because if x= –|w|,
then x +|w|=0

That means that since |w| is always positive, X must always be negative and equal to -w for the above condition to be true i.e. ( -w+|w| =0)


Given x = –|w|.

Arrange the equation and plug the values.

Absolute value properties:

When x≤0 then |x|=−x, or more generally when some expression≤0 then |some expression|=−(some expression). For example: |−5|=5=−(−5)

When x≥0 then |x|=x, or more generally when some expression≥0 then |some expression|=some expression. For example: |5|=5|5|=5


Then x + |w| = 0 is the question. Here we are not sure whether w has to be postive or negative. Follow the above property.

x or w has to be negative ( for ex x = 2 and w = -2 then we get 0 )

1. x= - w.

=> x + w = 0. if w ≤ 0 ; then w = -ve ; then we get 0 total.
if w > 0 ; then w = +ve ; then we get some total.

Not true. Two different answers.

2. x = w.

Same as the above explanation, depending upon w as +ve or -ve value we get 0 or some total.

3. \(x^2\) = w. Same as above explanation.

4. \(x^2\) = \(w^2\) .

Then \(x^2\) - \(w^2\) if the result has to be 0 then consider w = +ve or -ve , in both the cases we get 0 as the result. ( ex: x = 2 or w = +2/-2) .

5. \(x^3\) - \(w^3\) ; when w = +ve we get 0 as the result or when w = -ve we some total. For ex: ( \(2^3\) - \((-2)^3\) = 16 ).

For the 5th option I think it has to be x power cube and w power cube.
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 30 Jun 2016, 09:00
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x and w must be the same distance from zero. Therefore raising each to the same power will result in values that are also the same distance from zero.

And if the power they are raised to is EVEN, the result will be the same distance from zero and will be NON-NEGATIVE (if they were raised to the same odd value, the original values would keep their signs, so there would be a possibility that one would end up pos and one would end up neg)

Therefore, D MUST be true, because x any y (which have the same magnitude) are raised to the same even value.
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 30 Jun 2016, 09:05
Answer is D:

Find the given statement , no matter what sign W is , x is negative. so only D satisfies the equality
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If x = -|w|, which of the following must be true [#permalink]

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New post 09 Nov 2016, 10:48
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Corrrect answer D because

\(x^2 = ( - |w|)^ 2\)

DO NOT FORGET THAT by definition |w| = \((\sqrt{w})^2\) therefore

thus x^2 = \((-1)^2\) * \([ (\sqrt{w})^2 ] ^2\) = \(w^2\)
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 01 Jan 2017, 05:55
Hello,

Can anyone explain why the answer is not A

As x = -|w| then, negative sign multiplied by the absolute w will always get negative number
For example, if w is -2, x= -|-2|, x= -*2, x=-2
so x always equals -w

What is wrong with this approach?
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 01 Jan 2017, 06:07
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Zoser wrote:
Hello,

Can anyone explain why the answer is not A

As x = -|w| then, negative sign multiplied by the absolute w will always get negative number
For example, if w is -2, x= -|-2|, x= -*2, x=-2
so x always equals -w

What is wrong with this approach?



Remember that this is a Must be true question .
Consider , w= 2 then x is equal to -|2| = -2 .
Here x is NOT equal to w .
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If x = -|w|, which of the following must be true [#permalink]

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Zoser wrote:
Hello,

Can anyone explain why the answer is not A

As x = -|w| then, negative sign multiplied by the absolute w will always get negative number
For example, if w is -2, x= -|-2|, x= -*2, x=-2
so x always equals -w

What is wrong with this approach?



Zoser this is a tricky one because you probably forgeting the definition of the abs value in algebra terms.

So the thing that you need to remember when you solving abs questions is that |w| = \((\sqrt{w})^2\).

THEREFORE whatever is under the square root CANNOT be negative and hence has to be positive. This effectively means that if w = -1 then you will have
\((\sqrt{-1})^2\) which is not valid.
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 01 Jan 2017, 06:25
Quote:
Remember that this is a Must be true question .
Consider , w= 2 then x is equal to -|2| = -2 .
Here x is NOT equal to w .


Thanks for your reply. But even if w=2, why I cant consider the below
x= -*|2|, x=-*2, x=-2
as with w=-2, you get x=-*|-2|, x=-*2, x=-2
so x Always equals -2 and thus x must be -2

What do you think is wrong here?
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 01 Jan 2017, 06:39
Zoser wrote:
Quote:
Remember that this is a Must be true question .
Consider , w= 2 then x is equal to -|2| = -2 .
Here x is NOT equal to w .


Thanks for your reply. But even if w=2, why I cant consider the below
x= -*|2|, x=-*2, x=-2
as with w=-2, you get x=-*|-2|, x=-*2, x=-2
so x Always equals -2 and thus x must be -2

What do you think is wrong here?


As this is a must be true question ,if we can prove for one scenario where the given equation doesn't hold true then that choice can be eliminated .
For example if w=-2 , then Choice A doesn't hold true . So that choice can be eliminated .
x= -|w| => -|-2| x=-2
choice A , says x = -w , -2 (x) is not equal to -(-2) =2 .
Hope it is clear .

You can also refer Algebra approach posted for this question .
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 01 Jan 2017, 06:44
sb0541 wrote:
Zoser wrote:
Quote:
Remember that this is a Must be true question .
Consider , w= 2 then x is equal to -|2| = -2 .
Here x is NOT equal to w .


Thanks for your reply. But even if w=2, why I cant consider the below
x= -*|2|, x=-*2, x=-2
as with w=-2, you get x=-*|-2|, x=-*2, x=-2
so x Always equals -2 and thus x must be -2

What do you think is wrong here?


As this is a must be true question ,if we can prove for one scenario where the given equation doesn't hold true then that choice can be eliminated .
For example if w=-2 , then Choice A doesn't hold true . So that choice can be eliminated .
x= -|w| => -|-2| x=-2
choice A , says x = -w , -2 (x) is not equal to -(-2) =2 .
Hope it is clear .

You can also refer Algebra approach posted for this question .


Now I got it fully.

Thanks
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 15 Feb 2017, 12:01
nalinnair wrote:
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. \(x^3 = w^3\)


W |W| X X^2 X^3 w^2

0 0 0 0 0 0
-1 1 -1 1 -1 1
1 1 -1 1 1 1

So, from the above example case only X^2 = w^2 in all the three case.

Thanks
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 16 Feb 2017, 03:52
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Solve backwards( keep in mind x must be 0 or negative)
x=-2 w=-2 --> A and C are out
x=-2 w=2 ---> E and B are out
answ D
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 16 Feb 2017, 21:01
Best method for this question would be to simply plug numbers 2= -l2l ----> 2^2 = (-l2l)^2
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 20 Feb 2017, 08:28
x = -abs(w)

If w<=0 then x=w
If w >0 then x=-w

A. x=–w not always true (x=w when w<=0)
B. x=w similarly not always true
C. x^2=w means w^2=w, not always true (for instance 3^2 <> 3)
D. x^2=w^2 is equivalent to (-abs(w))^2=w^2, and the left side is exactly w^2, so D is always true
E. x^3=w^3 not always true (sign might not match). Try plugging w=1. x^3=-1 and w^3=1

So it is D
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Re: If x = -|w|, which of the following must be true [#permalink]

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New post 21 Feb 2017, 09:23
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nalinnair wrote:
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. \(x^3 = w^3\)


Since x = -|w| and -|w| is always nonpositive, we know that x must be nonpositive. However, we are unsure of the sign of w.

Thus, the only answer choice that must be true (because both results will be nonnegative) is x^2 = w^2.

Answer: D
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Re: If x = -|w|, which of the following must be true   [#permalink] 21 Feb 2017, 09:23
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