GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 05:36 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x = -|w|, which of the following must be true

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Current Student B
Status: Persevere
Joined: 09 Jan 2016
Posts: 117
Location: Hong Kong
GMAT 1: 750 Q50 V41 GPA: 3.52
If x = -|w|, which of the following must be true  [#permalink]

Show Tags

5
62 00:00

Difficulty:   15% (low)

Question Stats: 71% (00:53) correct 29% (00:51) wrong based on 1238 sessions

HideShow timer Statistics

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. $$x^3 = w^3$$
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

12
7
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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Retired Moderator G
Joined: 26 Nov 2012
Posts: 569
Re: OG question Absolute Value  [#permalink]

Show Tags

6
3
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.
General Discussion
SVP  B
Joined: 06 Nov 2014
Posts: 1873
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

5
1
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
Manager  B
Joined: 17 Jun 2015
Posts: 195
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

1
|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
_________________
Fais de ta vie un rêve et d'un rêve une réalité
Manager  B
Joined: 25 Jun 2016
Posts: 61
GMAT 1: 780 Q51 V46 Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

2
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.
Senior Manager  Joined: 23 Apr 2015
Posts: 285
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

Find the given statement , no matter what sign W is , x is negative. so only D satisfies the equality
Manager  B
Joined: 09 Aug 2016
Posts: 62
If x = -|w|, which of the following must be true  [#permalink]

Show Tags

3
2
Corrrect answer D because

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

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

thus x^2 = $$(-1)^2$$ * $$[ (\sqrt{w})^2 ] ^2$$ = $$w^2$$
Intern  B
Joined: 17 Nov 2016
Posts: 24
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

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?
Manager  S
Joined: 13 Apr 2010
Posts: 88
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

1
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 .
Manager  B
Joined: 09 Aug 2016
Posts: 62
If x = -|w|, which of the following must be true  [#permalink]

Show Tags

2
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.
Intern  B
Joined: 17 Nov 2016
Posts: 24
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

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?
Manager  S
Joined: 13 Apr 2010
Posts: 88
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

2
1
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 .
Intern  B
Joined: 17 Nov 2016
Posts: 24
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

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
Manager  S
Joined: 27 Nov 2016
Posts: 53
Location: India
Concentration: General Management, International Business
GPA: 2.71
WE: Consulting (Consulting)
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

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
Intern  B
Joined: 23 Jan 2017
Posts: 21
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

1
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
Intern  B
Joined: 24 Sep 2016
Posts: 33
Location: United States (CT)
Concentration: Finance, International Business
GPA: 3.81
WE: Analyst (Venture Capital)
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

1
Best method for this question would be to simply plug numbers 2= -l2l ----> 2^2 = (-l2l)^2
Current Student B
Joined: 28 Jan 2017
Posts: 31
Location: Chile
Concentration: General Management, Strategy
GMAT 1: 710 Q50 V35 GPA: 3.2
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

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
Manager  B
Joined: 10 Sep 2014
Posts: 77
GPA: 3.5
WE: Project Management (Manufacturing)
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

ScottTargetTestPrep, JeffTargetTestPrep. Please explain how have you eliminated other options. Thanks.
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: If x = -|w|, which of the following must be true  [#permalink]

Show Tags

1
ScottTargetTestPrep, JeffTargetTestPrep. Please explain how have you eliminated other options. Thanks.

We cannot be sure of answer choice A, because -w is negative if w is positive; but is positive if w is negative.

We cannot be sure of answer choices B and C, because, as explained in the previous response, we have no information about the sign of w.

Finally, we cannot be sure of answer choice E, because w^3 is negative if w is negative and is positive if w is positive.

For answer choice D, on the other hand, no matter the sign of w (and x), w^2 (and x^2) will always be positive. Needless to say that it also holds for the case where x = w = 0. That's why D is the correct option.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If x = -|w|, which of the following must be true   [#permalink] 23 Apr 2018, 17:47

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  