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

 It is currently 22 May 2019, 02:13

### 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

# If x<0, then root(-x*|x|) is:

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 276
Re: If x<0, then root(-x*|x|) is:  [#permalink]

### Show Tags

06 Aug 2017, 07:35
parker wrote:
Nice work whiplash! I agree 100% that plugging in numbers is often the most efficient (and least susceptible to careless errors) method on this kind of problem. One addt'l tip--it can be a timesaver to avoid 0, 1 (& -1), and numbers in the answer choices on a problem solving question (as opposed to on data sufficiency question, when you actually WANT to find the exceptions to the rule) because those are special numbers with special properties (the result of squaring 0 and 1 is the same as the number you put in, which is unusual) . Notice that the result of plugging in -1 is 1, which is choice A but it is *also* choice C. If you start with a small prime number like 2 or 3 (or in this case 2's negative relative, -2) you can sometimes save yourself a second pass.

hi

√- x^2

if the square root over and the square get cancelled out, we are left with "-x"

Manager
Joined: 24 Jun 2017
Posts: 121
If x<0, then root(-x*|x|) is:  [#permalink]

### Show Tags

06 Aug 2017, 09:02
I am not sure if my solution makes sense, but that's how I get it into my mind(negative values under the square root)

\sqrt{−x∗|x|} = -(x*|x|)^1/2= -(x^2)^1/2 = - (x) = -x
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: If x<0, then root(-x*|x|) is:  [#permalink]

### Show Tags

22 Nov 2017, 13:30
nss123 wrote:
If x<0, then $$\sqrt{-x|x|}$$ is:

A. -x
B. -1
C. 1
D. x
E. $$\sqrt{x}$$

Since x is less than zero, |x| = -x.

Thus, we have:

√(-x|x|) = √(-x(-x)) = √(x^2)

Recall that √(x^2) = |x|; however, |x| = -x, since x is less than zero, so we have:

√(-x|x|) = √(-x(-x)) = √(x^2) = |x| = -x

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

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.

Senior SC Moderator
Joined: 22 May 2016
Posts: 2747
If x<0, then root(-x*|x|) is:  [#permalink]

### Show Tags

22 Nov 2017, 18:09
1
cbh wrote:
I am not sure if my solution makes sense, but that's how I get it into my mind(negative values under the square root)

\sqrt{−x∗|x|} = -(x*|x|)^1/2= -(x^2)^1/2 = - (x) = -x

cbh and gmatcracker2018, read, above, from this post down tothis post. Your issue is discussed.

And to both . . .If you want comments, I think you will have better luck if you format properly. Speaking of, I think you both mean:

$$\sqrt{−x∗|x|}=$$

$$\sqrt{-(x*|x|)} =$$

$$\sqrt{-(x^2)} =$$

$$- (x) = -x$$

When it is written like that, does it look strange?
Any number squared is positive or 0 (non-negative). Full stop.

When was the last time you took the square root of a negative number? The people above articulate additional issues more eloquently than I can.

I learned to plug in an actual negative number in these kinds of questions. I recommend it.

santro789 , the negative of a negative is a positive. Change the parentheses, to emphasize "opposite of":
(-)-3 = 3

If $$x<0$$, then $$|x|= -x$$. This concept can be counterintuitive.

I listed a few ways of thinking about it here.

Then Bunuel added even more ways to think about it just after that, here.

Hope that helps.
_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions go to SC Butler, here.

Non-Human User
Joined: 09 Sep 2013
Posts: 10981
Re: If x<0, then root(-x*|x|) is:  [#permalink]

### Show Tags

24 Nov 2018, 10:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If x<0, then root(-x*|x|) is:   [#permalink] 24 Nov 2018, 10:08

Go to page   Previous    1   2   [ 25 posts ]

Display posts from previous: Sort by