Last visit was: 23 Jul 2024, 03:47 It is currently 23 Jul 2024, 03:47
Toolkit
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 < 0, then (-x*|x|)^(1/2) is:

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 08 Jul 2009
Posts: 5
Own Kudos [?]: 674 [424]
Given Kudos: 0
Math Expert
Joined: 02 Sep 2009
Posts: 94572
Own Kudos [?]: 643188 [182]
Given Kudos: 86728
Math Expert
Joined: 02 Sep 2009
Posts: 94572
Own Kudos [?]: 643188 [49]
Given Kudos: 86728
Math Expert
Joined: 02 Sep 2009
Posts: 94572
Own Kudos [?]: 643188 [28]
Given Kudos: 86728
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
12
Kudos
16
Bookmarks
LM wrote:
If x<0, then $$\sqrt{-x|x|}$$ is:

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

Given: $$x<0$$ Question: $$y=\sqrt{-x*|x|}$$?

Remember: $$\sqrt{x^2}=|x|$$.

As $$x<0$$, then $$|x|=-x$$ --> $$\sqrt{-x*|x|}=\sqrt{(-x)*(-x)}=\sqrt{x^2}=|x|=-x$$.

General Discussion
Intern
Joined: 02 Aug 2009
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 1
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
It is actually A.

suppose x is -2 then you have sqrt(2*2) = sqrt(4) = 2 = -x

note that x < 0 as otherwise the function does not exist.
Intern
Joined: 08 Apr 2010
Posts: 16
Own Kudos [?]: 1 [0]
Given Kudos: 0
GPA: 3.7
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
Hey I'm sorry guys, this still does not make sense. Everyone's argument here is that the square root of 4 is 2, that is just not true! The square root of 4 is 2 OR -2. We're just accustomed to thinking that 2 is the "standard root" but -2 is just as correct. Therefore the square of -2 (which is x in this case) is 4, and the squareroot of that is 2 OR -2! So it could be x or -x.

This seems wrong and no one's explanation makes any sense.
Math Expert
Joined: 02 Sep 2009
Posts: 94572
Own Kudos [?]: 643188 [6]
Given Kudos: 86728
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
1
Kudos
5
Bookmarks
shammokando wrote:
Hey I'm sorry guys, this still does not make sense. Everyone's argument here is that the square root of 4 is 2, that is just not true! The square root of 4 is 2 OR -2. We're just accustomed to thinking that 2 is the "standard root" but -2 is just as correct. Therefore the square of -2 (which is x in this case) is 4, and the squareroot of that is 2 OR -2! So it could be x or -x.

This seems wrong and no one's explanation makes any sense.

Red part is not correct.

THEORY:

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

Solution for the original question:

Given: $$x<0$$ Question: $$\sqrt{-x*|x|}=?$$.

Remember: $$\sqrt{x^2}=|x|$$.

As $$x<0$$, then $$|x|=-x$$ --> $$\sqrt{-x*|x|}=\sqrt{(-x)*(-x)}=\sqrt{x^2}=|x|=-x$$.

Hope it helps.
SVP
Joined: 09 Jun 2010
Status:Three Down.
Posts: 1763
Own Kudos [?]: 3487 [19]
Given Kudos: 210
Concentration: General Management, Nonprofit
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
7
Kudos
12
Bookmarks
The easiest way for you to solve this problem would be to plug in a number and see what happens.

Let's say $$x = -1$$

$$\sqrt{-x|x|}=\sqrt{-(-1)|-1|}=\sqrt{(1)(1)}=1 = -(-1)$$

Math Expert
Joined: 02 Sep 2009
Posts: 94572
Own Kudos [?]: 643188 [4]
Given Kudos: 86728
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
3
Kudos
1
Bookmarks
mbafall2011 wrote:
udaymathapati wrote:
If x < 0, then \sqrt{-x} •|x|) is
A. -x
B. -1
C. 1
D. x
E. \sqrt{x}

what is the source of this question. I havent seen any gmat question testing imaginary numbers

GMAT is dealing only with Real Numbers: Integers, Fractions and Irrational Numbers. So you won't see any question involving imaginary numbers.

This question also does not involve imaginary numbers as expression under the square root is non-negative (actually it's positive): we have $$\sqrt{-x*|x|}$$ --> as $$x<0$$ then $$-x=positive$$ and $$|x|=positive$$, so $$\sqrt{-x*|x|}=\sqrt{positive*positive}=\sqrt{positive}$$.

Hope it's clear.
Manager
Joined: 20 Jul 2010
Posts: 136
Own Kudos [?]: 249 [1]
Given Kudos: 9
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
1
Kudos
hailtothethief23 wrote:
It is actually A.

suppose x is -2 then you have sqrt(2*2) = sqrt(4) = 2 = -x

note that x < 0 as otherwise the function does not exist.

$$\sqrt{4}$$ = + or - 2. So answer should be + or - x. I don't get how can OA be -x
Math Expert
Joined: 02 Sep 2009
Posts: 94572
Own Kudos [?]: 643188 [3]
Given Kudos: 86728
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
2
Kudos
1
Bookmarks
shrive555 wrote:
Bunel: i've already seen all the explanation just one more question.

as If $$x<0$$, then $$\sqrt{-x*|x|}$$
Ans is -x
is Answer of the question depends on the condition x<0 or it depends on the sqrt (even root)

lets keep the condition same i.e x<0 and take odd root say cube root. i.e
$$\sqrt[3]{-x*|x}|$$ . what would be the answer, would it be x then ?

Thanks

About the odd roots: odd roots will have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.

So, if given that $$x<0$$ then $$|x|=-x$$ and $$-x*|x|=(-x)*(-x)=positive*positive=x^2$$, thus odd root from positive $$x^2$$ will be positive.

But $$\sqrt[3]{-x*|x}|$$ will equal neither to x nor to -x: $$\sqrt[3]{-x*|x|}=\sqrt[3]{x^2}=x^{\frac{2}{3}}$$, for example if $$x=-8<0$$ then $$\sqrt[3]{-x*|x|}=\sqrt[3]{x^2}=\sqrt[3]{64}=4$$.

If it were $$x<0$$ and $$\sqrt[3]{-x^2*|x}|=?$$, then $$\sqrt[3]{-x^2*|x}|=\sqrt[3]{-x^2*(-x)}=\sqrt[3]{x^3}=x<0$$. Or substitute the value let $$x=-5<0$$ --> $$\sqrt[3]{-x^2*|x}|=\sqrt[3]{-25*5}=\sqrt[3]{-125}=-5=x<0$$.

Now, back to the original question:

If x<0, then $$\sqrt{-x*|x|}$$ equals:
A. $$-x$$
B. $$-1$$
C. $$1$$
D. $$x$$
E. $$\sqrt{x}$$

As square root function cannot give negative result, then options -1 (B) and x (D) can not be the answers as they are negative. Also $$\sqrt{x}$$ (E) can not be the answer as even root from negative number is undefined for GMAT. 1 (C) also can not be the answer as for different values of x the answer will be different, so it can not be some specific value. So we are left with A.

Now, if it were x>0 instead of x<0 then the question would be flawed as in this case the expression under the even root would be negative (-x*|x|=negative*positive=negative).

Hope it's clear.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9461 [4]
Given Kudos: 91
Q51  V47
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
1
Kudos
2
Bookmarks
If x < 0, then |x| = -x. So by substituting, we have:

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

Now it's important to understand that √(x^2) is not necessarily equal to x. That is only true when x is positive (or zero). You can see, if you plug in any negative number here, say x = -3, that √(x^2) = √9 = 3, which is not equal to x because the sign changed; it's actually equal to -x. In general, √(x^2) is always equal to |x|. Since x < 0 in this question, √(x^2) = |x| = -x.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11793 [3]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
3
Kudos
Hi jchae90,

This question is perfect for TESTing VALUES.

We're told that X < 0, so let's TEST X = -2

We're asked to determine the value of..... √((-x)·|x|)

√((-(-2))·|-2|) = √(2)·|2|) = √4 = 2

So we're looking for an answer that equals 2 when X = -2

Answer A: –X = -(-2) = 2 This IS a match
Answer B: -1 NOT a match
Answer C: 1 NOT a match
Answer D: X = -2 NOT a match
Answer E: √X = √2 NOT a match

GMAT assassins aren't born, they're made,
Rich
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6616 [2]
Given Kudos: 1646
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
2
Bookmarks
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

GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4915
Own Kudos [?]: 7814 [0]
Given Kudos: 221
Location: India
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
Top Contributor
Let's take x= -5
=>So √ (-x |x|) = √ (-(-5)|-5|)
=> √ (5*5) = √ (25)
= 5
= -(-5)
= -x
(option a)
Senior Manager
Joined: 16 Nov 2021
Posts: 472
Own Kudos [?]: 28 [0]
Given Kudos: 5901
Location: United Kingdom
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
Hi brunel, Shouldn't −(−5) become +5?
Math Expert
Joined: 02 Sep 2009
Posts: 94572
Own Kudos [?]: 643188 [0]
Given Kudos: 86728
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
Kimberly77 wrote:
Hi brunel, Shouldn't −(−5) become +5?

Yes, -(-5) = 5, which is -x (x = -5).
Intern
Joined: 13 Jun 2022
Posts: 8
Own Kudos [?]: 3 [0]
Given Kudos: 6
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
Hi,
Isn't the output of mod supposed to be positive?
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1804
Own Kudos [?]: 2146 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
Top Contributor
Given that x < 0 and we need to find the value of $$\sqrt{-x|x|}$$

As x < 0, so assume x = -k where k is a positive number

=> $$\sqrt{-x|x|}$$ = $$\sqrt{-(-k)|-k|}$$
= $$\sqrt{k*k}$$ (As |Positive Number| = Positive Number)
= $$\sqrt{k^2}$$ = k = -x

Hope it helps!

Watch the following video to learn the Basics of Absolute Values

Non-Human User
Joined: 09 Sep 2013
Posts: 34046
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If x < 0, then (-x*|x|)^(1/2) is: [#permalink]
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 (-x*|x|)^(1/2) is: [#permalink]
Moderator:
Math Expert
94547 posts