Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Aug 2014, 19:19

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4.

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
VP
VP
User avatar
Joined: 29 Dec 2005
Posts: 1351
Followers: 6

Kudos [?]: 28 [0], given: 0

GMAT Tests User
 [#permalink] New post 21 Mar 2006, 06:56
HongHu wrote:
Square root of any positive number is a positive number. When we say x^2=a, we know that x=+/-sqrt(a). You can see that sqrt(a) itself is positive, but x could be positive sqrt(a) or negative sqrt(a).

Using an example, say x^2=25. We know that x=+/-sqrt(25), where sqrt(25)=5.

Hope this helps. :)


i just want to be/make clear on why sqrt (25) = 5.

suppose x^2 = 25
x = sqrt (25) or - sqrt (25)
and we are here dealing with only "sqrt (25)".

therefore, sqrt (25) = 5

thank you honghu.
Director
Director
User avatar
Joined: 04 Jan 2006
Posts: 928
Followers: 1

Kudos [?]: 12 [0], given: 0

GMAT Tests User
 [#permalink] New post 21 Mar 2006, 08:33
I still dont understand..

isnt |x| just the positive value of the number x?
VP
VP
avatar
Joined: 21 Sep 2003
Posts: 1071
Location: USA
Followers: 3

Kudos [?]: 30 [0], given: 0

GMAT Tests User
 [#permalink] New post 21 Mar 2006, 08:41
willget800 wrote:
I still dont understand..

isnt |x| just the positive value of the number x?


Yes. But what if the x is -ve (say x = -2), then the absolute value of x is 2
x = -2
|x| = 2 = -(-2) = -x

For more gyan (Hindi word for knowledge) :-D see..

http://www.purplemath.com/modules/absolute.htm
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

SVP
SVP
User avatar
Joined: 07 Nov 2007
Posts: 1829
Location: New York
Followers: 26

Kudos [?]: 441 [0], given: 5

GMAT Tests User
Re: No. Properties [#permalink] New post 25 Jan 2009, 06:50
study wrote:
If x<0, then [sqrt (-x absolute x )] is
(please note that both variables - minus x and absolute x - come under the root sign)

1
-1
sqrt x
x
-x


let say -x=y (y is positive)

sqrt (-x |x|) = sqrt (y|-y|) = sqrt (y^2) = y or -y

when y +ve --> answer =y = -x
wnen y -ve --> answer = -y=x

here y is +ve so answer =-x

E
_________________

Your attitude determines your altitude
Smiling wins more friends than frowning

Manager
Manager
avatar
Joined: 04 Jan 2009
Posts: 243
Followers: 1

Kudos [?]: 9 [0], given: 0

GMAT Tests User
Re: No. Properties [#permalink] New post 25 Jan 2009, 08:44
yes sir. sqrt(f) has to be positive otherwise, we run into the following problem:
2 is sqrt(4)
if we say sqrt(4)=-2 or 2
in one situation we run into situation where 2+2=0.
So, unless we are asked to find (-sqrt(f)) sqrt(f) always yields positive number.

x2suresh wrote:
study wrote:
If x<0, then [sqrt (-x absolute x )] is
(please note that both variables - minus x and absolute x - come under the root sign)

1
-1
sqrt x
x
-x


let say -x=y (y is positive)

sqrt (-x |x|) = sqrt (y|-y|) = sqrt (y^2) = y or -y

when y +ve --> answer =y = -x
wnen y -ve --> answer = -y=x

here y is +ve so answer =-x

E

_________________

-----------------------
tusharvk

Senior Manager
Senior Manager
avatar
Joined: 05 Oct 2008
Posts: 273
Followers: 3

Kudos [?]: 42 [0], given: 22

GMAT Tests User
Re: No. Properties [#permalink] New post 25 Jan 2009, 11:05
Thanks Ian for the explanation and for posting the question in mathematical format.

+2
Senior Manager
Senior Manager
User avatar
Joined: 20 Mar 2008
Posts: 455
Followers: 1

Kudos [?]: 67 [0], given: 5

GMAT Tests User
Root of the product of -x and |x| [#permalink] New post 31 Oct 2009, 21:40
Root of the product of -x and |x|
Attachments

root x mod x.JPG
root x mod x.JPG [ 9.55 KiB | Viewed 3667 times ]

Senior Manager
Senior Manager
User avatar
Joined: 20 Mar 2008
Posts: 455
Followers: 1

Kudos [?]: 67 [0], given: 5

GMAT Tests User
Re: Root of the product of -x and |x| [#permalink] New post 31 Oct 2009, 21:59
+1 to you.

Thanks for the explanation. When I saw this problem, I had a feeling there was something I was missing.
Intern
Intern
avatar
Joined: 22 Sep 2009
Posts: 36
Followers: 0

Kudos [?]: 13 [0], given: 3

Re: Root of the product of -x and |x| [#permalink] New post 01 Nov 2009, 04:38
x<0 ....... let a=-x. so a is +ve

hence y= sqrt{-x*|x|}=sqrt{a*|-a|}
y = sqrt{a*a}
y = +a or -a
y=-x or x

I don't follow why y be positive? Bunuel please explain
Intern
Intern
avatar
Joined: 28 Apr 2009
Posts: 48
Followers: 0

Kudos [?]: 6 [0], given: 2

Re: Root of the product of -x and |x| [#permalink] New post 14 Nov 2009, 06:11
Bunuel wrote:
I say that ycan not be negative as y=\sqrt{some expression}, and even root from the expression (some value) is never negative (as for GMAT we are dealing only with real numbers).

Consider this y=\sqrt{16} --> y=4 and not y=4 or y=-4.



But why ?? is this a standard formula ?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22146
Followers: 3412

Kudos [?]: 24958 [0], given: 2698

Re: Root of the product of -x and |x| [#permalink] New post 14 Nov 2009, 06:24
Expert's post
mbaquestionmark wrote:
Bunuel wrote:
I say that ycan not be negative as y=\sqrt{some expression}, and even root from the expression (some value) is never negative (as for GMAT we are dealing only with real numbers).

Consider this y=\sqrt{16} --> y=4 and not y=4 or y=-4.



But why ?? is this a standard formula ?


When the GMAT provides the square root sign for an even root, such as a square root, then the only accepted answer is the positive root.

That is, \sqrt{16} = 4, NOT +4 or -4. In contrast, the equation x^2 = 16 has TWO solutions, +4 and -4.

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, CBRT(64) = 4, CBRT(-27) = -3.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 23 Sep 2009
Posts: 11
Location: uzbekistan
Schools: Chicago booth,Dartmouth,Duke
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Square root - positive or negative? [#permalink] New post 31 Dec 2009, 03:22
I think the answer is 4. X


Coz: given that x<0 , -(-x) is positive and module x is also positive so we get x^2 , and end result is x

If you do not think so please correct me
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22146
Followers: 3412

Kudos [?]: 24958 [0], given: 2698

Re: Square root - positive or negative? [#permalink] New post 31 Dec 2009, 06:57
Expert's post
sher1978 wrote:
I think the answer is 4. X


Coz: given that x<0 , -(-x) is positive and module x is also positive so we get x^2 , and end result is x

If you do not think so please correct me


Answer to this question is A (-x). Please refer to the solutions above. Do ask if anything remains unclear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 365
Followers: 10

Kudos [?]: 201 [0], given: 47

GMAT ToolKit User GMAT Tests User
Re: Square root - positive or negative? [#permalink] New post 31 Dec 2009, 11:46
I guess the best way to solve this question is to plug in values and see how the result features.

Before we do the same, explanation by HongHu is perfect. (Cant post the link to his reply as I am new to the club :? )

i.e Square root of any positive number is a positive number

Now getting back to the actual question:

If x<0, then \sqrt{-x*|x|} equals:
1. -x
2. -1
3. 1
4. x
5. \sqrt{x}

Approach:
Since x <0, let use plug in a negative integer as x, for e.g.

Let x = -2 ---- [1]

Hence \sqrt{-x*|x|}= \sqrt{-(-2)*|-2|} = \sqrt{2*2} = \sqrt{4} ---- [2]

Now as per the discussion going on, the point of disagreement is that \sqrt{4} = 2 or -2. But as stated by HongHu, we would consider \sqrt{4} = 2 only! The reason for this conclusion is that the radical sign used in sqrt{x} is used to show the positive square root of a number x.

Therefore \sqrt{4} = 2 ---- [3]

Now as per Equation [1] marked above, x = -2 which can also be written as -x = 2 ---- [4]

Hence if we subsitute the values of \sqrt{4} from equation 2 ( i.e. \sqrt{-x*|x|} ) and value of 2 from equation [4] ( i.e. -x )... in equation [3], we get the following result:

\sqrt{-x*|x|} = -x and hence the correct answer is 1

This approach can be verified by another question which featured in the GMAT prep exams...

If x \neq 0, then \frac{\sqrt{x^2}}{x} equals:
1. -1
2. 0
3. 1
4. x
5. \frac{|x|}{x}

Approach:
In this question, we don't know whether x is negative or positive. Hence \sqrt{x^2} is always equal to |x|. Reason for the same is: x is a variable here and we dont know the exact value. The absolute value sign is needed when we are taking the square root of a square of a variable, which may be positive or negative

Therefore in this situation, the answer would be 5

Hope this helps!

Cheers!
JT
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~

Tuck Thread Master
User avatar
Joined: 20 Aug 2009
Posts: 312
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
Followers: 12

Kudos [?]: 88 [0], given: 69

GMAT Tests User
Re: if x<0 [#permalink] New post 08 Jan 2010, 03:17
No it's (A): -x

\sqrt{(-x)|x|}=\sqrt{(-x)(-x)}=\sqrt{x^2}=|x| = -x (because x<0)
Re: if x<0   [#permalink] 08 Jan 2010, 03:17
    Similar topics Author Replies Last post
Similar
Topics:
is |x-3|=|3-x|? 1) X not equal to 3 2)-x|x|<0 FN 5 18 May 2008, 07:20
If x<0, then sqrt (-x |x|) = ? 1: -x 2: -1 3: 1 4: x 5: abhi_ferrari 4 29 Jul 2007, 13:44
If x < 0, what is sqrt(-x|x|) ? 1) -x 2)-1 3) 1 4) x 5) yezz 2 11 Sep 2006, 09:16
is x<0, then sqrt(-x * |x|) 1. -x 2. -1 3. 1 4. x 5. sm176811 5 05 May 2006, 22:02
if x<0 then sqrt(-x|x|) is 1. -x 2. -1 3. 1 4. x 5. mbadownunder 6 27 Jan 2006, 22:50
Display posts from previous: Sort by

If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4.

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   3   [ 55 posts ] 



cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.