If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4. : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 16:48

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 15 Aug 2005
Posts: 136
Followers: 2

Kudos [?]: 23 [0], given: 0

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

### Show Tags

17 Mar 2006, 17:28
12
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

56% (01:20) correct 44% (00:22) wrong based on 605 sessions

### HideShow timer Statistics

If x <0 , then $$\sqrt{-x*|x|}$$ equals

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-0-then-root-x-x-is-100303.html
[Reveal] Spoiler: OA

Last edited by believe2 on 18 Mar 2006, 04:23, edited 2 times in total.
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 10

Kudos [?]: 60 [0], given: 0

### Show Tags

17 Mar 2006, 19:45
1
This post was
BOOKMARKED
believe2 wrote:
if x<0, then sqrt (-x|x|) equals
1. -x
2. -1
3. 1
4. x
5. sqrt(x)

i think the question is not completee cuz if x<0, then sqrt (-x|x|) equals sqrt (-x^2) and its sqrt value cannot be determined.
Manager
Joined: 01 Feb 2006
Posts: 100
Followers: 1

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

### Show Tags

17 Mar 2006, 19:55
Professor wrote:
believe2 wrote:
if x<0, then sqrt (-x|x|) equals
1. -x
2. -1
3. 1
4. x
5. sqrt(x)

i think the question is not completee cuz if x<0, then sqrt (-x|x|) equals sqrt (-x^2) and its sqrt value cannot be determined.
it would be sqrt(x|-x|) since x<0. e.g if x = -3......sqrt(3|-3|) = sqrt(9) = 3

ps: sqrt (-x^2) can also be determined.

Last edited by trublu on 17 Mar 2006, 19:59, edited 1 time in total.
Manager
Joined: 30 Jan 2006
Posts: 145
Followers: 1

Kudos [?]: 27 [1] , given: 0

### Show Tags

17 Mar 2006, 20:49
1
KUDOS
believe2 wrote:
if x <0 , then sqrt (-x |x|) equals

1. -x
2. -1
3. 1
4. x
5. sqrt(x)

Picking numbers:

If x <0 ---> x = -2

then the sqrt (-x |x|) = sqrt (-(-2)*|-2|) = sqrt (2*2) = sqrt (4) = 2

2 = -x = -(-2)
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 10

Kudos [?]: 60 [0], given: 0

### Show Tags

17 Mar 2006, 21:02
trublu wrote:
sqrt (-x^2) can also be determined.

i donot think we can, eventhough gmat doesnot deal with such numbers.
any way i am more than happy to see you soluton. .

Last edited by Professor on 18 Mar 2006, 05:57, edited 1 time in total.
Manager
Joined: 15 Aug 2005
Posts: 136
Followers: 2

Kudos [?]: 23 [0], given: 0

### Show Tags

18 Mar 2006, 04:27
1
This post was
BOOKMARKED
OA is .............. -x
no OE

What do you guys think abt the following:

I. if x < 0 then value of sqrt ( |x| )
II. if x < 0 then value of sqrt ( x )

(...do not have the OA for I & II)
SVP
Joined: 14 Dec 2004
Posts: 1702
Followers: 3

Kudos [?]: 137 [0], given: 0

### Show Tags

18 Mar 2006, 04:48
believe2 wrote:
OA is .............. -x
no OE

What do you guys think abt the following:

I. if x < 0 then value of sqrt ( |x| )
II. if x < 0 then value of sqrt ( x )

(...do not have the OA for I & II)

I. if x < 0 then value of sqrt ( |x| )
= sqrt(x)
II. if x < 0 then value of sqrt ( x )
= i*sqrt(x)
Manager
Joined: 15 Aug 2005
Posts: 136
Followers: 2

Kudos [?]: 23 [0], given: 0

### Show Tags

18 Mar 2006, 05:17
vivek123 wrote:
I. if x < 0 then value of sqrt ( |x| )
= sqrt(x)
II. if x < 0 then value of sqrt ( x )
= i*sqrt(x)

I think the following should be the solution:
I. if x < 0 then value of sqrt ( |x| )
= sqrt(-x)
II. if x < 0 then value of sqrt ( x )
= sqrt(x) - no change
(- but when x is assigned some numeric value like say -3 then sqrt ( x )=3i but we do not need the 'i' as long as the expression is in terms of x)

what do U think?
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 10

Kudos [?]: 60 [0], given: 0

### Show Tags

18 Mar 2006, 05:58
vivek123 wrote:
A) -x ?

I'll explain if correct

seems you have correct OA. but how? could you explain?
SVP
Joined: 14 Dec 2004
Posts: 1702
Followers: 3

Kudos [?]: 137 [0], given: 0

### Show Tags

18 Mar 2006, 07:02
Professor wrote:
vivek123 wrote:
A) -x ?

I'll explain if correct

seems you have correct OA. but how? could you explain?

This is my logic---->

We know that x<0, then -x > 0. In other words, -x*|x| = +x^2

so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")
SVP
Joined: 14 Dec 2004
Posts: 1702
Followers: 3

Kudos [?]: 137 [0], given: 0

### Show Tags

18 Mar 2006, 07:06
believe2 wrote:
vivek123 wrote:
I. if x < 0 then value of sqrt ( |x| )
= sqrt(x)
II. if x < 0 then value of sqrt ( x )
= i*sqrt(x)

I think the following should be the solution:
I. if x < 0 then value of sqrt ( |x| )
= sqrt(-x)

II. if x < 0 then value of sqrt ( x )
= sqrt(x) - no change
(- but when x is assigned some numeric value like say -3 then sqrt ( x )=3i but we do not need the 'i' as long as the expression is in terms of x)

what do U think?

If you want to keep it in the "x" form then YES, but ultimately, what I wrote too is not wrong! So, let us take it this way, look at the choices & decide
Manager
Joined: 01 Feb 2006
Posts: 100
Followers: 1

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

### Show Tags

18 Mar 2006, 07:09
Manager
Joined: 15 Aug 2005
Posts: 136
Followers: 2

Kudos [?]: 23 [0], given: 0

### Show Tags

18 Mar 2006, 07:44
vivek123 wrote:

If you want to keep it in the "x" form then YES, but ultimately, what I wrote too is not wrong! So, let us take it this way, look at the choices & decide

Agreed.
Also, your statement earlier "..We know that x<0, then -x > 0." is a very interesting way of looking [or - to look (..not sure if infinitive or -ing form is better here) ] at absolute values.
thanks
Manager
Joined: 20 Feb 2006
Posts: 213
Followers: 1

Kudos [?]: 8 [0], given: 0

### Show Tags

18 Mar 2006, 09:06
I saw this question earlier but could not find a logical explanation.
I still feel that sqrt(positive number) can be either positive or negative. In that case, the answer can be either x or -x.
For ex, sqrt(4) = 2 or -2.
Please explain why the OA is -x .... Thanks.
Intern
Joined: 13 Nov 2005
Posts: 9
Followers: 0

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

### Show Tags

18 Mar 2006, 10:07
A very nice explanation ( answer being -x )

Thank you very much.

way2go
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 10

Kudos [?]: 60 [0], given: 0

### Show Tags

18 Mar 2006, 10:08
vivek123 wrote:
Professor wrote:
vivek123 wrote:
A) -x ?

I'll explain if correct

seems you have correct OA. but how? could you explain?

This is my logic---->

We know that x<0, then -x > 0. In other words, -x*|x| = +x^2

so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.
Senior Manager
Joined: 09 Aug 2005
Posts: 285
Followers: 1

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

### Show Tags

18 Mar 2006, 17:59
vivek123 wrote:
Professor wrote:
vivek123 wrote:
A) -x ?

I'll explain if correct

seems you have correct OA. but how? could you explain?

This is my logic---->

We know that x<0, then -x > 0. In other words, -x*|x| = +x^2

so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

I am with you untill

sqrt(-x*|x|) = sqrt(x^2)
= +x or -x.

so sqrt(-x*|x|) is -ve or +ve

and its absolute value is |x|

x or -x

how do you conclude that the value of the expression sqrt(-x*|x|) is -x?
SVP
Joined: 14 Dec 2004
Posts: 1702
Followers: 3

Kudos [?]: 137 [0], given: 0

### Show Tags

18 Mar 2006, 19:38
Professor wrote:
vivek123 wrote:
Professor wrote:
vivek123 wrote:
A) -x ?

I'll explain if correct

seems you have correct OA. but how? could you explain?

This is my logic---->

We know that x<0, then -x > 0. In other words, -x*|x| = +x^2

so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

but we cannot have -x as one of the value of sqrt(x^2) because sqrt(x^2) has only one value that is x. any square under radical sign has only +ve value.

How do you say that? For example, "25" is a square of "5" & also of "-5".
sqrt(25) = +5 or -5. I didn't get your point.
SVP
Joined: 14 Dec 2004
Posts: 1702
Followers: 3

Kudos [?]: 137 [0], given: 0

### Show Tags

18 Mar 2006, 19:41
old_dream_1976 wrote:
vivek123 wrote:
Professor wrote:
vivek123 wrote:
A) -x ?

I'll explain if correct

seems you have correct OA. but how? could you explain?

This is my logic---->

We know that x<0, then -x > 0. In other words, -x*|x| = +x^2

so,
sqrt(-x*|x|) = sqrt(x^2)
= +x or -x. but since it is GIVEN that x < 0,

(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")

I am with you untill

sqrt(-x*|x|) = sqrt(x^2)
= +x or -x.

so sqrt(-x*|x|) is -ve or +ve

and its absolute value is |x|

x or -x

how do you conclude that the value of the expression sqrt(-x*|x|) is -x?

OD,
Frankly speaking, I'm not very comfortable with this problem. Ideally, answer should be "+/-x", but since it was already mentioned that x<0, (and most important: answer choice has both +x & -x, WE HAVE TO SELECT ONE CHOICE) the value that I selected is "-x"

For example, if we are solving sqrt(a) for something like age of a person, -ve value wouldn't make sense, we have to select +ve value.
Director
Joined: 17 Oct 2005
Posts: 932
Followers: 1

Kudos [?]: 203 [0], given: 0

### Show Tags

18 Mar 2006, 20:17
1
This post was
BOOKMARKED
lets plug in numbers

ie x=-2

-(-2) * abs(-2)= 2+2=4

sqrt (4)=+/-2

just because x<0 doesnt mean the value of the equation is less than zero

hence this is a messsed up q.
18 Mar 2006, 20:17

Go to page    1   2   3    Next  [ 55 posts ]

Similar topics Replies Last post
Similar
Topics:
4 If x<0 What is the value of [(x-3)^4]^1/4 + (-x|x|)^1/2 A. -3 B. x+3 3 20 Jan 2017, 19:01
4 If x is a positive integer such that (x-1)(x-3)(x-5)....(x-93) < 0, ho 2 29 Jan 2016, 02:14
4 If x = -1, then -(x^4 + x^3 + x^2 + x) = 7 03 Feb 2014, 00:23
1 If x = -1, then (x^4 - x^3 + x^2)/(x - 1) = 3 19 Dec 2012, 05:17
33 For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? 12 26 Jul 2012, 04:35
Display posts from previous: Sort by