If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4. : GMAT Problem Solving (PS)
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# If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4.

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

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17 Mar 2006, 17:28
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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.
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17 Mar 2006, 19:45
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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.
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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.
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17 Mar 2006, 20:49
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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)
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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.
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18 Mar 2006, 04:27
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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)
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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)
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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?
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18 Mar 2006, 05:58
vivek123 wrote:
A) -x ?

I'll explain if correct

seems you have correct OA. but how? could you explain?
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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 "-")
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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
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18 Mar 2006, 07:09
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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
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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.
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18 Mar 2006, 10:07
A very nice explanation ( answer being -x )

Thank you very much.

way2go
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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.
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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?
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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.
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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.
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18 Mar 2006, 20:17
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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

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