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If x <0 , then \sqrt{-x*|x|} equals 1. -x 2. -1 3. 1 4. [#permalink]
 17 Mar 2006, 18:28
Question Stats:
62% (01:13) correct
37% (00:26) wrong based on 83 sessions
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
Last edited by believe2 on 18 Mar 2006, 05:23, edited 2 times in total.
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Re: absolute value [#permalink]
17 Mar 2006, 20:45
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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Re: absolute value [#permalink]
17 Mar 2006, 20:55
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, 20:59, edited 1 time in total.
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Re: absolute value [#permalink]
17 Mar 2006, 21:49
believe2 wrote: if x <0 , then sqrt (-x |x|) equals
1. -x
2. -1
3. 1
4. x
5. sqrt(x)
Answer is -x, i.e. #1.
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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Re: absolute value [#permalink]
17 Mar 2006, 22:02
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, 06:57, edited 1 time in total.
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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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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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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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vivek123 wrote: A) -x ? I'll explain if correct  seems you have correct OA. but how? could you explain?
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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,
answer should be "-x".
(For any sqrt, answer is always "+" or "-" ; but if some condition is given, we can arrive at whether "+" OR "-")
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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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It's a bad question cos there are two possible answers.
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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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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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A very nice explanation ( answer being -x )
Thank you very much.
way2go
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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, answer should be "-x". (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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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, answer should be "-x". (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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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, answer should be "-x". (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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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, answer should be "-x". (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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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.
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close
