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Joined: 15 Aug 2005
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If x <0 , then \sqrt{x*x} equals 1. x 2. 1 3. 1 4.
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Updated on: 18 Mar 2006, 05:23
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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: ifx0thenrootxxis100303.html
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Originally posted by believe2 on 17 Mar 2006, 18:28.
Last edited by believe2 on 18 Mar 2006, 05:23, edited 2 times in total.



VP
Joined: 29 Dec 2005
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Re: absolute value
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17 Mar 2006, 20:45
believe2 wrote: if x<0, then sqrt (xx) 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 (xx) equals sqrt (x^2) and its sqrt value cannot be determined.



Manager
Joined: 01 Feb 2006
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Re: absolute value
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Updated on: 17 Mar 2006, 20:59
Professor wrote: believe2 wrote: if x<0, then sqrt (xx) 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 (xx) equals sqrt (x^2) and its sqrt value cannot be determined. it would be sqrt(xx) since x<0. e.g if x = 3......sqrt(33) = sqrt(9) = 3
ps: sqrt (x^2) can also be determined.
Originally posted by trublu on 17 Mar 2006, 20:55.
Last edited by trublu on 17 Mar 2006, 20:59, edited 1 time in total.



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Re: absolute value
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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
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Updated on: 18 Mar 2006, 06:57
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. .
Originally posted by Professor on 17 Mar 2006, 22:02.
Last edited by Professor on 18 Mar 2006, 06:57, edited 1 time in total.



Manager
Joined: 15 Aug 2005
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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)



SVP
Joined: 14 Dec 2004
Posts: 1516

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
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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?



VP
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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



Manager
Joined: 01 Feb 2006
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It's a bad question cos there are two possible answers.



Manager
Joined: 15 Aug 2005
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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



Manager
Joined: 20 Feb 2006
Posts: 194

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

A very nice explanation ( answer being x )
Thank you very much.
way2go



VP
Joined: 29 Dec 2005
Posts: 1221

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.



Senior Manager
Joined: 09 Aug 2005
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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?



SVP
Joined: 14 Dec 2004
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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.



Director
Joined: 17 Oct 2005
Posts: 861

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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