GMAT Prep -Sq Rt & Modulus

[aditikedia]

I'm not sure how this is done.. would appreciate an explanation..

Thanks!

[olika]

Not sure in my solution, but here it is

|x|, x positive if x greater or equal to 0,
x negative if x less than 0.
From the statement, we know that x less than 0, then x should be negative. Inserting it in the equation, we will get root((-x)(-x)) = root((x)^2), which is |x|. But we know that x less than 0, so x should be equal to -x.

[sudhir3127]

I have my own doubts abt the question because sq root (-) should be i ( if we read advanced quants i^2 = -1 )

the answer should be Xi.

but theres no answer like that...i leave to Ian, Stuart . Ron to reply ...

[pepeprepa]

Here is how I did it
If we take x=-2
It gives you sqrt (-(-2)*2)=sqrt4=2
so it is -x

[bourne159]

This is a tricky one.
This is a GMAT specific thing.

In GMAT sqrt(X**2) always denotes +X.
i.e sqrt(9) is always 3.
But the roots of sqrt(X**2) are +X and -X
Check page 114 in OG11.

So in this case sqrt(-X * |X|) = sqrt(X**2) = X(+ve value)
Since X <0 you can get a +ve value by negating the value of X which is -X.

[Ian Stewart]

This is a tricky one.
This is a GMAT specific thing.

In GMAT sqrt(X**2) always denotes +X.
i.e sqrt(9) is always 3.
But the roots of sqrt(X**2) are +X and -X
Check page 114 in OG11.

This is not a 'GMAT-specific thing'. In all of mathematics, the square root symbol means the non-negative square root. If you see the square root symbol over 16, that is equal to 4, and not -4, on the GMAT and in any other mathematical realm you venture into. There is no mathematics that is 'GMAT-specific'; the GMAT observes all of the standard rules of elementary (real, not complex) mathematics.

[pepeprepa]

I do not even understand the debate, please clarify if it is important.

[drgmatIL]

pepeprepa,
if you choose x=-5 for exaple
you get -(-5)*5 root = 5
so if you look the relation between x (-5) and equation below(5)
it's like x = -x

[raunekk]

As sudhir3127 said...

the answer shud be sumthg like Xi

i dont understand this...

[pepeprepa]

drgmatIL thanks to answer me but you repeat what I posted before.
I was talking about what bourne and Ian discuss and the i^2=-1 ...

[sudhir3127]

Hi all .. please find the link about the square root of negative numbers

https://en.wikipedia.org/wiki/Square_roo ... ex_numbers

i was wondering abt the answers because we in India are taught that to find the sq root of a negative numeber we introduce an imaginary number called i^2 ( because i^2 = -1 ) any square root a negative number would be the postive sq root of that number followed by i.

Hope the link helps. Ian and all require u all to kindly pitch in this case..

[sudhir3127]

I think i missed the point the that X<0 so negative of negative will be postive...

Apologies for creating confusion.. but in any case a negative sq root shud have a i followed by the number.

thanks all

[raunekk]

imaginary numbers on gmat????

[Ian Stewart]

Numbers on the GMAT are always real numbers- if you know what imaginary numbers are, do your best to forget about them! On the GMAT, you can't take the square root of a negative, so if you see a question like:

For which value of x is sqroot(x-4) not defined?
A) 3
B) 4
C) 5
D) 6
E) 7

the answer is, of course, A, because we can't take square roots of negatives on the GMAT. In more advanced math, square roots of negatives are defined (using i, the square root of -1, as Sudhir points out), but they are undefined on the GMAT.

[missionmba]

Here is how I did it
If we take x=-2
It gives you sqrt (-(-2)*2)=sqrt4=2
so it is -x

This is the best solution. We all know imaginary numbers are Out of GMATs Scope

If u put x = -y

It gives you sqrt (-(-y)*y)=sqrt (y^2) = y

=> -x

otherwise
there is no doubt that the answer should have i (sqrt(-1)) in it.