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Some questions from GMAT Prep - please help

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Neo2000 » Mon Mar 26, 2007 9:11 am
momentary_lapse wrote:Neo,

If x = -2 then the square root of X^2 is + or -2 right? Because x^2 is 4 and whether x is < 0 or > 0 the square root of a +ve number can be either the +ve root or the -ve root.
Yup the root can be either positive or negative. However, since we said X is <0 then we cannot have a value of X>0 which means the answer has to be -2
momentary_lapse wrote: What does the value of x have to do with this? Lets say x=-2, then the answer is -x which is -(-2) = 2. This defeats the reasoning you are giving saying that x < 0 therefore the answer should be -x.
My reasoning was as follows
Modulus function always give the positive value/max value/magnitude of X

Since X<0, value of X is negative say -y
Then -(-y)|-y|
= y(y) = y^2

So square root of this becomes +or- y
However we've already said that X<0 which means X cannot have a positive value so the value has to be -y
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by gabriel » Mon Mar 26, 2007 9:36 am
jayhawk2001 wrote:
Hmm, (2) just leads to 1/p > 0. However, if you combine
1 and 2, you get p = r = 0.

One can't cross-multiply this inequality when p = r = 0.
1/p > r/(r^2 + 2)

The question hence boils down to the following
Is 1/ 0 > 0 / (0 + 2)

I'm still not fully convinced that C is the correct answer but I guess
GMAT Prep answer is the final answer :-)
jay u r right according to the given statements... the answer shuld be E... even if both the staements are combined we wuld get ( as already stated by u ).... 1/0 and 0/ ( 0+2 )... and 1/0 is mathematically not defined....

the second statment is actually r>0.... by using this we get the answer as C...
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by gabriel » Mon Mar 26, 2007 10:53 am
momentary_lapse wrote:However the GMAT prep gave the options as -x,x,1,0 and square root of x. The answer is also supposed to be -x. How?? I just cant figure it out.

Ok.. the q asks to find the sq root ( -x mod (x))= sq root ( -x )* sq root ((mod(x)) = sq root (-x)* sq root(-x)... let this be eqn no. 1....

.. for understanding this u need to know the basics of complex numbers... the root of a negative qty -x can be written as sqroot (x)* sqroot (-1)... so applying this to eqn 1.... we get sqroot (x)*sqroot(-1) * sqroot(x)*sqroot(-1) .... that is sqroot (x)*sqroot(x)*sqroot(-1)*sqroot(-1)... which is equal to -x...

so basically sqroot ( (-x)^2) = -x..... similarly sqroot (-a) * sqroot(-b) is not equal to sqroot(ab)... but is equal to - sqroot(ab)... hope this helps...
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by momentary_lapse » Tue Mar 27, 2007 11:00 am
Well the questions says square root of (-x|x|) where x<0

So it seems to be asking for the square root of the product of -x and |x|

Im not sure how square root of (-x)(-x) is -x

Which property of complex numbers is this?
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by aim-wsc » Tue Mar 27, 2007 11:37 am
gabriel wrote:

Ok.. the q asks to find the sq root ( -x mod (x))= sq root ( -x )* sq root ((mod(x)) = sq root (-x)* sq root(-x)... let this be eqn no. 1....

.. for understanding this u need to know the basics of complex numbers... the root of a negative qty -x can be written as sqroot (x)* sqroot (-1)... so applying this to eqn 1.... we get sqroot (x)*sqroot(-1) * sqroot(x)*sqroot(-1) .... that is sqroot (x)*sqroot(x)*sqroot(-1)*sqroot(-1)... which is equal to -x...

so basically sqroot ( (-x)^2) = -x..... similarly sqroot (-a) * sqroot(-b) is not equal to sqroot(ab)... but is equal to - sqroot(ab)... hope this helps...
wow!
but dont make it complex by bringing complex numbers here! :lol:
even by hearing the word I almost got an heart attack there ;)


OK let me try 8)
1) If x<0 , what is square root of -x|x|

I thought if x<0, |x| = -x
THerefore square root becomes the root of x^2 which is + or - x

I wrote the answer as x but the GMAT Prep says that answer is -x. How???
first off: |x| CANNOT BE equal to -x (never)

now -x|x| = (-1)* (x) * mod (x).............(remember x has -ve value already! since x<0) so let x= (-1)* x' where x'= (+ve) x

=(-1)* (-1)x' * x'
= (-1)^2 * x'^2
I think it is very easy to sq rooting above value.
which equals to =(-1)* x'
=-x
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DS

by aim-wsc » Tue Mar 27, 2007 12:03 pm
momentary_lapse wrote:
2) Data Sufficiency:

Is 1/p > r/(r^2 + 2)

1) p=r
2) r=0
1) p=r is insufficient: reason +ve, -ve values...

2)r=0 insufficient: reason NO info about p

together: statement two (supports statement 1 &) tells about the exact sign of r and hence of p if related with statement 1. :)

let me explain it once again.
given equation if cross multiplied:
(r^2+2) > pr

Now p=r=0
2>0

gotcha 8)

ANSWER C
therefore
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by momentary_lapse » Wed Mar 28, 2007 1:09 am
aim,

thanks.. how is -x = -1 * x'?

if x<0 wont -x = -1 * x = x' ?
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by gabriel » Wed Mar 28, 2007 2:26 am
aim-wsc wrote: first off: |x| CANNOT BE equal to -x (never)

now -x|x| = (-1)* (x) * mod (x).............(remember x has -ve value already! since x<0) so let x= (-1)* x' where x'= (+ve) x

=(-1)* (-1)x' * x'
= (-1)^2 * x'^2
I think it is very easy to sq rooting above value.
which equals to =(-1)* x'
=-x

... in my own verbally challenged way this is exactly what i was tryin to explain.... may be i shuld try and avoid all those stupid jargon in the future... nywayz the explanation provided is one way at looking at the answer to the q...
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by aim-wsc » Wed Mar 28, 2007 4:07 am
momentary_lapse wrote:aim,

thanks.. how is -x = -1 * x'?

if x<0 wont -x = -1 * x = x' ?

I took x' as +ve sign of x.

... just to explain it i used the term, its not a std notation btw.
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by Stacey Koprince » Mon Apr 16, 2007 10:28 pm
1) If x<0 , what is square root of -x|x|
And answer choices are:
-x,x,1,0 and square root of x
Given x<0:
-x is a positive number.
|x| is a positive number

Therefore, we can simplify the expression "-x|x|" as x^2. The square root of x^2 = the positive and negative values of the given variable (x). We were told initially that x<0, so the only valid root is the negative one, or -x.

This is a confusing question because, in the beginning, we interpret "-x" to be a positive number, since we know x is negative. And then, at the end, we use that same "-x" to mean the negative value of the number. Looks the same - but it isn't. Try it with real numbers

x < 0. SQRT - (-2)*|-2| = SQRT 2*2 = SQRT 4 = +/- 2 If x is negative, then only -2 is the valid root. See, with these number, how the first "-x" [-(-2)] isn't the same thing as the second "-x" [-2]?
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by Stacey Koprince » Mon Apr 16, 2007 10:32 pm
As Gabriel noted, the second problem has been transcribed incorrectly.
) Data Sufficiency:

Is 1/p > r/(r^2 + 2)

1) p=r
2) r=0
The second statement should read "r>0." Which changes everything. :) I'll let you guys play with it now (note that this is a REALLY hard question - so don't feel badly if it's giving you fits!) - you can find the correct answer in OG11 #145.
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