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Some questions from GMAT Prep - please help

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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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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