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]?

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.