johnmayf wrote:

I took a practice test the other day and I came across a few DS questions that I was unable to figure out. If you know of a good way to break down these problems I would appreciate your help.

a) In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

1) r + s = 1

2) u = 1 - r and v = 1 - s

b) A certain jar contains only B black marbles, W white marbles, and R red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability than the probability that the marble chosen will be white?

1) R / B + W > W / B + R

2) B - W > R

Hi, welcome to the Gmat Club. The questions you are asking were discussed before, below are my solutions to them from earlier topics:

First question:Basically the question asks is \(r^2+s^2=u^+v^2\)?

(1) \(r+s=1\), no info about \(u\) and \(v\);

(2) \(u=1-r\) and \(v=1-s\) --> \(u^2+v^2=(1-r)^2+(1-s)^2=1-2r+r^2+1-2s+s^2=2-2(r+s)+ r^2+s^2\). We don't know the value of \(2-2(r+s)\), so not sufficient.

(1)+(2) \(r+s=1\) and \(u^2+v^2=2-2(r+s)+ r^2+s^2\) --> \(u^2+v^2=2-2+r^2+s^2=r^2+s^2\). Sufficient.

Answer: C.

Second question:The question is \(\frac{R}{R+B+W}>\frac{W}{R+B+W}\) true? Or is \(R>W\) true?

(1) \(\frac{R}{B+W} > \frac{W}{B+R}\) --> \(\frac{R}{B+W} +1> \frac{W}{B+R}+1\) --> \(\frac{R+B+W}{B+W}> \frac{W+B+R}{B+R}\) --> \(\frac{1}{B+W}> \frac{1}{B+R}\) --> \(B+R>B+W\) --> \(R>W\). Sufficient.

(2) \(B-W>R\), not sufficient to determine whether \(R>W\) or not.

Answer: A.

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