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# I took a practice test the other day and I came across a few

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I took a practice test the other day and I came across a few [#permalink]  10 Feb 2010, 11:41
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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
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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  10 Feb 2010, 12:13
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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.

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.

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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  10 Feb 2010, 17:23
Thanks for the help. I'm still confused on Statement 1 of the second question. Could you point me to your previous discussion or add further insight?

Thanks.
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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  10 Feb 2010, 17:51
Expert's post
johnmayf wrote:
Thanks for the help. I'm still confused on Statement 1 of the second question. Could you point me to your previous discussion or add further insight?

Thanks.

OK let me offer another way for statement (1):

Given: $$\frac{R}{B+W} > \frac{W}{B+R}$$ -->

Cross multiply, we can safely do this as $$B+W$$ and $$B+R$$ are more then zero.

We'll get $$R(B+R)>W(B+W)$$ --> $$RB+R^2>WB+W^2$$ --> $$(R^2-W^2)+(RB-WB)>0$$ --> $$(R-W)(R+W)+B(R-W)>0$$ --> $$(R-W)(R+W+B)>0$$.

As $$R+W+B>0$$, the above inequality to hold true $$R-W$$ must also be more then zero, so $$R-W>0$$ --> $$R>W$$.

Hope it's clear now.
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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  11 Feb 2010, 16:59
Thanks for the explanation. Very helpful.

Could anyone point me to answer explanations for more GMATPrep questions?

Thanks.
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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  11 Feb 2010, 17:12
Expert's post
johnmayf wrote:
Thanks for the explanation. Very helpful.

Could anyone point me to answer explanations for more GMATPrep questions?

Thanks.

On every page you can see "View tags list by forum". There you can find "Source: GmatPrep".
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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  13 Mar 2010, 19:18
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Thanks for the explanation
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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  14 Mar 2010, 02:31
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

1 clearly insufficient
2: distance (1-r)^2+(1-s)^2 = 1+r^2-2r+1+s^2-2s
we can't say it is equal to r^2+s^2

combining (1-r)^2+(1-s)^2 = r^2+s^2 so C.
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Re: Need Help with Two Difficult GMATPrep DS Problems [#permalink]  14 Mar 2010, 03:04
Thanks for the question and explanation
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Re: Need Help with Two Difficult GMATPrep DS Problems   [#permalink] 14 Mar 2010, 03:04
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