A certain jar contains only b black marbles, w white marbles

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A certain jar contains only b black marbles, w white marbles [#permalink]

16 Nov 2010, 06:43

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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 then the probability that the marble chosen will be white?

(1) r/(b+w) > w/(b+r)
(2) b-w > r

[Reveal] Spoiler: OA

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Re: a certain jar contains [#permalink]

16 Nov 2010, 06:52

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anilnandyala wrote:

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.

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

Cross multiply, we can safely do this as B+W and B+R are more than 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 than zero, so R-W>0 --> R>W.

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

Answer: A.
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Re: a certain jar contains [#permalink]

16 Nov 2010, 12:40

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anilnandyala wrote:

a certain jar contains only b black marbles, w white marbles & r red marbles. if one marble is to be chosen random from jar is the probability that the marble chosen will be red greater then the probability the marble chosen is white?
a) r/(b+w) > w/(b+r)
b) b-w > r

The probability that red marble is chosen will be greater than the probability that white marble is chosen if there are more red marbles than white marbles.
So the queestion is just: Is r > w

Statement 1: r/(b + w) > w/(b + r)
Cross multiply to get r(b + r) > w(b + w) .... [(b + w) and (b + r) are definitely positive so cross multiplying is not a problem.]
Now, if r > w, (b + r) has to be greater than (b + w)
If r were less than w, then (b + r) < (b + w) and the left side would have been smaller than the right side.
So this implies that r must be greater than w. Sufficient.

Statement 2: b > r + w
But we cant compare r and w so not sufficient.

Answer (A).
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Re: a certain jar contains [#permalink]

17 Nov 2010, 23:55

VeritasPrepKarishma and Bunuel - thanks a lot for ur explanations.

+1 from me... again.

keep up the good job.
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Re: a certain jar contains [#permalink]

23 Nov 2010, 23:36

Bunuel wrote:

anilnandyala wrote:

(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.

OR:
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.

Answer: A.

awesome explanation. I have translated the question to is r>w but did not know how to solve the (1). Now get it clear
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A certain jar contains only b black marbles, w white marbles and [#permalink]

22 May 2013, 07:40

lets rephrase the question first.
It says IS r/(w+r+b)> w(r+w+b)
Cross multiply because we know all the variables are positive. It becomes
Is br+r^2> bw+w^2 ?

Statement 1: when cross multiplying we ger br+ r^2 >bw+ w^2........Thus sufficient

Statement 2: clearly insufficient.

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Re: A certain jar contains only b black marbles, w white marbles [#permalink]

22 May 2013, 14:41

chose B. I hate my life!

Re: A certain jar contains only b black marbles, w white marbles [#permalink] 22 May 2013, 14:41

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A certain jar contains only b black marbles, w white marbles

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