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A certain jar contains only b black marbles...

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sbosshard
 Post subject: A certain jar contains only b black marbles...
 Post Posted: Sun Nov 29, 2009 4:11 pm 
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Students


Posts: 3
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 that the marble chosen will be white?

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

Can you help me figure out where to start when approaching this problem (answer according to GMAT prep CAT test is A.

Thanks,
Stephan
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cyber_office
 Post subject: Re: A certain jar contains only b black marbles...
 Post Posted: Wed Dec 02, 2009 7:08 pm 
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Students


Posts: 38
Hi,

My interpretation is as follows:

Since Statement 1 reads that r/(b+w) > w/(b+r), we can conclude that r/w must be > w/r since b is common to both denominators. It follows that r > w and hence r has a greater probability of being picked since there are more r marbles than w marbles.

Statement doesn't appear to provide much information: b - w > r. Alternatively, re-arranging, b - r > w. So it's a dead-end.

Not sure whether my logic is completely accurate, but the aforementioned approach is what I would have used on the test.

Regards.
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bortheratyourside
 Post subject: Re: A certain jar contains only b black marbles...
 Post Posted: Thu Dec 03, 2009 4:49 am 
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Students


Posts: 1
now the probability of choosing r = r / ( b + w + r) ; the probability of choosing w is w / ( b + w+ r)...

Now S(1) tells us r/ (b+w) > w/ (b + r).. notice in the denominator, the numerator terms does not exist. it it did exist then we could solve the problem
--------------------------------------------------------------------------------
now S(1) can be re written as..
b+w/ r < b +r / w

add 1 to both sides
((b+w)/r )+ 1 < ((b +r)/ w)+ 1

b + w + r/r < b + w + r / w

invert the inequality
r/ ( b + w +r) > w / ( b + w+ r)

-----------------------------------------------------------------------------
ergo
s1 is good
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RonPurewal
 Post subject: Re: A certain jar contains only b black marbles...
 Post Posted: Sat Jan 09, 2010 3:50 am 
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ManhattanGMAT Staff


Posts: 6765
look here:

a-certain-jar-contains-only-b-black-marbles-t881.html

12 posts, so your question is probably answered in there somewhere.
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