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

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Manager
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A certain jar contains only b black marbles, w white marbles [#permalink] New post 04 Apr 2007, 15:47
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A certain jar contains only b black marbles, w white marbles and r red marbles. If a marble is picked at random from the jar, is the probability that the marble chosen be red greater than the probability that the marble chosen will be white?
(1) r/(b+w)>w/(b+r)
(2) b-w>r
Answer is A

Could someone explain the answer?
Director
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 [#permalink] New post 06 Apr 2007, 02:29
Probability of choosing red marble = r/(b+w+r)
Probability of choosing white marble = w/(b+w+r)

To compare these two probabilities, we should know the relation between r and w
Lets consider the statement 1:
r/(b+w) > w/(b+r)
r(b+r) > (b+w)w
rb+r^2 -bw_w^2 > 0
b(r-w) + r^2 -w^2 > 0
b(r-w) + (r+w)(r-w) > 0
(r-w)(b+r+w) > 0
as we know b+r+w will always be positive
so r-w> 0
r > w
hence we can say the prob of choosing red marble is greater. SUFF

Statement2 : does not establish any relation between r and w. INSUFF

Hence the answer is 'A'
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 [#permalink] New post 08 Apr 2007, 03:30
I got A as well.

However, this seems like a difficult question for the GMAT; would something like this appear?
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 [#permalink] New post 08 Apr 2007, 05:00
StartupAddict wrote:
I got A as well.

However, this seems like a difficult question for the GMAT; would something like this appear?


YOu never know :)
Manager
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 [#permalink] New post 13 Oct 2007, 14:23
I had this question in GMATprep ... So you think about it


StartupAddict wrote:
I got A as well.

However, this seems like a difficult question for the GMAT; would something like this appear?
Director
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 [#permalink] New post 13 Oct 2007, 15:15
You Rock vshaunak !!

This question is from GMATPrep 2 ; So it is definately a GMAT level question. I have seen much more difficult problems on the REAL GMAT test.
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Re: DS Question Marbles [#permalink] New post 13 Oct 2007, 23:11
A,

r/(b+w+r) compare to w/(b+w+r)

since denominators are same, we need to compare only r and w

1) r/(b+w)> w/(b+r), since r,b, and w all are positive we can cross multiply.
r(b+r) > w(b+w)
b is same for both sides, thus r > w always. SUFF.

2) b-w>r, fastest is to try few numbers

w=3, r=2, b=5 -----------> r<w
w=2, r=3, b=5------------> r>w, thus INSUFF.
Re: DS Question Marbles   [#permalink] 13 Oct 2007, 23:11
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