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

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Joined: 31 Aug 2007
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A certain jar contains only b black marbles, w white [#permalink]

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30 Mar 2008, 11:43
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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 than the probability that the marble chosen will be white?

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

2) b - w > r

Kudos [?]: 158 [0], given: 1

Senior Manager
Joined: 20 Feb 2008
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Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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30 Mar 2008, 12:03
young_gun wrote:
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

I think the correct answer is E
A is insufficient because r/(b+w) does not take into account r in the denominator and w/(b+r) does not include w in the denominator.
B is sufficient because if b-w>r
If b=10 w=2 then 8>r
In this case P (R) can be greater or less than p(W)
C I cannot see a relationship
D Insufficient

What is the OA?

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Current Student
Joined: 31 Aug 2007
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30 Mar 2008, 13:06
I think the OA is A...I'm not sure why though.

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Intern
Joined: 31 Mar 2008
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31 Mar 2008, 20:31
1) r/(b+w) > w/(b+r)

because if the ratio of red to the rest is higher than the ratio of white to the rest while blacks remain constant then there must be more red than white

r > w * (b+w) / (b+r)
r(b+r) > w(b+w)
set b = 0
r^2 > w^2
r > w

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Senior Manager
Joined: 16 Aug 2004
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01 Apr 2008, 02:22
I choose A as the answer option. Essentially we have to find is...
r/(b+w+r) > w/(b+w+r)

By statement 1
r/(b+w) > w/(b+r) or
r(b+r) > w(b+w) or
rb + r^2 > wb + w^2 or
rb + r^2 + wr > wb + w^2 + wr (adding wr to both sides)
or simply
r/(b+w+r) > w/(b+w+r) (if you group the factors)

Hence the condition is sufficient. (ruling out b, c & d)

By statement 2
b - w > r
or b > r+w which means b is greater than the sum of r+w, but we won;t know the relation between r & w. This statement is not sufficient. Hence A

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Senior Manager
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01 Apr 2008, 10:16
1
KUDOS
r/(b+w) > w/(b+r)
r/(b+w) +1 > w/(b+r) +1
(r+b+w)/(b+w) > (r+b+w)/(b+r)
1/(b+w) > 1/(b+r)
inverting

(b+w) < (b+r)

w<r hence sufficient

Kudos [?]: 15 [1], given: 0

Re: DS marble probability   [#permalink] 01 Apr 2008, 10:16
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