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Jars

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Jars

by rish » Wed Sep 02, 2009 6:47 am
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
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Source: — Data Sufficiency |
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by gmatcoach » Wed Sep 02, 2009 10:43 am
rephrase the question:

P(red marble) > P(w marble) ==> r/(r+w+b) > w/(r+w+b) ==> Is r > w?

Let us begin with Stmt 2 as it looks easier:

b-w>r ==> b>w+r. But this says nothing about relative number of red and white marbles. So insuff.

Stmt1: r/(b+w) > w/(b+r) ==> (b+w)/r < (b+r)/w
Now add 1 to both sides: (b+w)/r +1 < (b+r)/w +1 ==>(b+w+r)/r < (b+r+w)/w ==> r/(b+w+r) > w/(b+w+r) ==> r > w. Sufficient

Answer is A.
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