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Gmatprep probability

by warraich » Sun Jun 05, 2011 6:04 pm
Jar contains only Black b, white w and red r marbles. One marble chosen at random. Is the probability marble chosen would be red greater than the proablity 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 vineeshp » Sun Jun 05, 2011 6:11 pm
Expert solution is already available on the site.

https://www.beatthegmat.com/marbles-prob ... 32705.html
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by smackmartine » Sun Jun 05, 2011 6:22 pm
IMO A
Asked whether r/(b+w+r) > w/(b+w+r)?

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

we know that b,r, and w are positive, so

lets inverse the inequality
(b+w)/r < (b+r)/w (sign changed)

Adding 1 on both side we get,
[(b+w)/r] +1 < [(b+r)/w] +1
(b+w+r)/r < (b+w+r)/w

Inverse the inequality again.

r/(b+w+r) > w/(b+w+r) , Sufficient.

2) b - w > r

from this statement we only know that b> r+w , which does not give any relation between r and w. Insufficient.
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by GMATGuruNY » Sun Jun 05, 2011 6:34 pm
warraich wrote:Jar contains only Black b, white w and red r marbles. One marble chosen at random. Is the probability marble chosen would be red greater than the proablity that the marble chosen will be white.

1) r/(b+w) > w/(b+r)
2) b - w > r
Almost no math is needed.

Statement 1: r/(b+w) > w/(b+r)
Tells us that the ratio of red to the other colors (blue and white) is greater than the ratio of white to the other colors (blue and red).
In other words, there are more red marbles than white marbles.
Sufficient.

Statement 2: b-w > r.
Rephrased, b > w+r.
No way to determine whether there are more red marbles than white marbles.
Insufficient.

The correct answer is A.
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by cans » Sun Jun 05, 2011 8:43 pm
b,w,r balls. total=b+w+r
prob(red) = r/(b+w+r) ; prob(white) = w/(b+w+r)
to find if r/(b+w+r) > w/(b+w+r)
cross multiply:- rb+wr + rr > wb+ww+wr. cancelling wr,
r(b+r) > w(b+w)
r/(b+w) > w/(b+r) (To find)
a) above statement is given. Thus sufficient.
b) b-w>r not sufficient. (we need to find if r>w. no information)
IMO A
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