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Probability Question from GMATPrep CAT

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by i_have_no_cool_username » Sat Nov 19, 2011 5:30 pm
A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is 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

Answer is A. Why?

Prompt help appreciated, my test is less than 48 hours away!

Thank you, all.
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Source: — Data Sufficiency |
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by GMATGuruNY » Sat Nov 19, 2011 6:35 pm
i_have_no_cool_username wrote:A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is 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

Answer is A. Why?

Prompt help appreciated, my test is less than 48 hours away!

Thank you, all.
Like many other DS problems, the one above is most quickly solved by using a little common sense. I posted an explanation here:

https://www.beatthegmat.com/probability-t74040.html
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by mehrasa » Sun Nov 20, 2011 11:50 am
if u want to calculate it algebraically
the Q ask whether p(r)>p(w) we know that p(r)= r/r+w+b and p(w)=w/w+b+r

stat1) r/b+w>w/b+r
first we reciprocate the fractions then the inequality sign flip ==> b+w/r<b+r/w ==> we can add i to both statement but wisely we add r/r to first side and w/w to the second side ===> b+w+r/r<b+r+w/w ==> now again reciprocate and the sign also flip ==> r/b+w+r > w/b+w+r
seems familiar ?! ya we found what we were looking for ==> sufficient
answer is A
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by pemdas » Sun Nov 20, 2011 12:24 pm
wow, such a plethora of reciprocals and changes in sign, why?
mehrasa wrote:if u want to calculate it algebraically
the Q ask whether p(r)>p(w) we know that p(r)= r/r+w+b and p(w)=w/w+b+r

stat1) r/b+w>w/b+r
first we reciprocate the fractions then the inequality sign flip ==> b+w/r<b+r/w ==> we can add i to both statement but wisely we add r/r to first side and w/w to the second side ===> b+w+r/r<b+r+w/w ==> now again reciprocate and the sign also flip ==> r/b+w+r > w/b+w+r
seems familiar ?! ya we found what we were looking for ==> sufficient
answer is A
p(r)>p(w)? OR r/(r+b+w) > w/(r+b+w)? OR r>w?
st(1) r(b+r)>w(b+w) here we have 'b' on both sides of the inequality, so this suggests r>w Sufficient
st(2) r<b-w we know only r<b and nothing about w <,>,= r Not Sufficient.

a
i_have_no_cool_username wrote:A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is 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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