Marbles

[crackgmat007]

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

OA - A
Rephrase --> is r>w

In stmt 1, since b is added to the both denominators, can I say that b = 0 (for computations sake) and get r/w > w/r; simplifying, I get rephrase r>w.

Is my approach correct? Thoughts pls!

[ashis979]

Yup, question is indeed asking "is r>w?"

I would have done it this way (probably the same thing as you have, but just makes more sense to me)

Let the total number of marbles be X. Therefore, X=b+w+r

Stmt 1:
r/(b+w)>w/(b+r)
=> r/(b+w+r-r)>w/(b+r+w-w)
=> r/(X-r)>w/(X-w)
=> rX-rw>wX-rw (okay to cross multiply because X has to be greater than both r and w)
=> rX>wX
=> r>w (okay to cancel out since X>0)
Therefore Stmt 1 is SUFFICIENT.

Stmt 2 obviously insufficent.