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
Target question: Is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?
We can rephrase the target question as...
REPHRASED target question: Is r > w?
Statement 1: r/(b + w) > w/(b + r)
Let's let T = the TOTAL number of marbles in the jar.
This means that b + w + r = T
This also means that b + w = T - r
And it means that b + r = T - w
So, we can take statement 1, r/(b + w) > w/(b + r), and rewrite it as...
r/(T - r) > w/(T - w)
Multiply both sides by (T - r) to get: r > w(T - r)/(T - w)
Multiply both sides by (T - w) to get: r(T - w) > w(T - r)
Expand both sides: rT - rw > wT - rw
Add rw to both sides: rT > wT
Divide both sides by T to get:
r > w
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: b - w > r
Add w to both sides to get: b > w + r
All this means is that there are more black marbles than there are white and red marbles combined.
Given this information, there's no way to determine whether or not r is greater than w
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
What I had in mind was: since, 1/3 > 1/5, we can readily simplify it as: 3 < 5. 
