Data Sufficiency

A question from GMATPrep.

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

I'll post the answer after a few repplies.
Hope one of you can help me out here.

Thnx,
-B

Answer should be A

Q asks "is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white ? "

this is possible only if r>w

stm1 :
r/(b+w) > w/(b+r)

i.e. r(b + r) > w (b + w)

now since b is same(constant) in both expressions so r>w to make the expression true

hence SUFF

stmt 2: b-w >r
this would be possible for both the cases r>w & w>r

i.e b =20 ,w =14 ,r =5

& b=10, w =2 & r = 6

so Insuff

Thanks.
The Ans is A.

So is brute force substitution the thumb for most such problems ? I was pretty pressed for time, tried a few values and couldn't get it right and moved on..

-B

I did this way:
the prob of taking red ball out = r/b+w+r
for white ball = w/b+w+r
the question is whether r/b+w+r > w/b+w+r
or we have to find whether r > w
According to 1
r/(b+w) > w/(b+r)
Add 1 to both sides
this makes r+b+w/b+w>r+b+w/b+r
this givesb+r > b+w which means r > w SUFF
2.b - w > r
here we don't know if w>r or w<r
hence A

nice trick! Thanks for the explanation!

-B

one more shot,

we need to prove

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

cross multiplying

= r^2 + br+wr > wr+bw+w^2
= r^2+br > bw+ w^2
= r/(b+w) > w/(b+r)

which is the given first condition
hence A is suff.

b is not suff because, b>r+w is given, but it doesnt say anything about r and w.