Probability Question from GMATPrep CAT

[i_have_no_cool_username]

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.

[GMATGuruNY]

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

[mehrasa]

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

[pemdas]

wow, such a plethora of reciprocals and changes in sign, why?

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

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