question stem: r > w ?

Statement I

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

Assume, b=0

r/w > w/r

r^2 > w^2

r > w, since balls cannot be in negative.

Another way of doing this will be by picking numbers, the only way this equation will be satisfied, when r > w.

if, r = 6, w=3 , b=1

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

6/4 > 3/7

if, r = 4, w=5, b=1

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

4/6 > 5/5


Therefore, r > w. Sufficient.

Statement II

b - w > r

We need to know individual values of b, w and r

if b=12, w=5, r= 6

12 -5 > 6

7> 6

but, r>w

if b=12, w=7, r=4

12 - 7 > 4

5 > 4

but, r < w

Insufficient.

Hence A.

Hope this helps.

This is a simple question if you know a definition of probability

P(red) = Red / Total

we are asked whether P(red) > P(white)

Statement I : r/b+w > w/b+r

r/b+w +1 > w/b+r +1

r+b+w /b+w > w+b+r/b+r

b+r > b+w

r > w , hence r/b+w+r > w/b+w+r or P(r)> P(w)

Hence statement I is sufficient


Statement II : b-w > r -------------> b > w+r insufficient

hence Ans = A