GMAT prep2 Probability
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- Morgoth
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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.
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.
-
- Master | Next Rank: 500 Posts
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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
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