WoundedTiger wrote:
chetan86 wrote:
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?
(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.
(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.
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Let there be R,Y and B red,yellow and blue balls be there initially. We need to find out Y-R = ?
St 1 basically says that
B+Y=14 ( many combinations possible )
B : Y
1:13
2:12
3:11
4:10....
Not sufficient
St 2 says
R+B=8R: B
1:7
2:6
3:5
4:4
5:3...
Combining we see that Blue balls cannot be more than 7, So if
B=7, R=1 and Y=7 Y-R=6
B=6,R=2, and Y=8 then 8-2=6
If B=4,R=4, then Y=10 Y-R=6..
For all values Y-R=6...
Ans is C
Little correction: it should be Y + B = 13 and R + B = 7.
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?We need to find Y - R.
(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.
This implies that Y + B = 13 because only if there are total of 13 blue and yellow marbles, removing 14 marbles guarantees getting a red one: you should pick all blue and yellow and the next one for sure will be red. But knowing that B + Y = 13 is not enough to get Y - R. Not sufficient.
(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.
The same ways as above this means that R + B = 7. Not sufficient.
(1)+(2) Subtract R + B = 7 from Y + B = 13: (Y + B) - (R + B) = 13 - 7 --> Y - R = 6. Sufficient.
Answer: C.
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80% (01:37) correct 
