jpfg259 wrote:
A bag contains a total of 20 only red and white marbles, fewer than half of which are red. Two marbles are to be drawn simultaneously from the bag. How many marbles in bag are red?
(1) The probability that the two marbles to be drawn will be red is 1/19.
(2) The probability that one marble to be drawn will be red and the other will be white is 15/19.
Let red marbles be x
White marbles be y
x + y = 20
We don’t know how much is x but we know it is less than 10
x could be 9,8,7,6,5 etc..
We are given a probability of 2 red marbles to be 1/19
This is a unique value and without any inputs it is enough to know how many red marbles. This sufficient, however for the sake of explaining how it is sufficient.
It is in this form (x/20)*(x-1)/19 = 1/19
It then becomes x^2 - x - 20 = 0
(x-5) (x+4) we know x cannot be negative so x = 5.
Sufficient.
We are given x/20 * y/19 = 15/19
x * y * 2 = 300
x * y = 150
x * (20 - x) = 150
20x - x^2 = 150
x^2 - 20x + 150 = 0
Here it seems something is off because the sum of roots = 20 however the product of the roots is 150 which is not possible.
However, as
GMATinsight mentioned something must be adjusted for it to give a sufficient answer.
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