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21 Apr 2015, 05:59
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D
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Difficulty:
65%
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Question Stats:
64% (02:30) correct
36%
(02:18)
wrong
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A jar contains only black marbles and white marbles. If two thirds of the marbles are black, how many white marbles are in the jar?
(1) If two marbles were to be drawn, simultaneously and at random, from the jar, there is a 5/12 probability that both would be black.
(2) If one white marble were removed from the jar, there would be a 1/4 probability that the next randomly-drawn marble would be white.
(1) If two marbles were to be drawn, simultaneously and at random, from the jar, there is a 5/12 probability that both would be black.
(2) If one white marble were removed from the jar, there would be a 1/4 probability that the next randomly-drawn marble would be white.
21 Apr 2015, 08:01
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Bunuel
1) probability of first blacck marble equal \(\frac{2}{3}\). if we multiply this probability on probability second black marble, we receive common probability \(\frac{5}{12}\)
Let's x be second probability
\(\frac{2}{3} * x = \frac{5}{12}\)
\(x = \frac{5}{8}\) and this probability after we remove one marble, so initially we have 9 marbles in total and \(\frac{1}{3}\) of them white: 3 white marbles
Sufficient
2) let's x be total marbles
\(\frac{1}{3}x-1 = \frac{1}{4}(x-1)\)
\(x = 9\) marbles in total and \(\frac{1}{3}\) of them white: 3 white marbles
Sufficient.
Answer is D
General Discussion
10 Mar 2016, 19:31
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suppose we have X white, and 2X black
total 3X
now..
1 - probability that 2 black is:
2/3 * Y(variable) = 5/12
y=5/12*3/2
y=5/8
since y must be: (x-1)/(3x-1)
it must be true that there are 9 marbles, out of which 6 black and 2 white. sufficient
2. to draw a second white is 1/4
it must be true that x-1/3x-1 = 1/4
4x-1 = 3x-1
x=3.
sufficient.
total 3X
now..
1 - probability that 2 black is:
2/3 * Y(variable) = 5/12
y=5/12*3/2
y=5/8
since y must be: (x-1)/(3x-1)
it must be true that there are 9 marbles, out of which 6 black and 2 white. sufficient
2. to draw a second white is 1/4
it must be true that x-1/3x-1 = 1/4
4x-1 = 3x-1
x=3.
sufficient.
