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A box contains white marbles and black marbles, all identical except f
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25 Oct 2021, 05:18
25 Oct 2021, 05:18
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Question Stats:
90% (01:50) correct
9% (00:49) wrong based on 22 sessions
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A box contains white marbles and black marbles, all identical except for color. If one marble is drawn at random, the probability that it is a white marble is \(\frac{7}{8}\) . Six white marbles are added to the box, but no black marbles are added. Now, if one marble is drawn at random, the probability that it is a white marble is \(\frac{x}{y}\)
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(\frac{x}{y}\) |
\(\frac{14}{15}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Re: A box contains white marbles and black marbles, all identical except f
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25 Oct 2021, 13:56
25 Oct 2021, 13:56
1
The minimum number of marbles in the box is 8 (7 of which are white). If we increase the number of marbles by 6, we have 13 white marbles and 14 total marbles, so the new probability is 13/14 < 14/15. In the general case, we have 7*N white marbles and 8*N total marbles to start, and 7*N + 6/8*N+6 after adding the 6 white marbles. To prove the general case, let 7N + 6/8N+6 <14/15, then
(7N+6)*15 < (8N+6)*14,
105N + 90 < 112N + 84,
-7N < -6,
N > 6/7,
which must be true since N is a positive integer. Therefore the correct answer is B
(7N+6)*15 < (8N+6)*14,
105N + 90 < 112N + 84,
-7N < -6,
N > 6/7,
which must be true since N is a positive integer. Therefore the correct answer is B
gmatclubot
Re: A box contains white marbles and black marbles, all identical except f [#permalink]
25 Oct 2021, 13:56
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