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13 Jan 2025, 01:30
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Difficulty:
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30% (02:11) correct
70%
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wrong
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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.
(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.
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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13 Jan 2025, 04:55
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Bunuel
r + w = 20
r < 10
r?
Statement 1 - rC2/20C2 = 1/19
(r*(r-1))/(20*19) = 1/19
r*(r-1) = 20
r = 5 or r = -4
As r needs to be positive, r = 5. Hence sufficient.
Statement 2 - rC1*wC1/20C2 = 15/19
(r*w)/(20*19/2) = 15/19
r*w = 15*10
r*(20-r) = 150
r^2 - 20r + 150 = 0
As b^2 - 4ac < 0, no integer solutions exist for this quadratic. Hence, insufficient.
IMO: A
Bunuel, Unless I missed something, is the probability value correct for Statement 2 as per GMAT standard? I haven't seen DS questions failing for non-real roots as mostly they fail for out of scope values.
13 Jan 2025, 07:00
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Bunuel
r (red) + w (white) = 20; r < 10
We need to find the vlaue of r
S1: p(both red) = rC2/20C2 = r(r-1)/380
=> r(r-1)/380 = 1/19 => r(r-1) = 20 => r = 5 (only viable solution) - Sufficient
S2: p(one red and one white) = rC1 * (20-r)C1 / 20C2 = r(20-r)/190
=> r(20-r)/190 = 15/19 => r(20-r) = 150.
However, for r(20-r), the max value would be when r = 10, making ech term 10, hence having product 100. Thus, there cannot be a solution to this equation, implying that the statement itself is wrong
## I feel that in a proper DS question, we need to assume that the information in the statements is correct and on that basis, check if a solution is possible. Here, however, the statement itself is wrong.
If we change the statement to " The probability that one marble to be drawn will be red and the other will be white is less than 15/19 ", then it will be fine since that will be true for all possible values of r and the statement will be insufficient.
