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14 Feb 2024, 08:07
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Blue: 40
Total: 100
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
83% (01:49) correct
17%
(01:51)
wrong
based on 691
sessions
History
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The probability of drawing a red ball from a bag containing only red and blue balls is 0.2 higher than the probability of drawing a blue ball.
Select for Blue the number of blue balls that could be in the bag, and select for Total the total number of balls that could be in the bag that would be jointly consistent with the given information. Make only two selections, one in each column.
Select for Blue the number of blue balls that could be in the bag, and select for Total the total number of balls that could be in the bag that would be jointly consistent with the given information. Make only two selections, one in each column.
| Blue | Total | |
| 10 | ||
| 40 | ||
| 50 | ||
| 60 | ||
| 100 |
ShowHide Answer
Official Answer
Blue: 40
Total: 100
03 Feb 2025, 02:43
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Bunuel
Official Solution:
We are given that P(red) = P(blue) + 0.2. Since there are only red and blue balls in the bag, we also have P(red) + P(blue) = 1.
Solving this system of equations gives P(blue) = 0.4 and P(red) = 0.6. This implies that the ratio of blue balls to the total number of balls is 4:10.
From the available options, only 40 for blue and 100 for the total maintains this ratio.
Correct answer:
Blue "40"
Total "100"
Attachment:
GMAT-Club-Forum-govw0lk4.png [ 8.13 KiB | Viewed 3280 times ]
23 Apr 2025, 21:11
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1. The question basically tells us to figure out the quantity of both colored balls.
2. Let the number of red and blue balls be r and b, respectively.
3. The probability of drawing a red ball is \(\frac{r}{r + b}\) and the probability of drawing a blue ball is \(\frac{b}{r + b}\). That means, \(\frac{r}{r + b} - \frac{b}{r + b} = 0.2 = \frac{r - b}{r + b} \rightarrow 0.2r + 0.2b = r - b \rightarrow 1.2b = 0.8r \rightarrow r = 1.5b\).
4. We're interested in finding a possible combination of b and r + b, in other words, b and 1.5b + b = 2.5b.
5. The only combination with a ratio of 2.5 is 40 and 100.
6. Our answer will be: Blue - 40 and Total - 100.
2. Let the number of red and blue balls be r and b, respectively.
3. The probability of drawing a red ball is \(\frac{r}{r + b}\) and the probability of drawing a blue ball is \(\frac{b}{r + b}\). That means, \(\frac{r}{r + b} - \frac{b}{r + b} = 0.2 = \frac{r - b}{r + b} \rightarrow 0.2r + 0.2b = r - b \rightarrow 1.2b = 0.8r \rightarrow r = 1.5b\).
4. We're interested in finding a possible combination of b and r + b, in other words, b and 1.5b + b = 2.5b.
5. The only combination with a ratio of 2.5 is 40 and 100.
6. Our answer will be: Blue - 40 and Total - 100.
