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E
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Difficulty:
45%
(medium)
Question Stats:
76% (02:28) correct
24%
(02:53)
wrong
based on 231
sessions
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Not Attempted Yet
12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
Three classes, Alpha, Beta, and Gamma, with no student overlap, take a test. The average (arithmetic mean) score in class Alpha is 40, in class Beta is 68, and in class Gamma is 62. The combined average score of classes Alpha and Beta is 61, while the combined average score of classes Alpha and Gamma is 42. What is the ratio of the number of students in classes Alpha, Beta, and Gamma?
A. 1:3:1
B. 1:3:10
C. 1:30:10
D. 5:15:1
E. 10:30:1
Three classes, Alpha, Beta, and Gamma, with no student overlap, take a test. The average (arithmetic mean) score in class Alpha is 40, in class Beta is 68, and in class Gamma is 62. The combined average score of classes Alpha and Beta is 61, while the combined average score of classes Alpha and Gamma is 42. What is the ratio of the number of students in classes Alpha, Beta, and Gamma?
A. 1:3:1
B. 1:3:10
C. 1:30:10
D. 5:15:1
E. 10:30:1
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20 Dec 2023, 06:42
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GMAT Club Official Explanation:
Three classes, Alpha, Beta, and Gamma, with no student overlap, take a test. The average (arithmetic mean) score in class Alpha is 40, in class Beta is 68, and in class Gamma is 62. The combined average score of classes Alpha and Beta is 61, while the combined average score of classes Alpha and Gamma is 42. What is the ratio of the number of students in classes Alpha, Beta, and Gamma?
A. 1:3:1
B. 1:3:10
C. 1:30:10
D. 5:15:1
E. 10:30:1
Let the number of students in classes Alpha, Beta, and Gamma be a, b, and g, respectively. Then the total scores for these classes will be 40a, 68b, and 62g, respectively.
Since the combined average score of classes Alpha and Beta is 61, then 40a + 68b = 61(a + b) (note that both sides of the equation represent the combined score of classes Alpha and Beta). Simplifying the equation, we get 3a = b.
Similarly, the combined average score of classes Alpha and Gamma being 42 means 40a + 62g = 42(a + g), which simplifies to a = 10g.
Thus, we have 3a = b and a = 10g. Therefore, the ratio a : b : g = a : (3a) : (a/10). Multiplying by 10 yields 10a : 30a : a, which simplifies to 10 : 30 : 1.
Answer: E.
General Discussion
19 Dec 2023, 13:09
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Bunuel
12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
Three classes, Alpha, Beta, and Gamma, with no student overlap, take a test. The average (arithmetic mean) score in class Alpha is 40, in class Beta is 68, and in class Gamma is 62. The combined average score of classes Alpha and Beta is 61, while the combined average score of classes Alpha and Gamma is 42. What is the ratio of the number of students in classes Alpha, Beta, and Gamma?
A. 1:3:1
B. 1:3:10
C. 1:30:10
D. 5:15:1
E. 10:30:1
Three classes, Alpha, Beta, and Gamma, with no student overlap, take a test. The average (arithmetic mean) score in class Alpha is 40, in class Beta is 68, and in class Gamma is 62. The combined average score of classes Alpha and Beta is 61, while the combined average score of classes Alpha and Gamma is 42. What is the ratio of the number of students in classes Alpha, Beta, and Gamma?
A. 1:3:1
B. 1:3:10
C. 1:30:10
D. 5:15:1
E. 10:30:1
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Number of students in Alpha = a
Number of students in Beta = b
Number of students in Gamma = g
(40a+68b)/(a+b) = 61
Solving we get b = 3a
(40a+62g)/(a+g) = 42
Solving we get a = 10g
b = 30g
10g : 30g : g
IMO E
