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A teacher gave the same test to three history classes: A, B,
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07 Sep 2020, 04:48
07 Sep 2020, 04:48
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Question Stats:
75% (01:23) correct
25% (00:31) wrong based on 52 sessions
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A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
A. 74
B. 75
C. 76
D. 77
E. 78
A. 74
B. 75
C. 76
D. 77
E. 78
Re: A teacher gave the same test to three history classes: A, B,
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07 Sep 2020, 04:49
07 Sep 2020, 04:49
Expert Reply
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
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A teacher gave the same test to three history classes: A, B,
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07 Sep 2020, 05:59
07 Sep 2020, 05:59
1
Carcass wrote:
A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
A. 74
B. 75
C. 76
D. 77
E. 78
A. 74
B. 75
C. 76
D. 77
E. 78
This is a weighted averages question, so we can use the following formula:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
Ratio of classes A, B, C = 4 : 6 : 5, respectively
4 + 6 + 5 = 15
So, class A represents 4/15 of the TOTAL population
Class B represents 6/15 of the TOTAL population
Class C represents 5/15 of the TOTAL population
So, weighted average of 3 groups combined = (4/15)(65) + (6/15)(80) + (5/15)(77)
= 260/15 + 480/15 + 385/15
= 1125/15
= 75
Answer: B
