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16 Sep 2014, 01:02
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The average (arithmetic mean) grade of students in Group 1 is 4, whereas in Group 2, it's 3. If the two groups were merged, what would be the average (arithmetic mean) grade of the combined group?
(1) There are twice as many students in Group 1 as in Group 2
(2) There are 4 more students in Group 1 than in Group 2.
(1) There are twice as many students in Group 1 as in Group 2
(2) There are 4 more students in Group 1 than in Group 2.
16 Sep 2014, 01:02
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Official Solution:
The average (arithmetic mean) grade of students in Group 1 is 4, whereas in Group 2, it's 3. If the two groups were merged, what would be the average (arithmetic mean) grade of the combined group?
This problem deals with weighted averages. Let \(x\) represent the number of students in Group 1 and \(y\) represent the number of students in Group 2. Then, the combined average score is given by: \(\text{average} = \frac{4x + 3y}{x + y}\).
(1) There are twice as many students in Group 1 as in Group 2.
From this, we deduce: \(x = 2y\). Substituting into our average equation, we get: \(\text{average} =\frac{4x + 3y}{x + y} = \frac{4*2y + 3y}{2y + y} =\frac{11}{3}\). Sufficient.
(2) There are 4 more students in Group 1 than in Group 2.
From this, we deduce: \(x = y + 4\). This information alone is not sufficient to determine the average score.
Answer: A
The average (arithmetic mean) grade of students in Group 1 is 4, whereas in Group 2, it's 3. If the two groups were merged, what would be the average (arithmetic mean) grade of the combined group?
This problem deals with weighted averages. Let \(x\) represent the number of students in Group 1 and \(y\) represent the number of students in Group 2. Then, the combined average score is given by: \(\text{average} = \frac{4x + 3y}{x + y}\).
(1) There are twice as many students in Group 1 as in Group 2.
From this, we deduce: \(x = 2y\). Substituting into our average equation, we get: \(\text{average} =\frac{4x + 3y}{x + y} = \frac{4*2y + 3y}{2y + y} =\frac{11}{3}\). Sufficient.
(2) There are 4 more students in Group 1 than in Group 2.
From this, we deduce: \(x = y + 4\). This information alone is not sufficient to determine the average score.
Answer: A
19 Oct 2023, 05:51
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
