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