NandishSS wrote:Prof Liu gave the same quiz to the students in her morning class and in her afternoon class. the average score for the two classes combined was 84. which class had more students?
(1) The average score for the students in the morning class was 80
(2) the average score for the students in the afternoon class was 86
Statement 1:
Case 1: Average score for the afternoon class was 86.
Here, the average for the MIXTURE of the two classes (84) is closer to the average for the afternoon class (86) than to the average for the morning class (80).
Since the average for the mixture is weighted toward the average for the afternoon class, the AFTERNOON class had more students.
Case 2: Average score for the afternoon class was 100.
Here, the average for the MIXTURE of the two classes (84) is closer to the average for the morning class (80) than to the average for the afternoon class (100).
Since the average for the mixture is weighted toward the average for the morning class, the MORNING class had more students.
INSUFFICIENT.
Statement 2:
Case 1 also satisfies Statement 2.
In Case 1, the AFTERNOON class had more students.
Case 3: Average score for the morning class was 83.
Here, the average for the MIXTURE of the two classes (84) is closer to the average for the morning class (83) than to the average for the afternoon class (86).
Since the average for the mixture is weighted toward the average for the morning class, the MORNING class had more students.
INSUFFICIENT.
Statements combined:
Only Case 1 satisfies both statements.
In Case, 1, the afternoon class had more students.
SUFFICIENT.
The correct answer is
C.
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