Bunuel wrote:
Three students were given three tests, the results of the first two tests are shown above. Student 1 and Student 3 received equal scores on Test 3. As a result, Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. What was the score Students 1 and 3 received on Test 3?
A. 33
B. 34
C. 35
D. 36
E. 39
We can let x = the score for student 1 and student 3 on test number 3. Thus, the average score for student 1 is:
(30 + 50 + x)/3 = (80 + x)/3
The average for student 3 is:
(14 + 28 + x)/3 = (42 + x)/3
Student 1’s average (arithmetic mean) score over the three tests was 50 percent higher than Student 3’s average. Using that fact, we can create the following equation to determine x:
(80 + x)/3 = 1.5[(42 + x)/3]
(80 + x) = 1.5(42 + x)
80 + x = 63 + 1.5x
17 = 0.5x
34 = x
Answer: B
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