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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