Multiple choice

A professor scores 15 of 20 exams himself and gives the other 5 to his teaching assistant to score. If the average score of the 15 exams graded by the professor is 87, and the average score of all 20 exams is 85, how many points lower is the average score of the teaching assistant’s 5 exams than the average score of the professor’s 15 exams?

  1. 8

  2. 10

  3. 79

  4. 81
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A Correct answer
Explanation

Total points = 20 * 85 = 1700. Professor's points = 15 * 87 = 1305. TA's points = 1700 - 1305 = 395. TA's average = 395 / 5 = 79. Difference = 87 - 79 = 8.

AI explanation

The total score for all 20 exams is 85 times 20, which equals 1700. The professor's 15 exams total 87 times 15, which equals 1305. The teaching assistant's 5 exams total 1700 minus 1305, which equals 395, making their average 395 divided by 5, or 79. The difference between the professor's average and the assistant's average is 87 minus 79, which is 8 points.

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