Multiple choice

The tests in John's arithmetic class always have 100 points. The teacher gives ten tests to the class. If the scores of John's first five tests are 80, 40, 60, 70, and 50 and he does not score lower than 50 in any of the remaining tests, his average points will always be

  1. greater than 50

  2. greater than 60

  3. between 40 and 50

  4. between 50 and 60

  5. between 80 and 90
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A Correct answer
Explanation

John has 5 tests with scores 80, 40, 60, 70, 50 (sum = 300). For the remaining 5 tests, he scores at least 50 each (minimum sum = 250). The total sum is at least 550, so the average is at least 550/10 = 55.

AI explanation

The total points from the first five tests is 80 plus 40 plus 60 plus 70 plus 50, which equals 300 points. If he scores exactly 50 points in each of the remaining five tests, the minimum possible total points for all ten tests becomes 300 plus 250, which equals 550. Dividing this minimum total by 10 gives a minimum possible average of 55. Since any score above 50 on the remaining tests will raise this average, his average will always be greater than 50.

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