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The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

Correct answer: D. 19

  • A. 0
  • B. 1
  • C. 10
  • D. 19

Explanation

If 19 numbers are greater than 0, the twentieth number can be negative enough to make the total 0, so 19 is possible. All 20 numbers cannot be greater than 0 because their sum would then be positive, not 0. The likely mistake is choosing 10 by assuming half the numbers must be positive and half negative.

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About Averages

An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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