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The average of non-zero number and its square is 5 times the number. The number is__________?

Correct answer: A. 9

  • A. 9
  • B. 17
  • C. 29
  • D. 295

Explanation

Let the non-zero number be n. Its average with its square is (n + n²) / 2, and this equals 5n. Since n is non-zero, dividing by n gives (1 + n) / 2 = 5, so n + 1 = 10 and n = 9. A student may choose 17 by mishandling the division by 2 or the factor n.

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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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