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The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?

Correct answer: B. 86

  • A. 58
  • B. 86
  • C. 49
  • D. None of these

Explanation

The total of the four integers is 4 × 69 = 276. After subtracting the highest and least integers, the remaining two have total 276 - 93 - 39 = 144. If their difference is 28, the higher one is (144 + 28) / 2 = 86. The likely mistake is choosing 58, which is the lower remaining integer, not the higher one.

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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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