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The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?

Correct answer: C. 5

  • A. 8
  • B. 6
  • C. 5
  • D. 2

Explanation

Let the four numbers be a, b, c and d. The first three sum to 3 x 16 = 48, the last three sum to 3 x 15 = 45, so d - a = -3; together with a + d = 13, this gives d = 5. The likely mistake is choosing 8 by subtracting the two three-number sums without also using the given sum of the first and last numbers.

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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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