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Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?

Correct answer: A. 1 year

  • A. 1 year
  • B. 1.5 years
  • C. 2 years
  • D. 2.5 years

Explanation

Three years ago, the six family members had a total age of 6 x 19 = 114 years. Today those six members together are 114 + 6 x 3 = 132 years old; with the boy included, the total for seven members at the same 19-year average is 7 x 19 = 133 years. Thus the boy's age is 133 - 132 = 1 year. The likely trap is 1.5 years, which results from distributing the three-year change incorrectly across the seven current members.

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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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