Problem:
There is a list of seven numbers. The average of the first four numbers is , and the average of the last four numbers is . If the average of all seven numbers is , then the number common to both sets of four numbers is
Answer Choices:
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Solution:
Since the average of all seven numbers is , the sum of the seven numbers is . The sum of the first four numbers is and the sum of the last four numbers is . Since the fourth number is used in each of these two sums, the fourth number must be .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions