SOLUTION: A set of five non-negative integers has a mean of 5, a median of 6 and a mode of 7. What is the smallest possible member of the set?

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Question 261179: A set of five non-negative integers has a mean of 5, a median of 6 and a mode of 7. What is the smallest possible member of the set?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
  1. If the mean of the five numbers is 5, then the sum of the five numbers must be 25.
  2. If the median of the five numbers is 6, then two of the five numbers must be lower than 6 and the other two numbers must be larger than 6.
  3. If the mode is 7 then there must be more 7's than any other number. Since there are two numbers above 6 (see #2), they both must be 7's!
  4. So four of the five numbers are: 5, 6, 7 and 7. These four numbers add up to 25. Since the five numbers must add up to 25 (see #1), then the fifth number must be 0!