Problem 13 · 2009 Math Kangaroo
Stretch
Logic & Word Problems
sum-constraintcasework
Maria can score 0, 1, 2, 3, 4 or 5 points on a test. After 4 tests she has a mean of exactly 4. One of the following statements therefore cannot be true. Which one is it?
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Answer: E — Maria scored 3 exactly three times.
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Hint 1 of 2
A mean of 4 over 4 tests means the four scores total 16.
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Hint 2 of 2
Check which statement forces a score above the maximum of 5.
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Approach: test each statement against total = 16 and max score 5
- Four scores averaging 4 must sum to 16, with each score between 0 and 5.
- Three scores of 3 already total 9, leaving 7 for the last test — impossible since the max is 5.
- Every other statement can be completed within the rules, so the impossible one is E.
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