2017 AMC 10 B
Complete problem set with solutions and individual problem pages
Last year Isabella took math tests and received different scores, each an integer between and , inclusive. After each test she noticed that the average of her test scores was an integer. Her score on the seventh test was . What was her score on the sixth test? (2017 AMC 10B Problem, Question#25)
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Since all of the scores arefrom , we can 'subtract' 90 off from all of the scores. Basically, we're looking at the units digits except for ; we're looking at in this case. Since the last score Was a , the sum of the scores from the first six tests must be mod and mod . Trying out a few cases, the only solution possibleis (this is from adding numbers ). The sixth test score must be mod because mod . The only possible test scores are and , so the answer is .
