2017 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 25 Hard

Last year Isabella took 7 math tests and received 7 different scores, each an integer between 91 and 100, inclusive. After each test she noticed that the average of her test scores was an integer. Her score on the seventh test was 95. What was her score on the sixth test? (2017 AMC 10B Problem, Question#25)

  • A.

    92

  • B.

    94

  • C.

    96

  • D.

    98

  • E.

    100

Answer:E

Since all of the scores arefrom 91- 100, we can 'subtract' 90 off from all of the scores. Basically, we're looking at the units digits except for 100; we're looking at 10 in this case. Since the last score Was a 95, the sum of the scores from the first six tests must be 2 mod 7 and 0 mod 6. Trying out a few cases, the only solution possibleis 30 (this is from adding numbers 1-10). The sixth test score must be 0 mod 5 because 30≡0 mod 5. The only possible test scores are 95 and 100, so the answer is \boxed{\left( \text{E}\right)100}.