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Washington State Math Olympiad
Hints and Solutions
2012 Grade 8 Number Sense
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1) Joey is playing a game where winning means getting the biggest product. He rolls a 6 sided die 5 times getting the numbers 1, 3, 4, 5, 6. He creates a 3 digit number and a 2
digit number using each digit once. He wins if the product of his two numbers is bigger than the products of his competitors. What should his 3 digit number be?
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2) Initially on Michael's hands there are 3.9 x 106
bacteria. He sprays his hands with a hand sanitizer, killing 99.5% of them. He then washes his hands twice, removing 10% of
the remaining bacteria each time. How many bacteria are left? Express your answer in scientific notation.
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3) The expression represented by the boxes is the
quotient of a 2-digit number raised to an exponent by a 2-digit number raised to an exponent. Each box represents a digit from the list 1, 2, 3, 4, 5, and 6 with no repeats. To make the resulting quotient as small as possible what is the second 2-digit number
represented by the fourth and fifth box?
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