Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 7 Number Sense
Problem

1) How many times larger is (1⁄9)3 than (1⁄3)9 ?

2) Emanuel's class average this week is 89.1, which is a 15.5% increase over last week. What was Emanuel's class average for the previous week? Express your answer to the nearest tenth.

3) Simplify the equations in the following sequence to fractions and solve for the 7th term in the sequence:

Problem

4) Carol has a collection of bottle caps. When she stacks them in piles of 5, she has 1 cap left over. When she stacks them in piles of 6, she has 3 caps left over. When she stacks them in piles of 7, she has 4 left over. What is the fewest number of bottle caps she could have in her collection?

5) A pirate crew divides a bounty of 1000 gold pieces between each other. The captain and the second mate take 1/4th and 1/10th of the loot, respectively. The first mate gets the average of what the previous two took. If the remaining 19 pirates split the rest of the gold evenly, how much does each of them receive?