Hands-on math!

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

1) How many times larger is (1⁄9)3 than (1⁄3)9 ?
  • Method 1: Brute force!
    Compute each term and divide
    (using your calculator that does exponents):



    = _____
  • Method 2: Combine the exponents



    = ______

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. 		Let x = Emanuel's average for the previous week.
Divide this week's average by 1 + the increase to get the original average = __________

3) Simplify the equations in the following sequence to fractions and solve for the 7th term in the sequence:
  • First term = 1 1⁄4 = _______________

  • Second term = ________________

  • Third term = _____________________
  • Calling the fraction A / B, each successive element is
    ____ / _____ of the previous element, so, extending this to the 7th term:
    Fourth term = ____________

    Fifth term = _____________

    Sixth term = _____________

    7th term = _______________

Problem
Hint

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? 		The only way this editor knows how to solve this kind of problem is the brute force method: list the combinations and find which ones have the same term
  • By 5s+1 : _____________________________

  • By 6s+3 : ______________________________

  • By 7s+4: _______________________________
Carol has at least ____ bottle caps.

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?
  1. The fractions taken by the captain and the second mate are:


    = _____
  2. The first mate gets _______________
  3. The captain, the second mate and the first mate get, together,
    = ___________________
  4. The remaining pirates get _______ gold pieces each