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WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD Session
II: SIXTH GRADE ALGEBRAIC SENSE |
6 |
1.
When a one-digit
number is multiplied by 6, it increases by 20. What is the one-digit number?
2.
There are bicycles
and tricycles in the yard. There are a
total of 30 seats and 70 wheels. How
many tricycles are there?
3.
The total number of
spheres (N) needed to make a triangular pyramid is given by the equation
N = X3 + X2 + X --- --- --- 6 2 3
where X is the number of layers. If I make a triangular pyramid with 8 layers, how many spheres are in the
bottom layer? 
4.
Twelve people rent a
boat. The boat rents for a flat rate,
no matter how many people rent the boat. By taking 8 more people, the cost to each person is reduced by $2.50. How much is the rent for the boat?
Megan is trying to open her combination bicycle lock. The first number was written in the form of a riddle, which read: "2/3 of the number, added to 16, will equal two times as much as the number? What is the first number in the combination?