Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 6 Number Sense

Problem

1) Guess this number from the clues: The least common multiple of this number and 42 is 630. The greatest common factor of this number and 42 is 6.

2) A food stand buys ice cream cones in packages of 8. Each carton of ice cream will make 12 cones. What is the least number of packages of ice cream cones and cartons of ice cream that need to be bought to have no leftover ice cream and no leftover cones?

3) Eddie has saved $1,200 which is 32% of the price of a used car that he wants to buy. What is the price of the car?

4) Rina loves to cook and really dislikes fractions. Every recipe she has she converts to decimals. The latest cookie recipe she has converted asks for 0.125 teaspoons of cloves. Her friend wants to triple the recipe. The only measuring teaspoon he has is the 1/4 teaspoon. How can he best measure the correct amount of cloves?

5) In the diagram the sum
1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96
represents the area of the shaded sections. If the area of the entire rectangle is 1, what is the sum of the areas of the two unshaded regions?