Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 6 Number Sense


Problem
1) Sally is thinking of a three digit number and she tells you this. All the digits are different. Arranging the digits in one order creates an odd number divisible by 5 and 3. Arranging the digits in another order makes a number divisible by 2 and 5. Arranging the digits in a third order creates a number which factors as the product of two primes. The number is the biggest one you can make with the three digits. What is the number?

2) A recipe for fruit punch says to use 8 ounces of orange juice for every 3 ounces of grape juice. Nicky made 99 ounces of fruit punch. How many more ounces of orange juice than grape juice were used?

3) Lance's sandwich shop sold 4 kinds of sandwiches yesterday. For every bologna sandwich sold, 3 turkey sandwiches were sold. For every turkey sandwich sold 1.5 ham sandwiches were sold. 30 roast beef sandwiches were sold. If only whole sandwiches were sold and bologna sandwiches made up 10% of the total number of sandwiches sold, how many bologna sandwiches were sold?

Problem

4) M is a mystery number. Take 2/3M, divide it by 0.1, multiply it by 1.2, and finally multiply it by 1/8. If the resulting number is N, what is M/N?

5) Rory draws a number line representing his street. His school is at 0. His house is at 4. Sam's house is at -12, Tina's is at -7, and Demi's is at 14. They each take turns being the first to leave their house and bike to the other three before arriving at school together. Compare Demi's shortest possible trip to Sam's shortest possible trip, whose is longer and by how many units?