Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 7 Number Sense
Problem
1) A game comes with three types of cards: Easy, Medium, and Hard. You can buy expansion packs to make you collection bigger. Every pack comes in the ratio 5:4:3, so for every 5 Easy cards there are 4 Medium cards and 3 Hard cards. Evan buys some expansion packs and now has a collection of cards that is complete and has 24 medium cards. How many cards are in his collection?

2) When you simplify the terms in the following sequence to reduced fractions an interesting pattern occurs. Find out what it is and use it to determine the value of the tenth term as a reduced fraction.

Problem
3) Junie hits on a phenomenal idea and sends text messages to 10 friends. These 10 friends simultaneously text 10 more friends. They then send the idea on by simultaneously texting 10 more friends. Assuming each text message always reaches a new person and each round of texting 10 friends takes 2 minutes, how long before 10 million people have Junie's idea texted to them?

4) How many fractions when reduced to lowest terms have denominators smaller than 10 and are between 0.29 and 0.81 on the number line?

5) Take a number with exactly 4 factors and another with exactly 3 factors. Multiply the two numbers. What is the difference between the greatest number of factors the product could have and the fewest number of factors the product could have?