Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 8 Number Sense

Problem
1) Cameron is trying to improve his catch percentage playing football. This season he has caught 60% of the 25 passes that have been thrown to him. After practicing, he is able to bring his catch percentage up to 70% after 25 more passes. How many of those passes did he catch in the second set of 25 passes?

2) If you insert four numbers between 2/7 and 7/2 to form an arithmetic sequence of six numbers, what would the sum of the sequence be? (Express your answer as an improper fraction.)

3) Marsha bakes a cake for a party. Several guests take 1/3rd of the cake and split it. A few more guests take half of what is left and split that. Marsha takes a third of the remaining cake for herself. If Marsha evenly divides what is left of the cake between the 4 remaining guests, what fraction of the original cake will each of them receive?

Problem
4) If the pattern below were continued, what number would be directly below 100?

5) How many numbers between 100 and 1,000 have exactly 3 factors?