Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 5 Number System

Problem
1) Malou has a collection action figures. If she puts them in groups of 2, there is 1 left over. If she puts them in groups of 3, there is 1 left over. When she puts them in groups of 5, there is 1 left over again. What is the least number of figures she can have?

2) Collectible cards come in packs of 4 or packs of 9. Vidan needs to buy exactly 110 cards. He wants to buy as many of the packs of 9 as he can as they are a better buy. How many packs of 9 should he buy?

3) Hunter, Brock, Sparrow, and Dane all brought pencils to share. Brock brought 3 more than Hunter. Sparrow brought 4 more than Brock, and Dane brought 3 more than Sparrow. They share the pencils evenly between the four of them. How many pencils will Hunter gain?

4) Rigoberto has a large rectangular board with sides 25 inches by 35 inches. He is arranging smaller squares on it in a grid. The side of each smaller square is 2 3/4 inches long. He wants to fit as many of the smaller squares onto the board as he can, but he can neither cut the smaller squares, nor let them overlap. How many of the smaller squares can he fit on the large board?

5) Jude and her friends mowed lawns and were paid with a bag of quarters. They give 3 quarters to Jude's little brother. Anouk then takes 1/5 of the remaining quarters. Then Sara takes 1/4 of what is left. Jude gets the rest, which is 1/2 of the original number of quarters. How many quarters did they originally get?