Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2015 Grade 5 Number Sense

Problem
1) Jason is playing with a stack of cards. He divides the cards into 3 equal piles. Then he takes one pile and divides it into 4 equal piles. Then he takes one of the four equally divided piles and further divides it into 5 equal piles. If one of the five equally divided piles contains 3 cards, how many cards in total are in Jason's stack?

2) The sum of two numbers is 22 and their product is 96. What is the ratio of the two numbers when expressed as a proper fraction in lowest terms?

3) Anna has 10 more sheets of paper than Mary. Mary has 7 more sheets of paper than Caroline. They decide to split all of the paper between them equally. How many less sheets of paper would Anna have?

4) Jeremy baked a cake. Sue cut the cake into equal-sized pieces and took one piece. Nathan took 1/5 of the remaining pieces. Finally, Jeremy took 1/3 of the remaining pieces. If 1?2 of the cake is still remaining, how many pieces did Sue cut the cake into?

5) Melissa is competing in a rowing race. She can row 4 miles in 30 minutes. How long would it take her to row the 30 miles in the race if she keeps the same pace? (Express your answer in hours and minutes)