Here are some challenging word problems that are similar to what 4th and 5th graders experience at a Math Olympiad. Math team members can use these for extra practice and everyone else can use them to help extend your problem solving skills. Solutions are at the bottom of this post.
1) Suppose today is Tuesday. What day of the week will it be 100 days from now?
2) The four-digit numeral 3AA1 is divisible by 9. What does A represent?
3) A purse contains 4 pennies, 2 nickels, 1 dime, and 1 quarter. Different values can be obtained by using one or more coins in the same purse. How many different values can be obtained?
1) Every 7 days from "today" will be Tuesday. Since 98 is a multiple of 7, the 98th day from today will be Tuesday. Then the 100th day from today will be Thursday.
2) If the number is divisible by 9, then the sum of its digits is divisible by 9. The digit sum is 3 + A + A + 1 = 4 + 2A. The digit sum cannot by 9, otherwise A = 2 1/2. So 4 + 2A = 18 which produces
A = 7.
3) The largest amount that can be made is $0.49. Using the given set of coins, any amount from $0.01 to $0.49 can be made. Therefore there are 49 different amounts that can be made.