Visit http://www.moems.org/zinger.htm to find out the answer to the November problem.
MOEMS posts a problem of the month each month at http://www.moems.org/zinger.htm
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.
1) The weight of a glass bowl and the marbles it contains is 50 ounces. If the number of marbles in the bowl is doubled, the total weight of the bowl and marbles is 92 ounces. What is
the weight of the bowl? (Assume that each of the marbles has the same weight).
2) Square ABCD and rectangle AEFG each have an area of 36 square meters. E is the midpoint of AB. What is the perimeter of rectangle AEFG?
3) A slow clock loses 3 minutes every hour. Suppose the slow clock and a correct clock both show the correct time at 9 A.M. What time will the slow clock show when the correct clock
shows 10 o'clock the evening of the same day?
1) Method 1: Since the weight of one bowl and the marbles it contains is 50 ounces, the weight of two bowls and twice as many marbles is 100 ounces. It is given that the weight of one
bowl and twice as many marbles is 92 ounces. Then the difference of weights between 100 ounces and 92 ounces is the weight of the bowl, or 8 ounces.
Method 2: The increase in weight from 50 ounces to 92 ounces occurs because the weight of the marbles is doubled. That increase therefore is the weight of the original set of
marbles, 42 ounces. If follows that the bowl weighs 8 ounces.
2) The length of a side of the square is 6m. The dimensions of rectangle AEFG are 3m and 12m. The perimeter of the rectangle is 2 x (3m + 12m) which is equivalent to 30 m.
3) There are 13 hours between 9 AM and 10 PM. Thus the slow clock will lose 13 x 3 or 39 minutes and show 9:21 or 21:21 on a 24-hour clock