Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 5 Probability & Statistics
Problem
Solution
1) What is the probability of rolling an odd product with two 12 sided dice each numbered 1 through 12? 1. The table to the right is the multiplication table for values up to 12. Study it in order to answer this question.
2. All multiplications that involve an even number result in an even product. This eliminates half the products.
3. Any odd number multiplied by an even number results in an even product. This eliminates half of the products that involve an odd number.
4. See the above figure for the remaining odd products.
There are 36/144 = 1⁄4 of the total products that are odd.
2) The pie chart shows the results of a parking lot survey at a mall on car color. If this survey was based on a sample size of 500 cars, about how many of them were either a red or a black car?
 Add the percentages of red and black cars and multiply by 500 =
    (19% + 13%) x 500 = 32% x 500 = 160 cars.

Problem
Solution
3) The gym teacher wants all 16 children in Mr. Rom's 1st grade class to get to know each other. His plan is to have them work with a different partner each day. How many different partner pairs are possible? This is a combinations problem.
1. How many ways to choose the first partner of a pairing? 16
2. After you choose that partner, how many students can he/she be paired with? 15
3. Since order doesn't count,
    (A paired with B is the same as B paired with A)
    divide this by 2 = (16 x 15)/2 = 120 pairings.
4) Fill in the blanks in the list of numbers such that the only mode for the list will be 9 and the median will be 15.
4, 9, __, __, 13, __, 17, 23, 23, 28
 1. Since there are two 23s in this list, the number of 9s must be 3 to make it the mode.
2. Since there are 10 numbers in this list, the median must be the average of the middle 2 numbers.
3. What number, averaged with 13 is 15?
    This number is (13 + 17)/2 = 15.
4. The completed list is:

    4, 9, 9, 9, 13, 17, 23, 23, 28

5) Joe's dad tells Joe he can have the bag of fruit chews he's holding if he can solve this riddle:
There are three flavors: strawberry, orange and lemon. There are 4 strawberry chews. The probability of getting orange is 3/7. The probability of getting lemon is 2/7. How many fruit chews are in the bag?		 1. Add the probabilities of orange and lemon chews =
    3/7 + 2/7 = 5/7 of the chews
2. Subtract this from 1 = 1 - 5/7 = 2/7.
    This is the probability of a strawberry chew.
3. Using this, compute the total number of chews =
    Let N be the total number of chews.
    (2/7) N = 4
    2N = 28
    N = 14 chews