Lower Elementary
Question: Sally has 6 glasses that each contain water. The first glass has 12 ounces of water, the second glass has 1 less ounce of water than the first, the third has 1 less ounce of water than the second, and so on. Find the total amount of water in all 6 glasses.
Answer: 57 ounces
Note: In decreasing order, the glasses each contain the following amounts of water: 12 oz., 11 oz., 10 oz., 9 oz., 8 oz., 7 oz. To find the total amount of water add the water in all six glasses, add 12 + 11 + 10 + 9 + 8 + 7 = 57.
Upper Elementary
Question: A rectangle has a length of 8 feet and a width of 3 feet. If both the length and width of the rectangle are doubled, what is the perimeter of the new rectangle?
Answer: 44 feet
Note: When the length is doubled it goes from 8 feet to 16 feet. When the width is doubled it goes from 3 feet to 6 feet. To find the perimeter add 16 + 16 + 6 + 6 = 44.
Middle School
Question: Caitlin wrote each of the numbers from 1 through 100. What percent of the numbers have at least one 3?
Answer: 19%
Note: She wrote a total of 100 numbers. There are 19 numbers that contain at least one 3 from 1 to 100.
Algebra and Up
Question: How many different four-digit integers can be formed if the digits 2, 4,5, and 8 must be used only once in each of the integers?
Answer: 48
Note: The four-digit integer can be either positive or negative. First, find the total number of positive integers that can be formed, and then double it to include the negatives of the integers. Now find the total number of combinations for the four digits.
To find the combinations for the positive integers we consider the four places ___ ___ ___ ___. The number of combinations will be the number of choices for the first digit times the number of choices for the second digit times the number of choices for the third digit times the number of choices for the fourth digit.
For the first place there are 4 digits to choose from _4_ ___ ___ ___. Once we’ve used a digit in the first place now we have 3 digits to chose from for the second place _4_ _3_ ___ ___. For the next place value there are only 2 digits to choose from _4_ _3_ _2_ ___. For the final place value there is only one digit left to use _4_ _3_ _2_ _1_. To find the total number of combinations multiply the choices for each of the place values: 4 x 3 x 2 x 1 = 24.
Then counting the opposites of each of these integers we multiply by 2, 24 x 2 = 48.
