zia
Problem 1
The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of 1-inch squares. What is the area of the logo in square inches?
Solution
Problem 2
Consider these two operations:What is the value of 
Solution
Problem 3
When three positive integers , , and  are multiplied together, their product is . Suppose . In how many ways can the numbers be chosen?
Solution
Problem 4
The letter M in the figure below is first reflected over the line  and then reflected over the line . What is the resulting image?
Solution
Problem 5
Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned  years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is  years. How many years older than Bella is Anna?
Solution
Problem 6
Three positive integers are equally spaced on a number line. The middle number is  and the largest number is  times the smallest number. What is the smallest of these three numbers?
Solution
Problem 7
When the World Wide Web first became popular in the s, download speeds reached a maximum of about  kilobits per second. Approximately how many minutes would the download of a -megabyte song have taken at that speed? (Note that there are  kilobits in a megabyte.)
Solution
Problem 8
What is the value of
Solution
Problem 9
A cup of boiling water () is placed to cool in a room whose temperature remains constant at . Suppose the difference between the water temperature and the room temperature is halved every  minutes. What is the water temperature, in degrees Fahrenheit, after  minutes?
Solution
Problem 10
One sunny day, Ling decided to take a hike in the mountains. She left her house at , drove at a constant speed of  miles per hour, and arrived at the hiking trail at . After hiking for  hours, Ling drove home at a constant speed of  miles per hour. Which of the following graphs best illustrates the distance between Ling’s car and her house over the course of her trip?
Solution
Problem 11
Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating  inches of pasta from the middle of one piece. In the end, he has  pieces of pasta whose total length is  inches. How long, in inches, was the piece of pasta he started with?
Solution
Problem 12
The arrows on the two spinners shown below are spun. Let the number  equal  times the number on Spinner , added to the number on Spinner . What is the probability that  is a perfect square number?
Solution
Problem 13
How many positive integers can fill the blank in the sentence below?
“One positive integer is _____ more than twice another, and the sum of the two numbers is .”
Solution
Problem 14
In how many ways can the letters in  be rearranged so that two or more s do not appear together?
Solution
Problem 15
Laszlo went online to shop for black pepper and found thirty different black pepper options varying in weight and price, shown in the scatter plot below. In ounces, what is the weight of the pepper that offers the lowest price per ounce?
Solution
Problem 16
Four numbers are written in a row. The average of the first two is  the average of the middle two is  and the average of the last two is  What is the average of the first and last of the numbers?
Solution
Problem 17
If  is an even positive integer, the  notation  represents the product of all the even integers from  to . For example, . What is the units digit of the following sum?
Solution
Problem 18
The midpoints of the four sides of a rectangle are  and  What is the area of the rectangle?
Solution
Problem 19
Mr. Ramos gave a test to his class of  students. The dot plot below shows the distribution of test scores.
Later Mr. Ramos discovered that there was a scoring error on one of the questions. He regraded the tests, awarding some of the students  extra points, which increased the median test score to . What is the minimum number of students who received extra points?
(Note that the median test score equals the average of the  scores in the middle if the  test scores are arranged in increasing order.)
Solution
Problem 20
The grid below is to be filled with integers in such a way that the sum of the numbers in each row and the sum of the numbers in each column are the same. Four numbers are missing. The number  in the lower left corner is larger than the other three missing numbers. What is the smallest possible value of ?