Define x @ y as (x3 − y)/x, for distinct positive integers x and y. What is the value of 5 @ 10? Evaluating 5 @ 10 yields (53 − 10)/5 = (125 − 10)/5 = 115/5 = 23. Define a # b as a2 − b2 − ab, for...
When Riya’s alarm went off on the first day of her senior year in high school, she hit the snooze button and slept for another 10 minutes. When the alarm sounded the next time, Riya got up and...
In preparation for Thanksgiving dinner, Mrs. Cobble decided to get a new tablecloth for the dining room table. Her rectangular table measures 3.5 feet by 6 feet, and she would like the tablecloth to...
This summer, Owen and Jack will both have part time jobs. Owen will be working as a lifeguard and Jack will be working as a server at a local restaurant. Owen plans to work 15 hours each week and will...
A town in South Dakota decides to have an “End of the Summer” pool party and invites all of the households in the town that have school aged children. Twenty-seven households are invited to the party...
The date of the beginning of the school year has long been a topic of debate in many areas across the United States, but the trend is leaning towards starting school earlier rather than later...
The Sprint Round of the MATHCOUNTS Chapter Competition has 30 questions and students are given 40 minutes to complete the round. Though it isn’t expected that most students will finish all 30...
According to “A History of Valentine’s Day Cards in America” by T.M. Wilson, in 1847 Esther Howland was the first to mass-produce Valentine’s Day cards. She made them out of lace, paint and expensive...
The following information and problems were submitted by a MATHCOUNTS volunteer, Emily Koithan. Thank you, Emily! Neuroscientists use a special type of brain scanning called functional magnetic...
For the following problems, assume that the snowballs are perfect spheres. Chiquita and Rhonda are each building a snowman. Rhonda tells Chiquita that she is making each of her 3 balls of snow 20%...