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...
Derrick received a total of 21 gift cards for graduation. He received gift cards in each of four denominations, $25, $50, $75 and $100. The number of $100 gift cards Derrick got was twice the number...
Ms. Cross leads The National Math Club at the middle school where she teaches. At the first club meeting of the school year, 60% of the students in attendance were 7th graders. If there was one fewer...
As the weather is turning cooler and daylight is arriving later in the morning and trees are starting to lose their leaves, many of us are noticing that summer is over and we’re well into fall. Or is...
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...
It’s Autumn, and that means leaves are falling! Amber’s house occupies 2650 ft2 in the middle of a 50-foot by 80-foot parcel of land, and the leaves that fall cover the ground all around her house. If...
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...
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%...
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...