In honor of this year’s School Competition being released to registered competition coaches for our 2019-2020 Competition Series, see some of last year’s School Competition questions below!

Sprint Round, 19

Josie selected a number n. She divided n by 2 and then subtracted ½ from the result. She took half of that result and then subtracted ½ to get the final result of 10. What is the value of n?

Grady, Sophia and Ella Zappone were going trick-or-treating together down a long road with houses only on the right side of the street.  The addresses of the first three houses were 296 Boo Blvd, 300 Boo Blvd and 304 Boo Blvd, and the house numbers continued to increase by 4 down the entire road.  The kids decided to take turns knocking on the doors of the houses, so that Grady knocked at house 296, Sophia knocked at house 300, Ella knocked at house 304, and then Grady started the sequence over at house 308.  Grady will knock on the doors of a lot of houses.  When Grady gets to the first ho

Some organizations are looking to make a lot of money off of the flu vaccine that is in such high demand.  A survey done last week reported that 55% of 677 hospital pharmacists who responded reported being offered the vaccine at highly inflated prices.  Of those, 84% said they would not buy the vaccine at those prices.  How many of the 677 hospital pharmacists did not say that they would not buy the vaccine at the high prices?  Express your answer to the nearest whole number.

The ratio of girls to boys in Mrs. Franks’ 7^th grade class is ¾ (excluding Mrs. Franks). On Monday, 4 girls and 6 boys got to go on a special field trip for honor roll students. Since no other students were absent on Monday, the ratio of girls remaining in the class to boys remaining in the class was 4/5. How many students are in Mrs. Franks’ class when everyone is present?

Nancy and Tim have an apple cider stand at their school every morning during the fall to raise money for their club. Since September 23 is the Autumnal Equinox, the first day of fall and their first day of business will be September 23.

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 and the ratio of 5-person households to 4‑person households to 3-person households to 2-person households invited is 1:4:3:1, respectively. (The invite list did not include households of any other sizes.)  How many people from households with less than 4 people are invited to the party?

After polling each student in her homeroom about their summer plans, Mrs. Baker discovered that each student planned to participate in one or more of the following activities:

The distinct letters from the word MEMORIAL are used to create set Z, such that Z = {M, E, O, R, I, A, L}. The letters from the word DAY are used to create set Y, such that Y = {D, A, Y}. If set X is the intersection of sets Z and Y, what are the letters in set X?

The intersection of two sets includes all the elements (or members) that are in both sets. So set X = {A}.

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.

Jessie and Marcus are moving from their apartment to a new condominium. Marcus is responsible for moving all his belongings and the living room furniture, while Jessie is responsible for moving all the kitchen items, including the dining table and chairs, and his personal belongings.