Best of 2018 School Competition

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?

Geometry of Gift Giving

Vanessa bought some round holiday dessert plates to give as a gift to her friend. However, the store only had 5 of the 8 plates she wanted. (All of the plates are the same.) The stack of five plates measured 1.5 inches tall, and when two plates were removed from the stack the remaining stack of three plates had a height of 1 inch. When Vanessa finally has all 8 of the plates she wants, how tall will the stack of 8 plates be, in inches? Express your answer as a decimal to the nearest hundredth.