How it Works › Forums › Advanced Problems (AMC 8 Problems 20-25 and beyond) › AMC 8 Review Session #1! (Geometry and Combinatorics)
November 4, 2016 at 2:28 pm #433
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Hey Math Circle Students!
Here are the introductory problems for the next $3$ days! These are more difficult than AMC 8 Problems 10-15 but they fit the range of $16-21$. Each of these problems are worth $5$ points to your leaderboard score! If you don’t understand one of the questions, feel free to post in the questions forum here
1. (Problem 23) In square $ABCE$, $AF=2FE$ and $CD=2DE$. What is the ratio of the area of $\triangle BFD$ to the area of square $ABCE$?
2. (Problem 25) A circle with radius $1$ is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle’s shaded area to the area between the two squares?
3. (Problem 20) In a room, $2/5$ of the people are wearing gloves, and $3/4$ of the people are wearing hats. What is the minimum number of people in the room wearing both a hat and a glove?
4. (Problem 24) One day the Beverage Barn sold 252 cans of soda to 100 customers, and every customer bought at least one can of soda. What is the maximum possible median number of cans of soda bought per customer on that day?
Remember that you can post your solutions below to these problems and I will keep a running leaderboards for the top 10 students who participate the most! I especially appreciate the same problem being solved in different ways!