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MathNet 2010 — Part 01 Question 194

Math Olympiad Vault · MathNet 2010 — Part 01

Question 194

26. Birthday Party - André's birthday party has less than 120 guests. For dinner, he can split guests into six-person tables or at full seven-person tables. In both cases, more than 10 tables are needed and all the guests are at a table. How many are the guests? 27. Measurement of the side - In the figure given, $ABCD$ is a rectangle and $\triangle ABE$ and $\triangle CDF$ are right triangles. The area of the triangle $\triangle ABE$ is $150\ \mathrm{cm}^2$ and the segments $AE$ and $DF$ measure, respectively, $15$ and $24\ \mathrm{cm}$. What is the length of segment $CF$?