National Champions Crowned at MATHCOUNTS National Competition - The Problems

May 14, 2001

Last Friday, 228 mathletes from 57 different states and territories competed at the MATHCOUNTS National Competition in Washington, D.C. (Results of the competition can be found on the MATHCOUNTS website.) These students earned the opportunity to participate by finishing in the top 4 places at their state competitions. Throughout the competition season, we have been giving you a glimpse of some of the problems competing mathletes have faced. Well, here are some problems from the finale of the 2000-2001 competition season!

Graphing and Probability: Sprint Round A point (x, y) is randomly selected such that 0 < x < 8 and 0 < y < 4. What is the probability that x + y < 4? Express your answer as a common fraction.

Going to a Party: Sprint Round When Cedric walked into a party, two-thirds of those invited had already arrived. Six more people arrived just after Cedric, bringing the number at the party to 5/6 of those invited. What was the total number of invited guests?

Playing the Stock Market: Target Round Otto’s investment portfolio consisted of shares of internet stock and copper stock. During the year, the value of his internet shares increased 10%, but the value of his copper shares decreased from $10,000 to $9,000. During the same year, the total value of his portfolio increased by 6%. What was the dollar value of his internet shares at the end of the year?

Little bit of Geometry: Team Round The Crunchy Peanut Butter Company plans to increase the height of its jars by 40%. By what percent will the radius of the jar need to be decreased to keep the volume the same? Express your answer as a decimal to the nearest tenth.