May 2014

VARIABLES
The MATHCOUNTS Challenge

In celebration of all the top middle school math students from around the country who will meet in Orlando May 8–11 for the 2014 Raytheon MATHCOUNTS National Competition, here’s your challenge:

The problems below were taken from the 2014 State Sprint Round in which students worked alone to complete 30 problems in 40 minutes. No calculators.

1. If n represents the number of seconds in a day, what is the largest prime factor of n?
2. The nonzero roots of the equation: x 2 + 6x + k = 0 are in the ratio 2:1. What is the value of k?
3. A cone is sliced by planes parallel to its base into three pieces of equal height. What fraction of the original volume is in the middle piece? Express your answer as a common fraction.
4. In base 5, what is the value of 2710 x 3145
5. A bag contains red marbles and blue marbles. If two marbles are chosen at random without replacement, the probability that both marbles are red is 1/5, and the probability that both marbles are blue is 1/5 also . How many marbles are in the bag?

Find the answers over at the MATHCOUNTS website!