Knewton Brutal Math Challenge - Week 3

by , Mar 31, 2010

Is it hump day already? Nope, it's Brutal Math day. Check this one out. Be the first to get it right (show your work!) and you'll win the new Knewton t-shirt.

A 6-student Senior Sports Committee is being selected from the seniors who play basketball, soccer, and football at a certain school. The committee consists of one student who is on both the basketball and soccer teams, one who is on both the football and soccer teams, and one who is on the basketball and football teams, as well as one additional student from each of the teams; the last three students may play on one or two teams. There are 10 seniors on the basketball team, 8 on the football team, and 6 on the soccer team. If more than one senior plays each pair of sports, and no senior plays all three sports, is the number of different 6-student committees that can be selected a multiple of 4?

1. The number of seniors on both the basketball team and the soccer team is the same as the number of seniors on both the football team and soccer team, and three less than the number of seniors on both the basketball and football team.

2. There are 5 seniors that play one pair of sports, 2 that play another pair, and 2 that play the last pair.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient.