Question. There are 20 students in the class. Half of them play basketball. Two-fifths play volleyball and one-tenth play both basketball and volleyball. How many students in this class do not play either game?
Answer. 4
What step-by-step reasoning justifies that answer?
Reasoning: Half of the students are playing basketball, which means 20 / 2 = 10 students play basketball. Two - fifths plays volleyball, which leaves us with 20 * 2 / 5 = 8 students. One - tenth play both games, which means 20 * 1 / 10 = 2 students. There are 10 + 8 = 18 students who play basketball or volleyball. Among these 18 students, 2 of them are playing both games, so that means 18 - 2 = 16 students play only one of the two games. So finally, 20 - 16 = 4 students do not play either game.