Carcass wrote:
Each of the 24 students in Mr. Martin’s class plays tennis, soccer, or both. If four students play both sports and eight students play only tennis, how many students play only soccer?
A. 12
B. 14
C. 16
D. 18
E. 20
One approach is to use the
Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- plays tennis or doesn't play tennis
- plays soccer or doesn't play soccer
So we can set up our Matrix as follows:
Important: Since every student plays tennis, soccer or both, we can conclude that there are ZERO students that play neither tennis nor soccer. That's why we have 0 in the bottom right corner. Given: 4 students play both sports and 8 students play only tennis.We can add this to the diagram:
Question: How many students play only soccer?At this point we have accounted for 12 of the 24 students, which means the remaining 12 must be placed in the last remaining box (which represents the number of students that play soccer but not tennis)
Answer: A