After polling a class of 20 music students by a show of hands

After polling a class of 20 music students by a show of hands, you find that 8 students play the guitar and 9 students play the piano. Given that information, what is the minimum number of students in this music class who play both the guitar and the piano?

  1. 0
  2. 1
  3. 8
  4. 9
  5. 17

Answer

The correct answer is A.

To find the minimum number of students in a class of 20 who play both guitar and piano when 8 play guitar and 9 play piano, you must look at the range for which the guitar and piano players may overlap. For instance, all 8 who play guitar could also play piano; that's the maximum.

The minimum would be the smallest overlap they can have. In this case, there are 20 total; the two groups could be disjoint because 9 + 8 or 17 is less than 20. Thus, the minimum is 0.