# Math reasoning Math Homework question

An example of a Math question from a Math reasoning class. The problem is from a Venn's diagram lesson.

The 65 students in a classical music lecture class were polled, with the results that 36 like Wolfgang Amadeus Mozart, 37 like Ludwig von Beethoven, 33 like Franz Joseph Haydn, 14 like Mozart and Beethoven, 21 like Mozart and Haydn, 15 like Beethoven and Haydn, and 8 like all three composers. Use a Venn diagram to complete parts (a) through (f) below.

a) How many of these students like exactly two of these composers?

b) How many of these students like exactly one of these composers?

c) How many of these students like none of these composers?

d) How many of these students like Mozart, but neither Beethoven nor Haydn?

e) How many of these students like Haydn and exactly one of the other two?

f) How many of these students like no more than two of these composers?