The average of a set of 15 consecutive even numbers is 64. What is the difference between the largest and the smallest numbers belonging to this set?

28

Sum of 15 consecutive odd number = 15 × 64 = 960

Let smallest odd number = a

a + ( a + 2) + ( a + 4) +  ( a + 6) +  ( a + 8) +  ( a + 10) +  ( a + 12) +  ( a + 14) +  ( a + 16) +  ( a + 18) +  ( a + 20) +  ( a + 22) +  ( a + 24) +  ( a + 26) +  ( a + 28) = 960

Difference in largest and smallest number = (a+28) - a = 28