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?

Let's assume the first even number among the given set is 'y'.

So the set of numbers will be y, (y+2), (y+4), (y+6), (y+8), (y+10), (y+12), (y+14), (y+16), (y+18), (y+20), (y+22), (y+24), (y+26), (y+28).

Difference between the largest and the smallest numbers belonging to this set = (y+28)-y

= 28

Here we got the required answer without obtaining the value of 'y'. However if needed we can obtain the value also.