Every whole number from 1 to 40 is placed in the correct region of the diagram. How many numbers go into the region marked ?

The ? region holds multiples of 3 that are neither even nor multiples of 5: 3, 9, 21, 27, 33 and 39 — six numbers. 7 keeps 15, which is a multiple of 5; 13 counts every multiple of 3 up to 40; and 11 removes 15 and 30 but keeps the even ones.