Every whole number from 1 to 100 is placed in the diagram of multiples of 2, 3 and 5. How many numbers lie in exactly one of the circles?

Only multiples of 2: $50-16-10+3=27$ (removing multiples of 6 and 10, adding back the 3 multiples of 30). Only 3: $33-16-6+3=14$. Only 5: $20-10-6+3=7$. Exactly one $=27+14+7=48$. 74 is the count inside at least one circle, 103 simply adds $50+33+20$, and 26 is the count outside every circle.