If all multiples of 3 and all multiples of 4 are removed from the list of whole numbers 1 through 1200, then how many whole numbers are left?
+2407 2/3 of the numbers will not be multiples of 3, and 3/4 of the numbers won't be multiples of 4.
1200 * 2/3 * 3/4 = 600
=^._.^=
+876 We try a complementary approach
Multiples of 3 from 1 - 1200: $\left \lfloor{\frac{1200 - 1 + 1}{3}}\right \rfloor = \left \lfloor{\frac{1200}{3}} \right \rfloor = 400$
Multiples of 4 from 1 - 1200: $\left \lfloor{\frac{1200 - 1 + 1}{4}}\right \rfloor = \left \lfloor{\frac{1200}{4}} \right \rfloor = 300$
Multiples of $4 \cdot 3 = 12$ from 1 - 1200: $\left \lfloor{\frac{1200 - 1 + 1}{12}}\right \rfloor = \left \lfloor{\frac{1200}{12}} \right \rfloor = 100$
$1200 - (400 + 300 - 100) = 1200 - 600 = \boxed{600}$
