How many numbers between 1 and 601 are multiples of 3 or multiples of 4?
(a) 100
(b) 150
(c) 250
(d) 300
(e) 430
The correct option is (d).

To find the number of multiples of 3 between 1 and 601, it is enough to use the division algorithm and observe that $601=200 \times 3+1$. This shows that $3 \times 1, 3 \times 2$, ..., $3 \times 200$ are the multiples of 3 between 1 and 601, that is, there are 200 of these multiples. Similarly, we see that there are 150 multiples of 4 between 1 and 601. In this total of $200+150=350$, some numbers are counted twice, as they are multiples of both 3 and 4; for example, 12, 36, and 60 were included in the 200 multiples of 3 and also in the 150 multiples of 4. Remember that multiples of 3 and 4 are also multiples of 12. The same argument used above shows that there are 50 multiples of 12 between 1 and 601. Therefore, the number of multiples of 3 or 4 between 1 and 601 is $350-50=300$.