jmc

Since $\frac{2005}{3}=668\frac{1}{3}$, there are 668 multiples of 3 between 1 and 2005. Since $\frac{2005}{4}=501\frac{1}{4}$, there are 501 multiples of 4 between 1 and 2005. Since $\frac{2005}{12}=167\frac{1}{12}$, there are 167 multiples of 12 between 1 and 2005.

Every multiple of 12 is also a multiple of 3 and of 4, so there are $668-167=501$ multiples of 3 that are not multiples of 12 and $501-167=334$ multiples of 4 that are not multiples of 12. That leaves $501+334=\boxed{835}$ numbers that are multiples of 3 or 4 but not 12. (Note: no number can be a multiple of 3 and 4 without also being a multiple of 12. So, no number is included twice in our count $501+334$.)