Sets $A$ and $B$, shown in the Venn diagram, have the same number of elements.
Their union has $2007$ elements and their intersection has $1001$ elements. Find
the number of elements in $A$.

$\mathrm{(A)}\ 503 \qquad \mathrm{(B)}\ 1006 \qquad \mathrm{(C)}\ 1504 \qquad \mathrm{(D)}\ 1507 \qquad \mathrm{(E)}\ 1510$
Let $x$ be the number of elements in $A$ and $B$ which is equal. 
Then we could form equation 
$2x-1001 = 2007$
$2x = 3008$
$x = 1504$. 
The answer is $\boxed{\textbf{(C)}\ 1504}$