Question

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 $A.$

$503$

$1006$

$1504$

$1507$

$1510$

Solution:

Let $x$ be the number of elements in each $A$ and $B.$ Also let $y$ be the number of elements in their intersection.

The conditions give us that $2x - y = 2007$ and $y = 1001.$ Plugging $y$ into the first equation yields $\begin{align*} 2x - 1001 &= 2007 \\ 2x &= 3008 \\ x &= 1504. \end{align*}$

Thus, C is the correct answer.

2007 AMC 8 Problem 13

Solution:

Problem 13 in Other Years