# SAT problem of the week, September 22, 2014 solution

Hint for process of elimination: In a ratio, the number before the word “to” belongs in the numerator, and the number after the word “to” belongs in the denominator. The SAT almost always give you ratios in the opposite order to test you, so you need to watch for that. Some of the choices are less than 1, which incorrectly imply that the area of $\triangle AED$ is smaller than the area of $\triangle ACB$. This eliminates choices B and C.

Also, note that unless the SAT says a figure is not drawn to scale, then the figure is almost definitely drawn to scale. That allows you to eliminate choices by estimating the size of the figures and eliminating choices that are too far off.

Read on for a full solution.

In the figure above, point, $C$ is the midpoint of line segment $\overline{AG}$ and point $E$ is the midpoint of line segment $\overline{CG}$. What is the ratio of the area of triangle $AED$ to the area of triangle $ACB$?
1. $\dfrac{2}{1}$ (check answer)
2. $\dfrac{2}{3}$ (check answer)
3. $\dfrac{4}{9}$ (check answer)
4. $\dfrac{3}{2}$ (check answer)
5. $\dfrac{9}{4}$ (check answer)