# SAT/ACT problem of the week, December 08, 2016 solution

Hint for process of elimination: Go through each of the three statements individually and consider them for validity. Remember that the angles measure of a full circle is $360\textdegree$. It also helps to know that supplementary angles two angles whose measures add to $latext 360\textdegree$.

Read on for a full solution.

# SAT problem of the week, December 08, 2014

In the diagram of six adjacent angles shown above, which of the following must be true?

1. The sum of the six angles is $360 \textdegree$
2. All six angles are congruent to each other.
3. Any pair of adjacent angles is supplementary
3. I and II, only (check answer)
4. I and III, only (check answer)
5. I, II, and III (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on December 14th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

# SAT/ACT problem of the week, September 22, 2016 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.

# SAT problem of the week, September 22, 2014

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)

# SAT problem of the week, December 08, 2014 solution

Hint for process of elimination: Go through each of the three statements individually and consider them for validity. Remember that the angles measure of a full circle is $360\textdegree$. It also helps to know that supplementary angles two angles whose measures add to $latext 360\textdegree$.

Read on for a full solution.

# SAT problem of the week, December 08, 2014

In the diagram of six adjacent angles shown above, which of the following must be true?

1. The sum of the six angles is $360 \textdegree$
2. All six angles are congruent to each other.
3. Any pair of adjacent angles is supplementary
3. I and II, only (check answer)
4. I and III, only (check answer)
5. I, II, and III (check answer)

Have a solution? Hint? Question? Drop it below. We’d love to hear from you. A full solution will be posted on December 14th. If you would like to learn how to enter math formulas into this blog, visit the WordPress LaTeX tutorial page.

# 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)