This GRE Math practice problem tests your understanding of angle relationships in a triangle.

In the figure above, $\overline{AB} \perp \overline{BC}$, and $\overline{AB} = \overline{AD}$. What is $y$ in terms of $x$ ?

1. $\quad x-90$
2. $\quad 2x-90$
3. $\quad 90-x$
4. $\quad 90-2x$
5. $\quad \dfrac{x}{2}$

 
This GRE quantitative comparison question tests your understanding of algebraic word translations.

After removing $6$ green balls from a container, there are twice as many red balls as green balls. Then $15$ red balls are removed from the container and there are three times as many green balls as red balls.

$\begin{array}{c c c c c c c c}
& & & \underline{\textrm{Quantity A}} & & & & \underline{\textrm{Quantity B}} \\
& & & & & & & \\
& & & \textrm{The total number of green and red balls in} & & & & 36 \\
& & & \textrm{the container before removing the 6 green balls.} & & & & \\
\end{array}$

1. $\quad \textrm{Quantity A is greater.}$
2. $\quad \textrm{Quantity B is greater.}$
3. $\quad \textrm{The two quantities are equal.}$
4. $\quad \textrm{The relationship cannot be determined from the information given.}$

 
This GRE Math practice problem tests your understanding of averages(arithmetic mean) in statistics.

The average (arithmetic mean) of a list of thirteen numbers is $17$. A new number is added to the list, and the average (arithmetic mean) of this new set of numbers is $18$. What number has been added?

1. $\quad 13$
2. $\quad 27$
3. $\quad 31$
4. $\quad 39$
5. $\quad \textrm{It cannot be determined based on the information above}$

 
This GRE quantitative comparison question tests your understanding of prime factorization.

$$ n = (15^3) (25^4) (12^6) (28^3) $$

$\begin{array}{c c c c c}
& \underline{\textrm{Quantity A}} & & & & \underline{\textrm{Quantity B}} \\
& & & & & \\
& \textrm{The number of distinct prime factors of $n$} & & & & 5 \\
\end{array}$

1. $\quad \textrm{Quantity A is greater.}$
2. $\quad \textrm{Quantity B is greater.}$
3. $\quad \textrm{The two quantities are equal.}$
4. $\quad \textrm{The relationship cannot be determined from the information given.}$

 
This GRE Math practice problem tests your understanding of sequences and identifying patterns.

Let $a_1, a_2, a_3, \ldots, a_n$ be a sequence of numbers where $a_1=-2$, $a_2=4$, and for $n \geq 3$, $a_n = \left(\dfrac{a_{n-1}}{a_{n-2}}\right)$. What is the sum of the first $99$ terms?

1. $\quad -16$
2. $\quad -12$
3. $\quad -8$
4. $\quad -4$
5. $\quad 0$