GRE Math Practice: This GRE quantitative comparison question tests your understanding of percent changes and area of right triangles.

Question#72: In right triangle $ABC$, the length of the height is increased by $25\%$ and the length of the base is decreased by $25\%$ to create a new right triangle $DEF$.
 
$\begin{array}{c c c c c c}
& \underline{\textrm{Quantity A}} & & & & \underline{\textrm{Quantity B}} \\
& & & & & \\
& \textrm{Area of triangle $ABC$} & & & & \textrm{Area of triangle $DEF$}\\
\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. $\quad \textrm{The relationship cannot be determined from the information given.}$

Choice A

Video explanation

 

 
Try this GRE math practice question that tests your ability to manipulate and rearrange algebraic expressions to isolate one variable in terms of another variable.

Question#71: If $y = \dfrac{m}{m-n}$ and $x = \dfrac{n}{m+n}$, what is $y$ in terms of $x$?

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

Choice A

Video explanation

 

 
Try this GRE math practice question that tests your ability to express the problem in terms of fractions and then recognize a pattern.

Question#70: One half of the water is poured out of a full container. Then one third of the remainder is poured out. Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one tenth of the original water remain?

1. $\quad 6$
2. $\quad 7$
3. $\quad 8$
4. $\quad 9$
5. $\quad 10$

Video explanation

 

 
Try this GRE math practice question that tests your ability to translate word relationships when given in terms of fractions.

Question#69: In the month of June, Ryan used $\dfrac{1}{12}$ of his monthly salary for his student loan payment. Ryan also paid $\dfrac{2}{3}$ more than the student loan payment for his rent. What fraction of his monthly salary was left after Ryan made the student loan and rent payment?

1. $\quad \dfrac{31}{36}$
2. $\quad \dfrac{7}{9}$
3. $\quad \dfrac{5}{8}$
4. $\quad \dfrac{3}{4}$
5. $\quad \dfrac{1}{4}$

Video explanation

 

 
Try this GRE quantitative comparison question on geometry that tests your understanding of how the right angle of a triangle changes when the dimensions of the legs are changed.

$\textrm{Note: Figure not drawn to scale}$
$\begin{array}{c c c c c c c c c c c}
& & & & & & \underline{\textrm{Quantity A}} & & & & \underline{\textrm{Quantity B}} \\
& & & & & & & & & & \\
& & & & & & x & & & & 90\\
\end{array}$

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