Try this GRE math practice question that tests your ability to manipulate and compare decimals expressed in exponent form.

Question#74:

Comparing the numbers $10^{-49}$ and $2 \cdot 10^{-50}$ we may say:

1. $\quad \textrm{the first exceeds the second by $8 \cdot 10^{-1}$}$

2. $\quad \textrm{the first exceeds the second by $2 \cdot 10^{-1}$}$

3. $\quad \textrm{the first exceeds the second by $8 \cdot 10^{-50}$}$

4. $\quad \textrm{the second is five times the first}$

5. $\quad \textrm{the first exceeds the second by 5}$

 
Try this GRE math practice question that tests your ability to simplify algebraic fractions.

Question#73: If $x > 0$, $y > 0$, and $xy \neq 1$, $\quad$ $x \ – \ \dfrac{1}{\dfrac{1}{x}-y}=$

1. $\quad \dfrac{xy}{1-xy}$
2. $\quad \dfrac{x^2 y}{xy-1}$
3. $\quad \dfrac{x^2 – xy – 1}{x}$
4. $\quad \dfrac{x-x^2y-1}{1-xy}$
5. $\quad \dfrac{x^2 y – 2x}{xy-1}$

 
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. $\quad \textrm{The relationship cannot be determined from the information given.}$

 
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. $\quad \dfrac{1-x}{x}$

 
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. $\quad 10$