This GRE quantitative comparison question tests your understanding of geometry and putting an algebraic structure to the question.

The perimeter of a square and a rectangle in feet are equal. The length of the rectangle is $1$ foot longer than the width.

$\begin{array}{c c c c c c c c c c c}
& & & & & & \underline{\textrm{Quantity A}} & & & & \underline{\textrm{Quantity B}} \\
& & & & & & & & & & \\
& & & & & & \textrm{Area of square} & & & & \textrm{Area of rectangle} \\
\end{array}$

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 counting multiples and using set principles to answer the question.

What is the number of integers from $1$ to $1000$ that are divisible by $24$ but not by $15$?

1. $\quad 33$
2. $\quad 35$
3. $\quad 37$
4. $\quad 39$
5. $\quad 41$

 
This GRE Math practice problem tests your understanding of dealing with quadratics that are presented in a different form.

If $12 x^{-2} – 5 x^{-1} = 2$, which of the following could be the value of $x$?

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

 
This GRE Math practice problem tests your understanding of dealing with divisibility, sets, and using Venn diagrams.

Set $A$ consists of all positive integers less than or equal to $100$ that are divisible by $4$. Set $B$ consists of all positive integers less than or equal to $100$ that are divisible by $6$. How many of the integers in Set $A$ are not in Set $B$?

1. $\quad 8$
2. $\quad 16$
3. $\quad 17$
4. $\quad 21$
5. $\quad 25$

 
This GRE Math practice problem tests your understanding of geometry problems that rely on algebraic restatement.

The length of rectangle $R$ is $50\%$ greater than the length of rectangle $S$, and the width of rectangle $R$ is twice the width of rectangle $S$. If the area of rectangle $R$ is $x$, then in terms of $x$, the area of rectangle $S$ is how much less than the area of rectangle $R$?

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