In this GRE strategy video lesson, I illustrate how best to compare algebraic expressions that occur in GRE quantitative comparison questions. I discuss when to plug in values and when to manipulate and rearrange algebraic expressions.
Comparing and Manipulating Algebraic Expressions: GRE Math Practice Question#90
This GRE math practice question on quantitative comparisons tests your ability to manipulate and compare algebraic expressions. See if you can find the fastest way to answer this question.
$$\dfrac{3x2}{3} \; – \; \dfrac{(2x1)}{6} = \dfrac{2x1}{3} \; – \; \dfrac{(3x2)}{6}$$
$\begin{array}{c c c c c c c c c c c}
& & & & & & \underline{\textrm{Quantity A}} & & & & \underline{\textrm{Quantity B}} \\
& & & & & & & & & & \\
& & & & & & 3x2 & & & & 2x1 \\
\end{array}$
 $\quad \textrm{Quantity A is greater.}$
 $\quad \textrm{Quantity B is greater.}$
 $\quad \textrm{The two quantities are equal.}$
 $\quad \textrm{The relationship cannot be determined from the information given.}$
Exponent manipulation: GRE quantitative reasoning question #89
Try the following GRE quantitative reasoning question that tests your ability to manipulate exponent expressions.
Question#88:
Let $n=8^{2022}$. Which of the following is equal to $\displaystyle \frac{n}{4}?$

$\quad 4^{1010}$

$\quad 2^{2022}$

$\quad 8^{2018}$

$\quad 4^{3031}$

$\quad 4^{3032}$
Prime factorization and perfect cubes: GRE quantitative reasoning question #88
Try the following GRE quantitative reasoning question that tests your understanding of prime factorization and how it applies to forming perfect cubes.
Question#88:
Suppose that $m$ and $n$ are positive integers such that $75m = n^{3}$. What is the minimum possible value of $m + n$?

$\quad 15$

$\quad 30$

$\quad 50$

$\quad 60$

$\quad 5700$
Arithmetic mean (average): GRE quantitative reasoning question #87
Try the following GRE quantitative reasoning question that tests your understanding of arithmetic mean(average).
Question#87:
The quiz scores of a class with $k > 12$ students have a mean of $8$. The mean of a collection of $12$ of these quiz scores is $14$. What is the mean of the remaining quiz scores in terms of $k$?

$\quad \displaystyle \frac{148}{k12}$

$\quad \displaystyle \frac{8k168}{k12}$

$\quad \displaystyle \frac{14}{12} – \frac{8}{k}$

$\quad \displaystyle \frac{14(k12)}{k^2}$

$\quad \displaystyle \frac{14(k12)}{8k}$
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