List of top Quantitative Aptitude Questions on Algebra asked in GRE

The integer \( v \) is greater than 1. If \( v \) is the square of an integer, which of the following numbers must also be the square of an integer? Indicate all such numbers.
Given that \( \dfrac{1-x}{x-1} = \dfrac{1}{x} \). Compare:
Quantity A: \( x \)
Quantity B: \( -\dfrac{1}{2} \)
Given that \( st = \sqrt{10} \). Compare:
Quantity A: \( s^2 \)
Quantity B: \( \dfrac{10}{t^2} \)
If \( 2x = 3y = 4z = 20 \), then \( 12xyz = \dots \)
The ratio of \( \frac{1}{3} \) to \( \frac{3}{8} \) is equal to the ratio of
A certain job pays \(\$\)24 per hour for the first 40 hours worked in a week and 1.5 times that rate for any additional hours. If an employee earns \(\$\)1,260 in one week, how many total hours did they work?
Solve for \( x \): \[ \frac{2}{x} + \frac{3}{x} = \frac{10}{15} \]
If \( x^2 - 9 = 16 \), what are the values of \( x \)?
A number is decreased by 40% and the result is 72. What was the original number?
If the average (arithmetic mean) of five consecutive integers is 25, what is the largest of these integers?
A dataset has the following values: 10, 12, 15, 15, 20, 22. What is the range and the median of the dataset?
Solve for \( x \) if \( \frac{x + 2}{x - 3} = 2 \).
If \( x^2 - 4x + 4 = 0 \), what is the sum of the roots?
If \( 3x + 2y = 6 \) and \( 2x - y = 4 \), what is \( x + y \)?
If \( f(x) = 2x^2 - 3x + 4 \), what is \( f(2) - f(-2) \)?
If \( a \) and \( b \) are positive integers such that \( a \times b = 36 \), and \( a \) is 3 less than twice \( b \), what is the value of \( a + b \)?
If \( x \) is an even integer and \( y = 3x + 5 \), which of the following must be odd?
If \( x^2 - 6x + 9 = y \), what is the value of \( y \) when \( x = 4 \)?
Simplify the expression: \( 3(x - 2) + 4 \).
If \( x \) is directly proportional to \( y \) and \( x = 10 \) when \( y = 2 \), what is \( x \) when \( y = 8 \)?
If \( 2x + 3 = 9 \), what is the value of \( x \)?
If \( x^2 = 16 \), what are the possible values of \( x \)?
If \( f(x) = x^2 - 3x + 2 \), find \( f(2) \).
Expand the expression \( (x + 3)(x - 2) \).
Solve for \( y \): \( 2y - 7 = 3y + 4 \).