GRE Algebra Practice Questions

A delivery company uses bicycles and trucks for shipments. The total number of vehicles is 7, and the product of bicycles and trucks is 12. If these quantities are the roots of the quadratic equation $x^2 + bx + c = 0$, what is the discriminant of this equation?

Quantity A: $\sqrt[3]{27x^6}$ Quantity B: $(3x^2)^2$

where $x$ is a positive real number.

A delivery company models the optimal number of packages per truck with a quadratic equation. If the equation's roots are 2 and 3, and it's written as $ax^2 - bx + c = 0$, what is the value of $b$ when $a = 1$?

For a quadratic equation in the form of $x^2 + bx + c = 0$, the sum of its roots is 5 and the product of its roots is twice their sum. What is the value of $c$?

Quantity A: $\sqrt{27} \times \sqrt[3]{8}$ Quantity B: $6 \times \sqrt{2}$

Quantity A: The product of the roots of the quadratic equation $x^2 - (3k + 1)x + 2k^2 = 0$ where $k$ is a positive integer Quantity B: The sum of the roots of the same quadratic equation

Quantity A: The number of points scored by a basketball team in a game where they made 8 more free throws than three-pointers, and each free throw is worth 1 point while each three-pointer is worth 3 points. Quantity B: The number of points scored by the same team in a game where they made twice as many free throws as three-pointers, under the same scoring rules. Additional information: In both scenarios, the team made at least one three-pointer and at least one free throw.

Quantity A: The sum of the points scored by a basketball team in their first 5 games, if they scored 20 more points in each subsequent game than the previous one, starting with x points in the first game. Quantity B: 5x + 100

x is a positive integer.

Quantity A: The number of points scored by a basketball team in the first half of a game where they scored 5 more points in the second half than in the first half, and the total points scored were between 70 and 90 Quantity B: 40

Quantity A: The sum of the solutions to the equation $3x + 5 = 2x - 7$ Quantity B: The product of the solutions to the equation $x^2 - 5x + 6 = 0$

Both equations have real solutions.