GRE 2024 Quantitative Reasoning Practice Test Set 14 Question Paper with Solutions PDF

Quantity A: The slope of a line parallel to \(4y + 18x = 13\).

Quantity B: The slope of a line perpendicular to \(6y - 16x = 15\).

Which of the following is true?

• (1) The two quantities are equal.
• (2) The relationship between the quantities cannot be determined from the information provided.
• (3) Quantity B is larger.
• (4) Quantity A is larger.

What is the equation of a line passing through the two points \((41,11)\) and \((4,-9)\)?

• (1) \(y = 2027x - 1415\)
• (2) \(y = 1714x - 14825\)
• (3) \(y = 2037x - 41337\)
• (4) \(y = 14x - 18\)
• (5) \(y = 72x - 853\)

Given circle \(O\) with a diameter of \(2\) and square \(ABCD\) inscribed within circle \(O\), what is the area of the shaded region (circle minus square)?

• (1) \(2\)
• (2) \(\pi - 2\)
• (3) \(4\)
• (4) \(4\pi - 2\)

Quantity A: Double the measure of a single interior angle of an equilateral triangle.

Quantity B: The measure of a single interior angle of a (regular) hexagon.

Which statement is true?

• (1) The relationship cannot be determined with the information given.
• (2) Quantity B is bigger.
• (3) The quantities are equal.
• (4) Quantity A is bigger.

A rectangle has a length that is twice its height. If the perimeter of that rectangle is \(20 in\), what is its area?

• (1) \(400 in^2\)
• (2) \(1507 in^2\)
• (3) \(2509 in^2\)
• (4) \(103 in^2\)
• (5) \(2009 in^2\)

A triangle has two sides with length \(a\) and one side length \(b\). The length of side \(b = 14\) yard. If the length of \(a = 2\) times the length of side \(b\), what is the perimeter of the triangle?

• (1) 14 yard
• (2) 612 yard
• (3) 712 yard
• (4) 13 yard
• (5) 54 yard

One side of an equilateral triangle is equal to 1. Quantity A: The area of the triangle. Quantity B: 12.

• (1) Quantity A is greater.
• (2) The relationship cannot be determined.
• (3) Quantity B is greater.
• (4) The two quantities are equal.

What is the length of the diagonal of a cube that has a surface area of \(726 \, in^2\)?

• (1) \(122\sqrt{in}\)
• (2) 22 in
• (3) 12 in
• (4) 11 in
• (5) \(113\sqrt{in}\)

A right circular cylinder of volume \(200\pi\) has a height of 8. Quantity A: 10. Quantity B: The circumference of the base.

• (1) Quantity B is greater.
• (2) The relationship cannot be determined.
• (3) The two quantities are equal.
• (4) Quantity A is greater.

If a sphere has a volume of \(268.08 \, in^3\), what is the approximate radius of the sphere?

• (1) 8 in
• (2) 4 in
• (3) 64 in
• (4) 4.5 in
• (5) 5.9 in

If \(w = 18\), then which of the following is equal to \(w^2\)?

• (1) 14
• (2) 116
• (3) 12
• (4) 132
• (5) 164

It takes no more than 40 minutes to run a race, but at least 30 minutes. What equation will model this in \(m\) minutes?

• (1) \(m + 35 > 5\)
• (2) \(m - 35 < 5\)
• (3) \(m + 35 < 5\)
• (4) \(m - 35 > 5\)
• (5) \(m - 35 = 5\)

Solve the inequality \(6(x-1)<7(3-x)\).

• (1) \(x > 1327\)
• (2) \(x < 2713\)
• (3) \(x < 127\)
• (4) \(x > -1327\)
• (5) \(x > -1117\)

Simplify: \(\dfrac{(x^3 \cdot 2x^4 \cdot 5y + 4y^2 + 3y^2)}{y}\).

• (1) \(10x^7 + 7y^3\)
• (2) None of the other answers
• (3) \(10x^7y + 7y^2\)
• (4) \(10x^{11} + 7y^3\)
• (5) \(10x^7 + 7y\)

Solve for \(x\): \(14x = 256\).

• (1) 256
• (2) 4
• (3) -14
• (4) 14
• (5) -4

If one mile is equal to 5,280 feet, how many feet are 100 miles equal to in scientific notation?

• (1) \(5280 \times 10^2\)
• (2) \(.528 \times 10^6\)
• (3) 528,000
• (4) \(5.28 \times 10^5\)
• (5) \(528 \times 10^3\)

If a cash deposit account is opened with
(7500 for a three year period at 3.5% interest compounded once annually, which of the following is closest to the positive difference between the interest accrued in the third year and the interest accrued in the second year?

• (1) 281.2
• (2) 81.41
• (3) 9.51
• (4) 0
• (5) 11.41

Let \(x\) and \(y\) be integers such that \(0 \leq x < 5\) and \(-4 \leq y \leq -1\). Compare:
\[ Quantity A: x - |y| \quad \quad Quantity B: 0 \]

• (1) Quantity B is greater
• (2) Quantity A and Quantity B are equal
• (3) The relationship cannot be determined from the information given
• (4) Quantity A is greater

Choose the answer which best simplifies the following expression: \(2p^2 + 3p2a - 5p3\).

• (1) \(15p - 10pab\)
• (2) \(6p + 9p - 10pab\)
• (3) \(6p^2 + 9p - 10p^6\)
• (4) \(6p^2 + 9p + 10pab\)
• (5) \(6p^2 + 9p - 10pab\)

Simplify the following: \(40 - \sqrt{420} - \sqrt{20} - \sqrt{160}\).

• (1) \(5 - \sqrt{(5+22-\sqrt{)}}\)
• (2) The expression cannot be simplified any further
• (3) \(\sqrt{810}\)
• (4) \(10 - \sqrt{(6+2-\sqrt{)}}\)
• (5) \(\sqrt{420}\)