GRE 2024 Quantitative Reasoning Practice Test Set 16 Question Paper with Solutions PDF

If the average of \(a\) and \(b\) is 70, and the average of \(b\) and \(c\) is 110, what is the value of \(c - a\)?

• (1) \(90\)
• (2) \(40\)
• (3) \(150\)

There is a line defined by two end-points, \( (11, -5) \) and \( (a, b) \). The midpoint between these two points is \( (-6, -21) \). What is the value of the point \( (a, b) \)?

• (1) \( (4, -19) \)
• (2) \( (12, -14) \)
• (3) \( (-14, -25) \)
• (4) \( (-23, -37) \)

What is the slope of the line shown?

• (1) \(-3\)
• (2) \(\tfrac{1}{3}\)
• (3) \(3\)
• (4) \(-\tfrac{1}{3}\)

Quantity A: The slope of the line parallel to \( 5x = 15y - 12 \)

Quantity B: The slope of the line parallel to \( 2y = -23x - 14 \)

Which of the following is true?

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

If \(m\) is a line that has a \(y\)-intercept of 3 and an \(x\)-intercept of 7, which of the following is the equation of a line that is perpendicular to \(m\)?

• (1) \( y = (3x + 11)7 \)
• (2) \( y = (7x + 15)3 \)
• (3) \( y = x + 73 \)
• (4) \( y = (-3x - 24)7 \)

Quantity A: The diameter of a circle with area of \( 109\pi \)

Quantity B: The diameter of a circle with circumference of \( 22\pi \)

Which of the following is true?

• (1) Quantity B is larger.
• (2) The relationship between the quantities cannot be determined.
• (3) Quantity A is larger.

Which point could lie on the circle with radius 5 and center \( (1, 2) \)?

• (1) \( (4, 6) \)
• (2) \( (3, 4) \)
• (3) \( (3, -2) \)
• (4) \( (-3, 6) \)

If rectangle \(ABCD\) has a perimeter of 68, and the longer edge is 2.4 times longer than the shorter edge, then how long is the diagonal \(AC\)?

• (1) 26
• (2) 32
• (3) 30
• (4) 24

The diagram represents a square \(ABCD\) with a semi-circle directly attached to its side. If the area of the figure is \(16 + 2\pi\), what is its outer perimeter?

• (1) 16
• (2) None of the other answers
• (3) \(12 + 2\pi\)
• (4) \(16 + 2\pi\)

An acute isosceles triangle has two sides with length \(a\) and one side length \(b\). The length of side \(a = 39\) ft. If the length of \(b = \tfrac{1}{2}a\), what is the perimeter of the triangle?

• (1) 1 foot
• (2) 46 foot
• (3) 26 foot
• (4) 10 inches

Quantity A: the area of a right triangle with sides 10, 24, 26

Quantity B: twice the area of a right triangle with sides 5, 12, 13

Which of the following is true?

• (1) Quantity A is greater.
• (2) The relationship cannot be determined.
• (3) Quantity B is greater.

What is the length of an edge of a cube with a surface area of \(1350 \, in^2\)?

• (1) 225 in
• (2) 15 in
• (3) 25 in
• (4) 305 in

Quantity A: The volume of a cylinder with radius 3 and height 4

Quantity B: 3 times the volume of a cone with radius 3 and height 4

Which of the following is true?

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

This triangular prism has a height of 3 feet and a length of 7 feet.
What is the surface area of the prism? Round to the nearest tenth.

• (1) \(90 \, ft^2\)
• (2) \(80.7 \, ft^2\)
• (3) \(80 \, ft^2\)

How much does the volume of a sphere increase if its radius is increased by 50%?

• (1) 237.5%
• (2) 50%
• (3) 337.5%
• (4) 150%