GRE 2024 Quantitative Reasoning Practice Test 5 Question Paper with Solutions PDF

If \( 3x + 2 = 11 \), what is the value of \( x \)?

• (A) \( 5 \)
• (B) \( 3 \)
• (C) \( 4 \)
• (D) \( 2 \)

The average (arithmetic mean) of 5, 10, 15, and 20 is:

• (A) \( 12.5 \)
• (B) \( 15 \)
• (C) \( 10 \)
• (D) \( 13 \)

If a car travels 150 miles in 2.5 hours, what is the average speed in miles per hour?

• (A) \( 50 \) miles per hour
• (B) \( 55 \) miles per hour
• (C) \( 60 \) miles per hour
• (D) \( 65 \) miles per hour

Solve for \( y \): \( 2y - 7 = 3y + 4 \).
 

• (A) \( -11 \)
• (B) \( 11 \)
• (C) \( -7 \)
• (D) \( 7 \)

If \( f(x) = x^2 - 3x + 2 \), find \( f(2) \).
 

• (A) \( 0 \)
• (B) \( 2 \)
• (C) \( -2 \)
• (D) \( 4 \)

Expand the expression \( (x + 3)(x - 2) \).
 

• (A) \( x^2 + x - 6 \)
• (B) \( x^2 - x - 6 \)
• (C) \( x^2 + 6x - 6 \)
• (D) \( x^2 - 6x - 6 \)

If \( x^2 = 16 \), what are the possible values of \( x \)?
 

• (A) \( 4 \)
• (B) \( -4 \)
• (C) \( 4 \) or \( -4 \)
• (D) \( 0 \)

What is the area of a triangle with a base of 8 cm and a height of 5 cm?
 

• (A) \( 20 \, cm^2 \)
• (B) \( 30 \, cm^2 \)
• (C) \( 40 \, cm^2 \)
• (D) \( 10 \, cm^2 \)

What is the circumference of a circle with a radius of 7 cm?
 

• (A) \( 43.96 \, cm \)
• (B) \( 44.96 \, cm \)
• (C) \( 40.96 \, cm \)
• (D) \( 38.96 \, cm \)

Find the length of the hypotenuse of a right triangle with legs of length 6 cm and 8 cm.
 

• (A) \( 12 \, cm \)
• (B) \( 10 \, cm \)
• (C) \( 8 \, cm \)
• (D) \( 6 \, cm \)

What is the volume of a cylinder with a radius of 3 cm and a height of 5 cm?
 

• (A) \( 141.3 \, cm^3 \)
• (B) \( 120.5 \, cm^3 \)
• (C) \( 135.5 \, cm^3 \)
• (D) \( 150.5 \, cm^3 \)

The mean of five numbers is 8. If four of the numbers are 7, 9, 12, and 5, what is the fifth number?
 

• (A) \( 7 \)
• (B) \( 8 \)
• (C) \( 9 \)
• (D) \( 10 \)

A survey of 200 people found that 120 like coffee, 150 like tea, and 80 like both. How many people do not like either coffee or tea?
 

• (A) \( 10 \)
• (B) \( 20 \)
• (C) \( 30 \)
• (D) \( 40 \)

A dataset contains the numbers 5, 7, 9, 11, and 13. What is the median?
 

• (A) \( 7 \)
• (B) \( 9 \)
• (C) \( 11 \)
• (D) \( 13 \)

A jar contains 4 red, 5 blue, and 6 green marbles. If one marble is picked at random, what is the probability it is blue?
 

• (A) \( \frac{1}{3} \)
• (B) \( \frac{5}{15} \)
• (C) \( \frac{4}{15} \)
• (D) \( \frac{2}{5} \)

Simplify the expression: \( 3(x - 2) + 4 \).
 

• (A) \( 3x - 2 \)
• (B) \( 3x + 2 \)
• (C) \( 3x - 4 \)
• (D) \( 3x + 4 \)

If \( x \) is directly proportional to \( y \) and \( x = 10 \) when \( y = 2 \), what is \( x \) when \( y = 8 \)?
 

• (A) \( 30 \)
• (B) \( 40 \)
• (C) \( 50 \)
• (D) \( 60 \)

If \( 2x + 3 = 9 \), what is the value of \( x \)?
 

• (A) \( 1 \)
• (B) \( 2 \)
• (C) \( 3 \)
• (D) \( 4 \)

A right triangle has one leg of 5 cm and a hypotenuse of 13 cm. What is the length of the other leg?
 

• (A) \( 10 \, cm \)
• (B) \( 12 \, cm \)
• (C) \( 15 \, cm \)
• (D) \( 14 \, cm \)