GRE 2024 Quantitative Reasoning Practice Test Set 3 Question Paper with Solutions PDF

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Updated on, Oct 13, 2025

byShivam Yadav

GRE 2024 Quantitative Reasoning Practice Test Set 3 Question Paper with Solutions PDF is available for download. The overall test time is about 1 hour and 58 minutes. GRE has total 5 sections:

  • Analytical Writing  (One "Analyze an Issue" task, Alloted time 30 minutes)
  • Verbal Reasoning  (Two Sections, with 12 questions and 15 questions respectively)
  • Quantitative Reasoning (Two Sections, with 12 questions and 15 questions respectively)

GRE 2024 Qantitative Reasoning Practice Test Set 3 Question Paper with Solutions PDF

GRE 2024 Quantitative Reasoning Set 3 Question Paper with Solutions PDF download iconDownload Check Solutions
GRE 2024 Qantitative Reasoning Practice Test Set 3 Question Paper with Solutions PDF

Question 1:

Reduce the following fraction: \[ \frac{a^2b^2 + c^2}{5ab^2} \div \frac{5ab + c}{5c} \]

  • (A) \( \frac{bc(ab + c)}{5a} \)
  • (B) \( \frac{ac(ab + c)}{5b} \)
  • (C) \( \frac{ah(ab + c)}{5c} \)
  • (D) \( \frac{5abh(ab + c)}{c} \)

Question 2:

If \( x = 55 \), \( x + y = 23 \), and \( y - x = 2 \), find the value of \( 2x + y \).

  • (A) 16
  • (B) 17
  • (C) 15
  • (D) 9
  • (E) 5

Question 3:

Which of the following are answers to the equation below? \[ x^2 - 4 = 0, \quad x^2 + 5x + 6 = 0 \]
I. \( x = 2 \)

II. \( x = -2 \)

III. \( x = -3 \)

  • (A) I and III
  • (B) II and III
  • (C) I, II, and III
  • (D) I only
  • (E) II only

Question 4:

Find the relationship between Quantity A and Quantity B: \[ (a + b)^2 = 34, \quad \frac{ab}{2} = 6 \]
Quantity A: \( a^2 + b^2 \)

Quantity B: 11

  • (A) The two quantities are equal.
  • (B) Quantity A is greater.
  • (C) Quantity B is greater.
  • (D) The relationship cannot be determined.

Question 5:

The arithmetic mean of \( a, b, c, d \) is 14.

Quantity A: 32

Quantity B: The arithmetic mean of \( a + b \), \( c + d \), and \( a - b + c - d = 48 \)

  • (A) Quantity A and Quantity B are equal.
  • (B) Quantity A is greater.
  • (C) Quantity B is greater.
  • (D) The relationship between Quantity A and Quantity B cannot be determined.

Question 6:

Compare Quantity A and Quantity B:
\[ Quantity A: (x + y)^3, \quad Quantity B: x^3 + y^3 \]
Given that \( x < 0 \) and \( y > 0 \), compare the two quantities.

  • (A) The relationship cannot be determined.
  • (B) The two quantities are equal.
  • (C) Quantity B is greater.
  • (D) Quantity A is greater.

Question 7:

Compare Quantity A and Quantity B: \[ Quantity A: (x + y)^3, \quad Quantity B: x^3 + y^3 \]
Given that \( x < 0 \) and \( y > 0 \), compare the two quantities.

  • (A) The relationship cannot be determined.
  • (B) The two quantities are equal.
  • (C) Quantity B is greater.
  • (D) Quantity A is greater.

Question 8:

Find the algebraic expression to represent the following statement:

The square of \( x \) multiplied by 3, the result has 18 subtracted from it and the final result divided by 15.

  • (A) \( \frac{3x^2 - 18}{15} \)
  • (B) \( \frac{(3x^2) - 18}{15} \)
  • (C) \( \frac{3(x^2 - 18)}{15} \)
  • (D) \( \frac{(3x^2 - 18)^2}{15} \)
  • (E) \( \frac{3x^2}{15} - 18 \)

Question 9:

Compare Quantity A and Quantity B and determine which is larger.
\[ Quantity A: x^3 - 6, \quad Quantity B: x + 1 \]
For when \( x < 2 \), compare the two quantities.

  • (A) Quantity A is larger.
  • (B) The two quantities are equal.
  • (C) Quantity B is larger.
  • (D) Can't be determined from the information provided.

Question 10:

How many real solutions are there for the following equation? \[ x^4 + 5x^2 - 14 = 0 \]

  • (A) 1
  • (B) 0
  • (C) 4
  • (D) 2

Question 11:

Simplify the following expression: \[ 3\sqrt{27} + 5\sqrt{18} - 3\sqrt{147} \]

  • (A) \( 8\sqrt{3} \)
  • (B) \( 5\sqrt{72} \)
  • (C) \( 5\sqrt{3} \)
  • (D) \( 2\sqrt{76} \)
  • (E) Cannot be simplified further

Question 12:

Simplify the following expression: \[ 0.327 + \left( \frac{3}{8} \times (0.048 + 2.176) \right) \]

  • (A) 0.0532
  • (B) 1.242
  • (C) 0.793
  • (D) 1.522

Question 13:

Which of the following is true? \[ Quantity A: \frac{12}{11} \div \frac{7}{6}, \quad Quantity B: \frac{17}{8} \div \frac{7}{6} \]

  • (A) The relationship between the quantities cannot be determined.
  • (B) Quantity B is larger.
  • (C) The two quantities are equal.
  • (D) Quantity A is larger.

Question 14:

If the product of two distinct integers is 143, which of the following could not represent the sum of those two integers?

  • (A) 144
  • (B) -144
  • (C) 24
  • (D) -24
  • (E) 11

Question 15:

A cake order cost 45.40 before tax. If the tax rate is 6.5%, what is the price of the cake after tax is applied?

  • (A)48.99
  • (B)5.34
  • (C)49.42
  • (D)48.35
  • (E)2.95

Question 16:

At an overpriced department store there are 112 customers. If 43 have purchased shirts, 57 have purchased pants, and 38 have purchased neither, how many purchased both shirts and pants?

  • (A) 74
  • (B) 26
  • (C) 38
  • (D) 14
  • (E) The answer cannot be determined.

Question 17:

The arithmetic mean of \( a, b, \) and \( c \) is 13.

Quantity A: The arithmetic mean of \( 2a + b, b + 3c, 39 - c \)

Quantity B: 39

  • (A) The two quantities are equal.
  • (B) Quantity B is greater.
  • (C) The relationship cannot be established.
  • (D) Quantity A is greater.

Question 18:

A boy with a lemonade stand sells cups of lemonade for a quarter each. He has bought 20 worth of supplies and is able to make 500 cups of lemonade with the supplies. If he has to pay a business tax of 4% for each cup he sells, how many cups will he have to sell in order to break even?

  • (A) 83.2 cups
  • (B) 84 cups
  • (C) 83 cups
  • (D) It is impossible for him to profit from this business venture.
  • (E) 92 cups

Question 19:

The average of five consecutive integers is 6. What is the largest of these integers?

  • (A) 7
  • (B) 6
  • (C) 12
  • (D) 8
  • (E) 10

Question 20:

Simplify: \[ \frac{1}{2} + \frac{x}{4} \]

  • (A) \( 1 + \frac{x}{16} \)
  • (B) \( \frac{3x + 4}{8} \)
  • (C) \( x + \frac{6}{32} \)
  • (D) \( x + \frac{12}{3} \)
  • (E) \( 1 + \frac{x}{4} \)

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