GRE 2024 Quantitative Reasoning Practice Test Set 20 Question Paper with Solutions PDF

GRE 2024 Quantitative Reasoning Practice Test Set 20 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 20 Question Paper with Solutions PDF

GRE 2024 Quantitative Reasoning Set 20 Question Paper with Solutions PDF download iconDownload Check Solutions
GRE 2024 Qantitative Reasoning Practice Test Set 20 Question Paper with Solutions PDF

Question 1:

Given the equations \(x30y=4\) and \(1797+3y=15x\), compare Quantity A and Quantity B.

Quantity A: y

Quantity B: 1

  • (A) The relationship cannot be determined from the information given.
  • (B) The quantities are equal.
  • (C) Quantity A is greater.
  • (D) Quantity B is greater.

Question 2:

John has 50 for soda and he must buy both diet and regular sodas. His total order must have at exactly two times as many cans of diet soda as cans of regular soda. What is the greatest number of cans of diet soda John can buy if regular soda is 0.50 per can and diet soda is 0.75 per can?

  • (A) None of the other answers
  • (B) 51
  • (C) 25
  • (D) 75
  • (E) 50

Question 3:

Find the intersection of the following two equations:

3x + 4y = 6

15x - 4y = 3

  • (A) (1, 0.5)
  • (B) (0.2, 0)
  • (C) (18, 0)
  • (D) (3, 4)
  • (E) (0.5, 1.125)

Question 4:

One of the roots of the equation x² + kx - 12 = 0 is 3, and k is a constant.

Quantity A: The value of k

Quantity B: -1

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

Question 5:

Two cars start 25 miles apart and drive away from each other in opposite directions at speeds of 50 and 70 miles per hour. In approximately how many minutes will they be 400 miles apart?

  • (A) 200
  • (B) 3.33
  • (C) 187.5
  • (D) None of the other answers
  • (E) 3.125

Question 6:

What is the value of (5 + x)(10 - y) when x = 3 and y = -3?

  • (A) 104
  • (B) 108
  • (C) 38
  • (D) 56

Question 7:

If 2x + y = 9 and y - z = 4 then 2x + z = ?

  • (A) 5
  • (B) 13
  • (C) Cannot be determined
  • (D) 29
  • (E) 21

Question 8:

11/(x - 7) + 4/(7 - x) = ?

  • (A) 15/(7 - x)
  • (B) 15/(x - 7)
  • (C) 7/(7 - x)
  • (D) 15
  • (E) (-7)/(7 - x)

Question 9:

If 6h - 2g = 4g + 3h, in terms of g, h = ?

  • (A) g
  • (B) 4g
  • (C) 2g
  • (D) 5g
  • (E) 3g

Question 10:

Audrey, Penelope and Clementine are all sisters. Penelope is 8 years older than Clementine and 2 years younger than Audrey. If the sum of Penelope and Clementine's age is Audrey's age, how old is Clementine's age?

  • (A) 4
  • (B) 2
  • (C) 8
  • (D) 3

Question 11:

If \(3x + y = 13\) and \(x - 2y = -12\), what is the value of x?

  • (A) 3
  • (B) 1
  • (C) 2
  • (D) \(\frac{1}{3}\)
  • (E) \(\frac{2}{3}\)

Question 12:

A given university has an average professor pay of $40,000 a year and an average administrator pay of $45,000 per year. If the ratio of professors to administrators is 4 to 3, and the total pay for professors and administrators in a year is 40,415,000, how many professors does the college have?

  • (A) 500
  • (B) 375
  • (C) 411
  • (D) 548
  • (E) 475

Question 13:

Given \(x > 0\).

Quantity A: \(-5x + 4\)

Quantity B: \(8 - 2x\)

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

Question 14:

A theme park charges $10 for adults and $5 for kids. How many kids tickets were sold if a total of 548 tickets were sold for a total of $3750?

  • (A) 431
  • (B) 157
  • (C) 346
  • (D) 248
  • (E) 269

Question 15:

Given the following information:

Sally is 2 years younger than Abby.

Daisy is 5 years older than Tracy.

Abby is 6 years older than Tracy.



Quantity A: Sally's age

Quantity B: Daisy's age

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

Question 16:

Given the equations:
\(x^2 + 5x - 24 = 0\)
\(y^2 - 9y + 20 = 0\)



Quantity A: x

Quantity B: y

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

Question 17:

Jen and Karen are travelling for the weekend. They both leave from Jen's house and meet at their destination 250 miles away. Jen drives 45mph the whole way. Karen drives 60mph but leaves a half hour after Jen. How long does it take for Karen to catch up with Jen?

  • (A) 1.5 hours
  • (B) She can't catch up.
  • (C) 3 hours
  • (D) 1 hour
  • (E) 2 hours

Question 18:

Solve for z: \(3(z + 4) - 7 = 17\)

  • (A) 4
  • (B) 8
  • (C) 2
  • (D) -8
  • (E) -2

Question 19:

If \(5(3x + y) = 15\), what is x in terms of y?

  • (A) \(x = 10 - \frac{y}{3}\)
  • (B) \(x = 3 - 3y\)
  • (C) \(x = 10 + \frac{y}{3}\)
  • (D) \(x = 15 + \frac{5y}{3}\)
  • (E) \(x = 1 - \frac{y}{3}\)

Question 20:

Given:
\(y = x^2 - 10\)
\(y = 15\)



Quantity A: \(y/3\)

Quantity B: x

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

Question 21:

If \(a = \frac{1}{3}b\) and \(b = 4c\), then in terms of c, \(a - b + c = ?\)

  • (A) c
  • (B) \(\frac{7}{3}c\)
  • (C) \(-\frac{5}{3}c\)
  • (D) \(-\frac{11}{3}c\)

Question 22:

If \(14x - 16y = 16\) and \(yz = 12\), then what is the value of \(3x - z\)?

  • (A) 1
  • (B) 2
  • (C) 4
  • (D) 6
  • (E) 3

Question 23:

If \(x^3 = 8\), then \(x^2(4/(3-x))(2/(4-x)) - (4/x^2) = ?\)

  • (A) 16
  • (B) 35
  • (C) 0
  • (D) 15
  • (E) 22

Question 24:

Sarah's current age is three times Ron's age two years ago. Sarah is currently 14 years older than Ron. What is the sum of Sarah and Ron's current age?

  • (A) 24
  • (B) 36
  • (C) 34
  • (D) 32

Question 25:

Jack has 14 coins consisting of nickels and dimes that total
(0.90. How many nickels does Jack have?

  • (A) 10
  • (B) 8
  • (C) 4
  • (D) 6
  • (E) 12

Question 26:

Abby works at a car dealership and receives a commission "c" which is a percent of the profit the dealership makes from the sale, which is the difference between the price "p" of the car and the value "v" of the car. How much, in dollars, does the dealership earn per transaction?

  • (A) \((p - v)(0.01c)\)
  • (B) \((p - v)(1 - 0.01c)\)
  • (C) \(p(v - 0.01c)\)
  • (D) \((p - v)(1 - c)\)
  • (E) \(pv(0.01c)\)

Question 27:

If \(8s - 6k = 4s - 2k\), then, in terms of s, k=?

  • (A) Cannot be determined
  • (B) 3s
  • (C) 5s
  • (D) 2s
  • (E) s

Question 28:

Kim is twice as old as Claire. Nick is 3 years older than Claire. Kim is 6 years older than Emily. Their ages combined equal 81. How old is Nick?

  • (A) 22
  • (B) 27
  • (C) 17
  • (D) 13

Question 29:

The sum of two consecutive odd integers is 32. What is the value of the next consecutive odd integer?

  • (A) 33
  • (B) 21
  • (C) 17
  • (D) Cannot be determined
  • (E) 19

Question 30:

A store sells potatoes for
(0.24 and tomatoes for
)0.76. Fred bought 12 individual vegetables. If he paid
(6.52 total, how many potatoes did Fred buy?

  • (A) 5
  • (B) 8
  • (C) 7
  • (D) 2

Question 31:

Jon invested part of
(16,000 at 3% and the rest at 5% for a total return of
)680.

Quantity A: The amount Jon invested at 5% interest

Quantity B: The amount Jon invested at 3% interest

  • (A) The two quantities are equal
  • (B) Quantity A is greater
  • (C) The relationship cannot be determined from the information given
  • (D) Quantity B is greater

Question 32:

Given the system of equations:
\(3x + 4y = 5\)
\(x - y = 6\)



Quantity A: x

Quantity B: y

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

Question 33:

Bill and Bob are working to build toys. Bill can build k toys in 6 hours. Bob can build k toys in 3 hours. How long would it take Bob and Bill to build 4k toys working together?

  • (A) 8 hours
  • (B) 12 hours
  • (C) 9 hours
  • (D) 2 hours
  • (E) 4 hours

Question 34:

If x = 4, and y = 3x + 5, then 2y - 1 equals

  • (A) 47
  • (B) 22
  • (C) 15
  • (D) 33

Question 35:

A hybrid car gets 40 miles per gallon. Gasoline costs $3.52 per gallon. What is the cost of the gasoline needed for the car to travel 120 miles?

  • (A) $9.54
  • (B) $10.56
  • (C) $10.36
  • (D) $14.08
  • (E) $12.53

Question 36:

Two palm trees grow next to each other in Luke's backyard. One of the trees gets sick, so Luke cuts off the top 3 feet. The other tree, however, is healthy and grows 2 feet. How tall are the two trees if the healthy tree is now 4 feet taller than the sick tree, and together they are 28 feet tall?

  • (A) 8 and 20 feet
  • (B) 11 and 17 feet
  • (C) 12 and 16 feet
  • (D) cannot be determined
  • (E) 14 and 14 feet

Question 37:

Given the system of equations:
\(x + y = 12\)
\(2x - y = 6\)



Quantity A: x

Quantity B: y

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

GRE Questions

  • 1.
    Three years ago, because of flooding at the Western Palean Wildlife Preserve, 100 lions and 100 western gazelles were moved to the East Palean Preserve, an area that is home to most of the same species that are found in the western preserve, though in larger numbers, and to the eastern gazelle, a close relative of the western gazelle.
    Write a response in which you discuss one or more alternative explanations that could rival the proposed explanation and explain how your explanation(s) can plausibly account for the facts presented in the argument.


      • 2.
        Should we really care for the greatest actors of the past could we have them before us? Should we find them too different from our accent of thought, of feeling, of speech, in a thousand minute particulars which are of the essence of all three? Dr. Doran's long and interesting records of the triumphs of Garrick, and other less familiar, but in their day hardly less astonishing, players, do not relieve one of the doubt. Garrick himself, as sometimes happens with people who have been the subject of much anecdote and other conversation, here as elsewhere, bears no very distinct figure. One hardly sees the wood for the trees. On the other hand, the account of Betterton, "perhaps the greatest of English actors," is delightfully fresh. That intimate friend of Dryden, Tillatson, Pope, who executed a copy of the actor's portrait by Kneller which is still extant, was worthy of their friendship; his career brings out the best elements in stage life. The stage in these volumes presents itself indeed not merely as a mirror of life, but as an illustration of the utmost intensity of life, in the fortunes and characters of the players. Ups and downs, generosity, dark fates, the most delicate goodness, have nowhere been more prominent than in the private existence of those devoted to the public mimicry of men and women. Contact with the stage, almost throughout its history, presents itself as a kind of touchstone, to bring out the bizarrerie, the theatrical tricks and contrasts, of the actual world.


          • 3.
            Complete the paragraph from the given words. It is refreshing to read a book about our planet by an author who does not allow facts to be (i) _________ by politics: well aware of the political disputes about the effects of human activities on climate and biodiversity, this author does not permit them to (ii) _________ his comprehensive description of what we know about our biosphere. He emphasizes the enormous gaps in our knowledge, the sparseness of our observations, and the (iii) _________, calling attention to the many aspects of planetary evolution that must be better understood before we can accurately diagnose the condition of our planet. Fill in the blanks from the following:

              • overshadowed
              • invalidated
              • illuminated
              • enhance
              • obscure

            • 4.
              Melvin’s little sister was so ________ that she would believe anything he told her, and his burgeoning sense of maturity rendered him increasingly loath to gull her.

                • dogged
                • tenable
                • fractious
                • frivolous
                • credulous

              • 5.
                “Color photography has eliminated the need for realism in artistic painting, in the opinion of a number of art scholars and artists. At the same time, many members of the art community still feel that realistic artwork is still valuable and worthwhile.”

                  • Agree, because color photography has eliminated the need for realistic art.
                  • Disagree, as realism in art serves as an important expression of human creativity.
                  • Agree, but only in some cases, color photography does not affect all artistic forms.
                  • Disagree, as traditional forms of art hold inherent value independent of color photography.

                • 6.
                  It has been suggested that long-term prisoners, on release from jail, be given a reasonable state pension to reduce the likelihood of their resorting to crime. Most people instinctively reject the suggestion as they feel it would be like rewarding criminal activity. The supporters of the prisoners' pension scheme have criticized those who reject this possibility, by claiming that for the critics...
                  Which of the following is the most logical completion of the sentence above?

                    • emotion is more important than justice
                    • punishment for criminals is more important than crime prevention
                    • crime prevention is not an important issue
                    • money has too high a value
                    • the law should not be concerned with what happens after jail

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