GRE 2024 Quantitative Reasoning Practice Test 6 Question Paper with Solutions PDF

GRE 2024 Quantitative Reasoning Practice Test 6 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 6 Question Paper with Solutions PDF

GRE 2024 Quantitative Reasoning Question Paper with Solutions PDF download iconDownload Check Solutions
GRE 2024 Qantitative Reasoning Practice Test 6 Question Paper with Solutions PDF

Question 1:

A number \( n \) is 20% less than another number \( m \). If \( m = 50 \), what is \( n \)?
 

  • (A) \( 35 \)
  • (B) \( 40 \)
  • (C) \( 42 \)
  • (D) \( 45 \)
  • (E) \( 48 \)

Question 2:

If \( a \) and \( b \) are positive integers such that \( a \times b = 36 \), and \( a \) is 3 less than twice \( b \), what is the value of \( a + b \)?
 

  • (A) \( 11 \)
  • (B) \( 13 \)
  • (C) \( 15 \)
  • (D) \( 17 \)
  • (E) \( 19 \)

Question 3:

A bakery sells cupcakes in packs of 6 and packs of 9. If \( p \) packs of 6 and \( q \) packs of 9 are bought, and the total number of cupcakes is 90, what is the smallest possible value of \( p + q \)?
 

  • (A) \( 7 \)
  • (B) \( 8 \)
  • (C) \( 9 \)
  • (D) \( 10 \)
  • (E) \( 11 \)

Question 4:

If \( x \) is an even integer and \( y = 3x + 5 \), which of the following must be odd?
 

  • (A) \( x \)
  • (B) \( y \)
  • (C) \( 2x + y \)
  • (D) \( x + y \)
  • (E) \( 2y \)

Question 5:

If a number \( n \) leaves a remainder of 3 when divided by 5, what is the remainder when \( 2n \) is divided by 5?
 

  • (A) \( 1 \)
  • (B) \( 2 \)
  • (C) \( 3 \)
  • (D) \( 4 \)
  • (E) \( 0 \)

Question 6:

If \( x^2 - 6x + 9 = y \), what is the value of \( y \) when \( x = 4 \)?
 

  • (A) \( 4 \)
  • (B) \( 5 \)
  • (C) \( 6 \)
  • (D) \( 7 \)
  • (E) \( 8 \)

Question 7:

Solve for \( x \) if \( \frac{x + 2}{x - 3} = 2 \).
 

  • (A) \( 4 \)
  • (B) \( 5 \)
  • (C) \( 6 \)
  • (D) \( 7 \)
  • (E) \( 8 \)

Question 8:

If \( f(x) = 2x^2 - 3x + 4 \), what is \( f(2) - f(-2) \)?
 

  • (A) \( 20 \)
  • (B) \( 22 \)
  • (C) \( 24 \)
  • (D) \( 26 \)
  • (E) \( 28 \)

Question 9:

If \( 3x + 2y = 6 \) and \( 2x - y = 4 \), what is \( x + y \)?
 

  • (A) \( 0 \)
  • (B) \( 1 \)
  • (C) \( 2 \)
  • (D) \( 3 \)
  • (E) \( 4 \)

Question 10:

If \( x^2 - 4x + 4 = 0 \), what is the sum of the roots?
 

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

Question 11:

In triangle \( ABC \), if \( AB = 6 \), \( BC = 8 \), and \( AC = 10 \), what is the area of the triangle?
 

  • (A) \( 24 \)
  • (B) \( 25 \)
  • (C) \( 26 \)
  • (D) \( 27 \)
  • (E) \( 28 \)

Question 12:

A rectangle has a length that is twice its width. If the perimeter is 48 units, what is the area of the rectangle?
 

  • (A) \( 96 \)
  • (B) \( 108 \)
  • (C) \( 120 \)
  • (D) \( 132 \)
  • (E) \( 144 \)

Question 13:

In a circle with a radius of 5, what is the length of an arc that subtends a central angle of 120 degrees?
 

  • (A) \( \frac{5\pi}{3} \)
  • (B) \( \frac{10\pi}{3} \)
  • (C) \( 5\pi \)
  • (D) \( 10\pi \)

Question 14:

A cube has a surface area of 54 square units. What is the volume of the cube?
 

  • (A) \( 27 \)
  • (B) \( 36 \)
  • (C) \( 45 \)
  • (D) \( 54 \)
  • (E) \( 64 \)

Question 15:

A cube has a surface area of 54 square units. What is the volume of the cube?
 

  • (A) \( 27 \)
  • (B) \( 36 \)
  • (C) \( 45 \)
  • (D) \( 54 \)
  • (E) \( 64 \)

Question 16:

A dataset has the following values: 10, 12, 15, 15, 20, 22. What is the range and the median of the dataset?
 

  • (A) Range: 10, Median: 15
  • (B) Range: 12, Median: 15
  • (C) Range: 12, Median: 16
  • (D) Range: 10, Median: 16
  • (E) Range: 10, Median: 15.5

Question 17:

In a survey, 60% of respondents prefer coffee, 30% prefer tea, and the remaining prefer neither. If 100 people responded, how many prefer neither?
 

  • (A) 5
  • (B) 10
  • (C) 15
  • (D) 20
  • (E) 25

Question 18:

A dataset has the following values: 10, 12, 15, 15, 20, 22. What is the range and the median of the dataset?
 

  • (A) Range: 10, Median: 15
  • (B) Range: 12, Median: 15
  • (C) Range: 12, Median: 16
  • (D) Range: 10, Median: 16
  • (E) Range: 10, Median: 15.5

Question 19:

In a survey, 60% of respondents prefer coffee, 30% prefer tea, and the remaining prefer neither. If 100 people responded, how many prefer neither?
 

  • (A) 5
  • (B) 10
  • (C) 15
  • (D) 20
  • (E) 25

Question 20:

A bag contains 3 red, 5 blue, and 7 green balls. If a ball is drawn at random, what is the probability it is either red or blue?
 

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

GRE Questions

  • 1.
    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.


      • 2.
        The following appeared in a health newsletter.
        "Nosinia is an herb that many users report to be as effective as prescription medications at fighting allergy symptoms. Researchers recently compared Nosinia to a placebo in 95 men and women with seasonal allergies to ragweed pollen. Participants in the study reported that neither Nosinia nor the placebo offered significant relief. However, for the most severe allergy symptoms, the researchers reported that Nosinia was more effective than the placebo in providing relief. Furthermore, at the end of the study, participants given Nosinia were more likely than participants given a placebo to report feeling healthier. We, therefore, recommend using Nosinia to help with your severe allergy symptoms."

          • How reliable is the study's sample size?
          • How does the severity of symptoms affect the results?
          • Was the placebo truly effective in reducing allergy symptoms?
          • Is there any independent evidence for Nosinia’s effectiveness?

        • 3.
          The following appeared as a letter to the editor from the owner of a skate shop in Central Plaza.
          "Two years ago the city council voted to prohibit skateboarding in Central Plaza. They claimed that skateboard users were responsible for litter and vandalism that were keeping other visitors from coming to the plaza. In the past two years, however, there has been only a small increase in the number of visitors to Central Plaza, and litter and vandalism are still problematic. Skateboarding is permitted in Monroe Park, however, and there is no problem with litter or vandalism there. In order to restore Central Plaza to its former glory, then, we recommend that the city lift its prohibition on skateboarding in the plaza."

            • What is the current level of litter and vandalism in Central Plaza?
            • How much foot traffic has increased in Monroe Park compared to Central Plaza?
            • Has the local economy in the plaza improved since the ban on skateboarding?
            • How successful has the Monroe Park skateboarding program been in other cities?

          • 4.
            Claim: Though often considered an objective pursuit, learning about the historical past requires creativity.
            Reason: Because we can never know the past directly, we must reconstruct it by imaginatively interpreting historical accounts, documents, and artifacts.
            Write a response in which you discuss the extent to which you agree or disagree with the claim and the reason on which the claim is based.


              • 5.
                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

                • 6.
                  “Reviving the practice of using elements of popular music in classical composition, an approach that had been in hibernation in the United States during the 1960s, composer Philip Glass (born 1937) embraced the ethos of popular music in his compositions. Glass based two symphonies on music by rock musicians David Bowie and Brian Eno, but the symphonies' sound is distinctively his. Popular elements do not appear out of place in Glass's classical music, which from its early days has shared certain harmonies and rhythms with rock music. Yet this use of popular elements has not made Glass a composer of popular music. His music is not a version of popular music packaged to attract classical listeners; it is high art for listeners steeped in rock rather than the classics.

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