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GRE Quant Practice Worksheets & Answer Key

Download an 8-question GRE Quant worksheet with a separate answer and explanation section. The selected text questions work without a screen or an account.

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Version 2026-10-27 · Original foundation materials · No sign-up

What this collection covers

Quantitative Reasoning foundation practice; not Verbal or Analytical Writing.

This fixed sample includes one question per selected skill before additional families. Questions requiring a separate diagram are excluded from this text worksheet. It is an untimed study resource with working space, rather than an official mock examination.

Author-reviewed learning materials. Independent educator review is pending; question difficulty has not been calibrated with learner results. Check coverage and gaps before planning your preparation.

Inside the printable worksheet

8 original questionsSeparate explanationsUS Letter · PDF · Version 2026-10-27

Print the question section first. Keep the answer section separate until you have written your method or reason. Use the linked lessons to review a missed idea, then start a new set in the practice tool.

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Questions included in this PDF

QUESTION 1 · Integer structure

An integer n equals 50. What remainder does 3n + 1 leave when divided by 6?

  1. 3
  2. 0
  3. 1
  4. 2
  5. 4
Read the answer and explanation

Answer: 1

  1. n leaves remainder 2 on division by 6.
  2. Therefore 3n + 1 has the same remainder as 3(2) + 1 = 7.
  3. Reduce 7 modulo 6: the remainder is 1.
Review the lesson
QUESTION 2 · Equations and restrictions

If 2x + 12 = 28, what is 3x − 2?

  1. 40
  2. 58
  3. 22
  4. 8
  5. 26
Read the answer and explanation

Answer: 22

  1. Subtract 12 and divide by 2 to obtain x = 8.
  2. Substitute into the requested expression, not just x.
  3. 3(8) − 2 = 22.
Review the lesson
QUESTION 3 · Geometry with explicit conditions

A rectangle has length twice its width and perimeter 48 cm. What is its area in square centimeters?

  1. 48
  2. 24
  3. 256
  4. 128
  5. 512
Read the answer and explanation

Answer: 128

  1. If width is w, length is 2w and perimeter is 6w.
  2. Therefore w = 8, and length = 16.
  3. Area = 8 × 16 = 128.
Review the lesson
QUESTION 4 · Distribution summaries

One group has 6 values with mean 10; another has 8 values with mean 20. What is the combined mean?

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Answer: 110/7

  1. Group totals are 60 and 160.
  2. Add totals and divide by the combined size 14.
  3. The combined mean is 110/7.
Review the lesson
QUESTION 5 · Quantitative comparison strategy

Let x be any positive real number. Quantity A: x/3. Quantity B: 3/x.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined.
Read the answer and explanation

Answer: The relationship cannot be determined.

  1. If x = 3, the quantities are equal.
  2. If x = 6, Quantity A is 2 and Quantity B is 1/2.
  3. Both assignments are allowed, so no single relationship is forced.
Review the lesson
QUESTION 6 · Fractions and magnitude

What is the exact value of 1/3 + 1/4?

Read the answer and explanation

Answer: 7/12

  1. Use common denominator 12.
  2. The numerator becomes 4 + 3 = 7.
  3. The reduced result is 7/12.
Review the lesson
QUESTION 7 · Functions and quadratic structure

The functions f(x) = 2x + 10 and g(x) = −x + 34 have equal values at what x?

  1. 34
  2. -8
  3. 8
  4. 26
  5. 44/3
Read the answer and explanation

Answer: 8

  1. Equate the outputs: 2x + 10 = −x + 34.
  2. Collect terms: 3x = 24.
  3. Thus x = 8.
Review the lesson
QUESTION 8 · Coordinates encode geometry

A line is perpendicular to y = 2x + 6 and passes through (12, 9). What is its y-intercept?

  1. 15
  2. 9
  3. 21
  4. -15
  5. 3
Read the answer and explanation

Answer: 15

  1. The perpendicular slope is −1/2.
  2. In y = −x/2 + b, substitute (12,9).
  3. b = 9 + 6 = 15.
Review the lesson

Sources and preparation route

These prompts and explanations are the site's original learning materials. The reference links below support the selected skills; they are not endorsements or official examination questions.

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