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GRE Sets and Relations — practice questions — page 3

Explore 101 free Sets and Relations questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sets and Relations questions and exercises with answers

Showing questions 61–90 of 101.

The MAXIMUM possible measure of an exterior angle of a regular polygon is:Read the answer and worked solution →Which of the following is a perfect cube?Read the answer and worked solution →How many perfect cubes are there from 1 to 1000 (both included)?Read the answer and worked solution →What is the cube of 12?Read the answer and worked solution →Which of the following numbers is NOT a perfect cube?Read the answer and worked solution →The units (one's) digit of (78)³ is:Read the answer and worked solution →Sum of the consecutive odd numbers needed to obtain 5³ = 125 is:Read the answer and worked solution →The smallest natural number by which 392 must be MULTIPLIED to make it a perfect cube is:Read the answer and worked solution →How many digits at MAXIMUM can the cube of a 2-digit number have?Read the answer and worked solution →A cuboid of plasticine has sides 5 cm, 2 cm and 5 cm. The MINIMUM number of such cuboids needed to form a perfect cube (without leftover) is:Read the answer and worked solution →Compute 25³ − 24³ using the pattern (n+1)³ − n³ = 1 + 3·n·(n+1):Read the answer and worked solution →Is 1188 a perfect cube? If not, the smallest natural number by which 1188 must be DIVIDED to make the quotient a perfect cube is:Read the answer and worked solution →A child stacks unit cubes (side 1 cm) to make a larger cube of side 4 cm. The number of unit cubes used is:Read the answer and worked solution →Which of the following statements is TRUE?Read the answer and worked solution →The cube of which number among the following is a 7-digit number?Read the answer and worked solution →Find the smallest perfect cube that is divisible by both 8 and 27.Read the answer and worked solution →A rational number is any number that can be written in the form p/q, where p and q are integers and:Read the answer and worked solution →The multiplicative identity for rational numbers is:Read the answer and worked solution →Find 3/4 − 5/6.Read the answer and worked solution →Find (−4/5) × (3/7) × (15/16) × (−14/9).Read the answer and worked solution →Does the rational number 0 have a multiplicative inverse?Read the answer and worked solution →Which of the following is the WHOLE NUMBER that is closest to 0 but is NOT a natural number?Read the answer and worked solution →Solve for x: x = (4/5)(x + 10)Read the answer and worked solution →Using distributivity, find: (3/5) × [(−7/9) + (4/9)].Read the answer and worked solution →Which of the following is NOT a rational number?Read the answer and worked solution →The additive identity for rational numbers is:Read the answer and worked solution →The additive inverse of 5/8 is:Read the answer and worked solution →Which statement is TRUE for the set of rational numbers?Read the answer and worked solution →The mean of two rational numbers a and b is (a + b)/2. The mean of 1/3 and 1/2 is:Read the answer and worked solution →Simplify using commutativity and distributivity: (2/5) × (−3/7) − (1/14) − (3/7) × (3/5)Read the answer and worked solution →

Worked practice questions

The MAXIMUM possible measure of an exterior angle of a regular polygon is:

  1. 120° (for a triangle)
  2. 90° (for a square)
  3. 60° (for a hexagon)
  4. 30° (for a 12-gon)
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Correct answer: A. 120° (for a triangle)

In a regular polygon, each exterior angle = 360° / n. The fewer the sides, the larger each exterior angle. The smallest regular polygon is the equilateral triangle (n = 3), with each exterior angle = 360°/3 = 120°. This is the maximum possible value. Correspondingly, the MINIMUM possible interior angle of a regular polygon is 180° − 120° = 60°.

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Which of the following is a perfect cube?

  1. 100
  2. 216
  3. 250
  4. 500
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Correct answer: B. 216

216 = 6 × 6 × 6 = 6³, a perfect cube. None of the others equal a natural number cubed (5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512).

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How many perfect cubes are there from 1 to 1000 (both included)?

  1. 8
  2. 9
  3. 10
  4. 20
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Correct answer: C. 10

The cubes from 1 to 1000 are 1³, 2³, 3³, …, 10³ = 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. That is exactly 10 perfect cubes in this range.

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits