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GRE Sets and Relations — practice questions — page 4

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 91–101 of 101.

Which property is shown by: (−2/3) + (3/5) = (3/5) + (−2/3)?Read the answer and worked solution →How many rational numbers exist between 1/3 and 1/2?Read the answer and worked solution →Solve for x: (x − 5)/3 = (x − 3)/5Read the answer and worked solution →Using distributivity, the value of (7/5) × (−3/12) + (7/5) × (5/12) is:Read the answer and worked solution →For which rational number a is the statement 'a is its own additive inverse' TRUE?Read the answer and worked solution →Three rational numbers a, b, c are given. Which of the following is ALWAYS true?Read the answer and worked solution →Which of the following is NOT a perfect square?Read the answer and worked solution →Which of the following is a perfect square?Read the answer and worked solution →The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 equals:Read the answer and worked solution →Using prime factorisation, √324 equals:Read the answer and worked solution →How many PERFECT SQUARES lie strictly between 100 and 200?Read the answer and worked solution →

Worked practice questions

Which property is shown by: (−2/3) + (3/5) = (3/5) + (−2/3)?

  1. Associativity of addition
  2. Commutativity of addition
  3. Distributivity
  4. Closure under addition
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Correct answer: B. Commutativity of addition

a + b = b + a is the commutative property of addition the two sides differ only in the order of the addends.

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How many rational numbers exist between 1/3 and 1/2?

  1. Only one
  2. Exactly five
  3. Exactly ten
  4. Infinitely many
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Correct answer: D. Infinitely many

Between any two distinct rational numbers there are infinitely many rationals. **One way to see this:** keep finding the mean of the previous interval — every mean is a new rational number strictly between the two, and the process never ends. This is a key feature distinguishing rationals from integers.

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Solve for x: (x − 5)/3 = (x − 3)/5

  1. x = 4
  2. x = 8
  3. x = 12
  4. x = 16
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Correct answer: B. x = 8

Cross-multiply: 5(x − 5) = 3(x − 3) We have → 5x − 25 = 3x − 9 → 2x. So → 5x − 25 = 16. → x = 8. Check: LHS = 3/3 = 1, RHS = 5/5 = 1. ✓

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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