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GRE Mensuration — practice questions

Explore 57 free Mensuration questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Mensuration questions and exercises with answers

Showing questions 1–30 of 57.

Solve for z: 3(5z − 7) − 2(9z − 11) = 4(8z − 13) − 17Read the answer and worked solution →Square root of 144 is:Read the answer and worked solution →Which of these cannot possibly be the LAST digit (units digit) of a perfect square?Read the answer and worked solution →How many non-square natural numbers lie between 9² and 10² (exclusive of both)?Read the answer and worked solution →What is 35² without direct multiplication?Read the answer and worked solution →By how much does (n+1)² exceed n²?Read the answer and worked solution →The square root of 0.81 is:Read the answer and worked solution →Using the identity (2m, m² − 1, m² + 1) for Pythagorean triplets, the triplet generated by m = 4 is:Read the answer and worked solution →A Pythagorean triplet has one member equal to 12, and the OTHER TWO members differ by 2. The triplet is:Read the answer and worked solution →What is the smallest natural number by which 180 must be MULTIPLIED so that the product becomes a perfect square?Read the answer and worked solution →What is the smallest natural number by which 1620 must be DIVIDED so that the quotient is a perfect square?Read the answer and worked solution →Compute 99² (without long multiplication, using (a + b)² or (a − b)²):Read the answer and worked solution →Compute 105² without direct multiplication:Read the answer and worked solution →Compute the square root of 12.96 (a decimal).Read the answer and worked solution →What is the units digit of (1234)²?Read the answer and worked solution →How many digits will be in the square root of a perfect square with EXACTLY 8 digits?Read the answer and worked solution →Two square fields have areas in the ratio 16 : 9. The ratio of their PERIMETERS is:Read the answer and worked solution →A square garden has area 2025 m². What is its side?Read the answer and worked solution →In a right triangle, if one leg is 9 cm and hypotenuse is 15 cm, the other leg isRead the answer and worked solution →In an equilateral triangle of side 6 cm, the area isRead the answer and worked solution →The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle isRead the answer and worked solution →Two similar triangles have their sides in the ratio 3 : 5. The ratio of their areas isRead the answer and worked solution →In triangle ABC, AB = AC and angle A = 40 degrees. Then angle B isRead the answer and worked solution →The circumference of a circle with diameter 14 cm is (use pi = 22/7)Read the answer and worked solution →If two chords AB and CD of a circle intersect at P inside the circle, with PA = 4, PB = 9, PC = 6, then PD isRead the answer and worked solution →The radius of a circle whose area is 154 cm^2 is (use pi = 22/7)Read the answer and worked solution →The angle subtended by a diameter at any point on the circle isRead the answer and worked solution →Sum of all interior angles of a regular hexagon isRead the answer and worked solution →Each interior angle of a regular octagon isRead the answer and worked solution →The number of sides of a regular polygon whose each exterior angle is 30 degrees isRead the answer and worked solution →

Worked practice questions

Solve for z: 3(5z − 7) − 2(9z − 11) = 4(8z − 13) − 17

  1. z = 1
  2. z = 2
  3. z = 3
  4. z = −2
Show answer and solution

Correct answer: B. z = 2

Expand: LHS = 15z − 21 − 18z + 22 = −3z + 1. RHS = 32z − 52 − 17 = 32z − 69. So −3z + 1 = 32z − 69, giving 35z = 70 and z = 2.

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Square root of 144 is:

  1. 11
  2. 12
  3. 13
  4. 14
Show answer and solution

Correct answer: B. 12

12 × 12 = 144, so √144 = 12. (Strictly the equation x² = 144 has two solutions, ±12; by convention √144 denotes the positive root, 12.)

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Which of these cannot possibly be the LAST digit (units digit) of a perfect square?

  1. 1
  2. 4
  3. 7
  4. 9
Show answer and solution

Correct answer: C. 7

By checking units digits of n² for n = 0,1,2,…,9: possible last digits of a perfect square are {0,1,4,5,6,9}. So 2, 3, 7 and 8 can NEVER be the units digit of a perfect square. **Option C (7) is therefore correct.**

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann Sums