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GMAT Quant Practice Questions - Geometry

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You may get five to seven questions from Geometry in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts tested include lines, angles, triangles, quadrilaterals, circles, coordinate geometry and solid geometry. A collection of GMAT practice questions from Geometry is given below. Attempt these questions and check whether you have got the correct answer. If you have not go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

  1. Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?

    1. Square
    2. Rectangle but not a square
    3. Rhombus
    4. Parallelogram but not a rhombus
    5. Kite
    • Correct AnswerChoice (C).
      The quadrilateral is a Rhombus.
      Correct answer
    • Explanatory Answer
    • Quadrilaterals
    • Medium
  2. What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150o?

    1. 24 sq units
    2. 48 sq units
    3. 24 under root 3
    4. 48 under root 3
    5. Such a triangle does not exist
    • Correct AnswerChoice (A).
      The area of the obtuse angled triangle is 24 sq units.
      Correct answer
    • Explanatory Answer
    • Triangle Area
    • Easy
  3. What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?

    1. 6
    2. 4
    3. 24.5
    4. 20.5
    5. 12.5
    • Correct AnswerChoice (D).
      The radius of the circumscribing circle is 20.5 units.
      Correct answer
    • Explanatory Answer
    • Right triangle properties
    • Medium
  4. If the sum of the interior angles of a regular polygon measures 1440o, how many sides does the polygon have?

    1. 10 sides
    2. 8 sides
    3. 12 sides
    4. 9 sides
    5. None of these
    • Correct AnswerChoice (A).
      The regular polygon has 10 sides.
      Correct answer
    • Explanatory Answer
    • Regular Polygons
    • Easy
  5. What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?

    1. 2 units
    2. 12 units
    3. 6.5 units
    4. 6 units
    5. 7.5 units
    • Correct AnswerChoice (A).
      The radius of the inscribed circle is 2 units.
      Correct answer
    • Explanatory Answer
    • Right Triangle : Inradius
    • Medium
  6. How many diagonals does a 63-sided convex polygon have?

    1. 3780
    2. 1890
    3. 3843
    4. 3906
    5. 1953
    • Correct AnswerChoice (B).
      The 63-sided convex polygon has 1890 diagonals.
      Correct answer
    • Explanatory Answer
    • Convex Polgons : Properties
    • Easy
  7. If 10, 12 and 'x' are sides of an acute angled triangle, how many integer values of 'x' are possible?

    1. 7
    2. 12
    3. 9
    4. 13
    5. 11
    • Correct AnswerChoice (C).
      9 integer values are possible for x.
      Correct answer
    • Explanatory Answer
    • Properties of triangles
    • Medium
  8. Is triangle ABC obtuse angled?

    1. a2 + b2 > c2.
    2. The center of the circle circumscribing the triangle does not lie inside the triangle.
    1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
    2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
    3. BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked.
    4. EACH statement ALONE is sufficient to answer the question asked.
    5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked; additional data specific to the problem is needed.
    • Correct AnswerChoice (E).
      The two statements together are NOT sufficient.
      Correct answer
    • Explanatory Answer
    • Properties of obtuse triangles
    • Hard
  9. Is triangle ABC with sides a, b and c acute angled?

    1. Triangle with sides a2, b2, c2 has an area of 140 sq cms.
    2. Median AD to side BC is equal to altitude AE to side BC.
    1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
    2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
    3. BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked.
    4. EACH statement ALONE is sufficient to answer the question asked.
    5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked; additional data specific to the problem is needed.
    • Correct AnswerChoice (A).
      Statement 1 ALONE sufficient; statement 2 is NOT.
      Correct answer
    • Explanatory Answer
    • Properties of acute triangles
    • Hard
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