GMAT Questions | Geometry & Solid Geometry

You may get three to five questions from Geometry and Solid 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, solid geometry, finding the area, perimeter of two dimensional geometric shapes and surface area, volume, longest diagnal of solids including cones, cylinders, cube, rectangular cube, sphere, and hemisphere.

Curated sample GMAT questions from these topics are presented here below. Attempt these questions and check if you have got the correct answer. One can use the explanatory answer or Video explanation made available (wherever provided) to help crack important GMAT quant questions.

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.

   Explanation Video Solution

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2. What is the area of an isosceles triangle if two of its sides measure 6 and 12?

   1. 8 √5
   2. 15 √5
   3. 9 √15
   4. 9 √5
   5. 12 √5

   Correct AnswerChoice C
   9 √15

   Explanation Video Solution

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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.

   Explanation Video Solution

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4. If the sum of the interior angles of a regular polygon measures 1440°, 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.

   Explanation Video Solution

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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.

   Explanation Video Solution

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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.

   Explanation Video Solution

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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 values.

   Explanation Video Solution

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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.

   Correct AnswerChoice E

   Explanation Video Solution

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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.

   Correct AnswerChoice A

   Explanation Video Solution

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10. A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

    1. 9
    2. 61
    3. 98
    4. 54
    5. 64

    Correct AnswerChoice D
    54 1cc cubes will have exactly one of their sides painted.

    Explanation Video Solution

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11. A wheel of a car of radius 21 cms is rotating at 600 RPM. What is the speed of the car in km/hr?

    1. 79.2 km/hr
    2. 47.52 km/hr
    3. 7.92 km/hr
    4. 39.6 km/hr
    5. 3.96 km/hr

    Correct AnswerChoice B
    The speed of the car is 47.52 km/hr.

    Explanation Video Solution

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12. The area of a square field is 24200 sq m. How long will a lady take to cross the field diagonally at the rate of 6.6 km/hr?

    1. 3 minutes
    2. 0.04 hours
    3. 2 minutes
    4. 2.4 minutes
    5. 2 minutes 40 seconds

    Correct AnswerChoice C
    The lady will take 2 minutes to cross the filed diagonally.

    Explanation Video Solution

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13. A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 211 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year?

    1. 11236
    2. 11025
    3. 14400
    4. 12696
    5. Cannot be determined

    Correct AnswerChoice A
    She produced 11236 cabbages this year.

    Explanation Video Solution

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14. The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = \\frac{22}{7}) in your calculations.

    1. 1696 sq m
    2. 1694 sq m
    3. 1594 sq m
    4. 1756 sq m
    5. 1896 sq m

    Correct AnswerChoice B
    The cow will be able to graze an additional 1694 sq m.

    Explanation Video Solution

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