GMAT Quant Practice Questions  Geometry
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.
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?
 Square
 Rectangle but not a square
 Rhombus
 Parallelogram but not a rhombus
 Kite
 Correct AnswerChoice (C).
The quadrilateral is a Rhombus. Correct answer  Explanatory Answer
 Quadrilaterals
 Medium
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 150^{o}?
 24 sq units
 48 sq units
 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
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
 6
 4
 24.5
 20.5
 12.5
 Correct AnswerChoice (D).
The radius of the circumscribing circle is 20.5 units. Correct answer  Explanatory Answer
 Right triangle properties
 Medium
If the sum of the interior angles of a regular polygon measures 1440^{o}, how many sides does the polygon have?
 10 sides
 8 sides
 12 sides
 9 sides
 None of these
 Correct AnswerChoice (A).
The regular polygon has 10 sides. Correct answer  Explanatory Answer
 Regular Polygons
 Easy
What is the radius of the incircle of the triangle whose sides measure 5, 12 and 13 units?
 2 units
 12 units
 6.5 units
 6 units
 7.5 units
 Correct AnswerChoice (A).
The radius of the inscribed circle is 2 units. Correct answer  Explanatory Answer
 Right Triangle : Inradius
 Medium
How many diagonals does a 63sided convex polygon have?
 3780
 1890
 3843
 3906
 1953
 Correct AnswerChoice (B).
The 63sided convex polygon has 1890 diagonals. Correct answer  Explanatory Answer
 Convex Polgons : Properties
 Easy
If 10, 12 and 'x' are sides of an acute angled triangle, how many integer values of 'x' are possible?
 7
 12
 9
 13
 11
 Correct AnswerChoice (C).
9 integer values are possible for x. Correct answer  Explanatory Answer
 Properties of triangles
 Medium
Is triangle ABC obtuse angled?
 a^{2} + b^{2} > c^{2}.
 The center of the circle circumscribing the triangle does not lie inside the triangle.
 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
 Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
 BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked.
 EACH statement ALONE is sufficient to answer the question asked.
 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
Is triangle ABC with sides a, b and c acute angled?
 Triangle with sides a^{2}, b^{2}, c^{2} has an area of 140 sq cms.
 Median AD to side BC is equal to altitude AE to side BC.
 Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
 Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
 BOTH statements (1) and (2) TOGETHER are sufficient but NEITHER statement ALONE is sufficient to answer the question asked.
 EACH statement ALONE is sufficient to answer the question asked.
 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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