GMAT Hard Math Questions | Geometry

Must solve GMAT practice questions in Geometry. The following topics are covered in the GMAT quant section from Geometry:

1. Triangles
2. Lines and angles
3. Quadrilaterals
4. Circles
5. Coordinate Geometry
6. Solids

1. GMAT 700 800 Level Question | Geometry | Area of Circles

   In the figure given below, ABC and CDE are two identical semi-circles of radius 2 units. B and D are the mid points of the arc ABC and CDE respectively. What is the area of the shaded region?

   1. 4π - 1
   2. 3π - 1
   3. 2π - 4
   4. ½(3π - 1)
   5. 2π - 2

   Correct AnswerChoice C
   The area of the shaded region is
   (2π - 4) sq units.

   Solution Video Solution

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2. GMAT Data Sufficiency | Hard Math Question | Geometry

   a, b, and c are sides of a right triangle. What is the area of the triangle?

   Statement 1:a = 4.
   Statement 2: a + b + c = 4.

   Correct AnswerChoice C
   Statements Together Sufficient

   Solution Video Solution

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3. GMAT DS Sample Question | Geometry | Triangles

   Is the triangle ABC right angled at B an isosceles triangle?

   Statement 1: All 3 sides are integers.
   Statement 2: The square of the hypotenuse is twice the product of the other two sides.

   Correct AnswerChoice D
   Statements are Independently Sufficient to answer the question.

   Solution Video Solution

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4. GMAT 700 800 Level Question | Coordinate Geometry & Permutation Combination

   Rectangle ABCD is constructed in the xy-plane so that sides AB and CD are parallel to the x-axis. Both the x and y coordinates of all four vertices of the rectangle are integers. How many rectangles can be constructed if x and y coordinates satisfy the inequality 11 < x < 29 and 5 ≤ y ≤ 13?

   1. 153
   2. 153C₄
   3. 4896
   4. 2448
   5. 5508

   Correct AnswerChoice C
   4896 rectangles can be constructed.

   Solution Video Solution

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5. Geometry | Coordinate Geometry DS Practice | GMAT Challenging Math Question

   Does the line L whose equation is y = mx + c cut the x-axis in the positive direction of x-axis?

   Statement 1: The intercepts of Line K, perpendicular to L, are of the opposite signs.
   Statement 2: Line L passes through the 4th quadrant.

   Correct AnswerChoice E
   Statements Together are NOT Sufficient

   Solution Video Solution

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6. GMAT Challenging Question | Geometry DS | Coordinate Geometry & Quadratic Equations

   If y = (x - p)(x - q), is the sum of integers p and q positive?

   Statement 1: The curve cuts the y-axis at -20
   Statement 2: Minimum value of y is -36

   Correct AnswerChoice E
   Data Insufficient

   Solution Video Solution

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7. GMAT Hard Math | Geometry Right Triangles | GMAT 750 Level Data Sufficiency

   In right triangle ABC, what is the ratio in which point D divides the hypotenuse AC? BD is perpendicular to AC.

   Statement 1: BC = 2BD
   Statement 2: AC = 2AB

   Correct AnswerChoice D
   Statements INDEPENDENTLY sufficient.

   Solution Video Solution

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