Geometry Questions for GMAT Quant Section

Being a gateway to MBA and other top post graduate management courses in the world, GMAT (Graduate Management Admission Test) is the most sought-after management entrance exams among the students wanting to land into their dream B-schools and universities abroad. When it comes to the Mathematical or Quantitative section of the Geometry questions altogether amp up the difficulty level of GMAT making it one of the most difficult MBA entrance exams in the world. If you are looking forward to studying abroad and have been going through some difficulty preparing the geometry questions of the quantitative section, then we are here to help you tackle these challenges like a pro. Read on to know more.

Important Geometry Questions  

When it comes to preparing for the GMAT examination, the quantitative section tests the problem-solving abilities and critical thinking skills of the candidates. While the GMAT exam dates are nearing and aspirants are on the prepping spree, it is important for students to get a hang of some of the important geometry questions that they will be facing on the day of the GMAT examination. To ease out your GMAT preparation process and get you an idea of how the questions are going to be, here are some of the most important geometry questions that you should definitely know about.

Geometry Questions 1. ABCDE is a regular pentagon given. Determine the measurement of ∠ACE.

Solution:
It is sure that the sum of any ‘n-sided’ polygon equals to (n-2) x 180°. Then, in the given pentagon ABCDE, it will be,  (5-2) x 180° = 540°. Which further means that for a regular pentagon, all the five angles are equal making each angle of 540 / 5 = 180°
Now, in the isosceles triangle ABC, the ∠B equals to 108°, so the other two angles (∠A and ∠C) should be 36°. This is because the sum of all the angles in a triangle should be 180°. 
Which further implies that if ∠BAC = 36° and ∠DCE = 36°, then 
∠ACE is also equal to 36°.

Geometry Questions 2. There is a circle of radius 7 which has inscribed a square. Calculate the area of the circle which is outside the square. 

Solution:
First of all, let us find the area of the circle
A = r𝛑^2= 7𝛑^2= 49
Using the Pythagoras Theorem, let us calculate the length of the sides of the inscribed square.
7^2 + 7^2 = a^2 [Where, a = base of the triangle = side of the square]
Which implies,
a^2 = 49 + 49
a^2=98
a = sq root (98)
Now, subtract the area of the square with the area of the inscribed circle to determine the area of the required portion. 
Therefore, the right answer is 49 𝛑 – 98

Geometry Questions 3. Calculate the area of an obtuse-angeled triangle with sides 12 & 8 and 150° angle between them.

Solution:
If the sides and angle of a triangle are given then the formula for determining the area of the triangle is,

Area of the Triangle = ½  x (product of sides) x sin y
Substituting the values from the question, we get
Area of the Triangle =  ½ x [8 x 12] x sin 150° {sin 150° = ½ }
=  24 units square
Therefore, the required answer is 24 units square.

Geometry Questions 4. The sum of the interior angle of a polygon is 1440°. Determine the number of sides the polygon would have.

Solution: 
Using the formula, 
The sum of all interior angles of a convex polygon = (n – 2) x 180
Which implies, 
⇒ (n – 2) x 180 = 1440
⇒ n – 2 = 8
⇒ n = 10

Therefore, the total number of sides of the given polygon is 10 sides.

You may also check our blogs on GMAT Paper Pattern, GMAT Syllabus and Algebra Formulas!

List of Other Questions

• Calculate the radius of a circle inside a triangle with sides equal to 13, 5 and 12 units.
• A right cylindrical water tank has a height of 10 meters. Being filled at a rate of 4 gallons per minute, the tank gets filled after 10 minutes. Determine the radius of the cylindrical tank.
• Calculate the radius of a circle which circumscribes a triangle with sides 40, 9 & 41
• Calculate the number of diagonals a 63 sided convex polygon would have. 
• An acute angles triangle has the sides – 12, 10 & ‘s’. how many values of ‘s’ can you find?

Also Read: GMAT 2024 – A Complete Study Guide to know GMAT Inside Out

FAQs

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