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25+ Geometry Questions for CAT with SOLUTIONS

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Geometry Questions for the CAT are part of the Quantitative Aptitude section in the CAT exam. Through geometry questions, aspirants are tested on concepts related to circles, triangles, polygons, and other geometry-related topics. The difficulty level of the Geometry questions can be easy to moderate.

Best Geometry Questions for the CAT Exam

Question 1. Jay has 3 types of boxes: Large, medium and small. He first puts 10 large boxes on a table. He leaves some of these boxes empty and in all the other boxes puts 7 empty medium sized boxes. He then leaves some of the medium sized boxes empty and places 7 empty small boxes in the other medium sized boxes. If 82 boxes on the table were empty, then what is the total number of boxes he used? (All large boxes are of the same size, all medium boxes are of the same size and all small boxes are of the same size)

A. 88

B. 90

C. 94

D. 98

Answer: C

Question 2. The sum of all two-digit numbers that give a remainder of A when they are divided by 7 is 654. What is the value of A?

Answer: 2

Question 3. 207 people who attend "Bold Gym" in Kondapur take four types of juices Apple, Orange, Pomegranate and Mango. There are a few people who do not take any of the juices. It is known that for every person in the Gym who takes atleast 'N' types of juices there are 2 persons who take atleast 'N-1' juices for N = 2, 3 and 4. If the number of people who take all four types of juices is equal to the number of people who do not take any juice at all, what is the number of people who take exactly 2 types of juices?

A. 23

B. 46

C. 69

D. 92

Answer: C

Question 4. Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

A. 33

B. 27

C. 30

D. 36

Answer: A

Question 5. Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

A. 22

B. 21

C. 20

D. 19

Answer: C

What are the most important geometry questions for the CAT 2024 exam?

Question 6. The mean of all 4-digit even natural numbers of the form 'aabb',where a > 0, is

A. 4466

B. 5050

C. 4864

D. 5544

Answer: D

Question 7. Among 100 students, have birthdays in January, have birthdays in February, and so on. If , then the smallest possible value of is

A. 8

B. 9

C. 10

D. 12

Answer: B

Question 8. How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Answer: 21

Question 9. A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

Answer: 62

Question 10. In a school, every student likes one of the three sports - Cricket, Football, Rugby. 65% of the students like Cricket, 86% like Football and 57% of the students like Rugby. What is the maximum percentage of students who like exactly two sports?

A. 92%

B. 80%

C. 54%

D. 46%

Answer: A

What are the must-do geometry questions for the CAT exam?

Question 11. In the below figure, ΔABC is right-angled and AC = 100 cm. Also, AD = DE = EF = FC. Find the value of: BD2 + BE2 + BF2 (in cm2).


A. 10,000 cm2

B. 5,000 cm2

C. 8,750 cm2

D. 12,500 cm2

Answer: C

Question 12. Perimeter of a △ with integer sides is equal to 15. How many such triangles are possible?

A. 7

B. 8

C. 6

D. 5

Answer: A

Question 13. The radius of the incircle of a Δ is 4 cm and the segments into which one side is divided by the point of contact are 6 cm and 8 cm, then the length of the shortest side of the Δ is

A. 12 cm

B. 15 cm

C. 13 cm

D. 14 cm

Answer: C

Question 14: A quadrilateral ABCD is inscribed in a circle such that AB:CD = 2:1 and BC: AD = 5:4. If AC and BD intersect at the point E, then AE:CE equals

A. 2 :1

B. 5: 8

C. 8 : 5

D. 1: 2

Answer: A

Question 15. In a right-angled triangle △ ABC, the altitude AB is 5 cm, and the base BC is 12 cm . P and Q are two points on BC such that the areas of △ ABP △ ABQ, and △ ABC are in arithmetic progression. If the area of △ ABC is 1.5 times the area of △ ABP, the length of PQ, in cm, is

A. 2

B. 6

C. 3

D. 7

Answer: C

Is geometry important for the CAT Exam?

Yes, Geometry questions are important for the CAT Exam. Geometry is an important topic of the CAT Quantitative Aptitude section. Around 7-8 questions are in majorly from geometry. So, never skip the geometry questions since they are easy to score well in the CAT Exam.

What topics are covered in Geometry Questions for the CAT exam?

The topics that need to be covered in Geometry for the CAT exam are:

Quadrant System

Areas Polygon, Triangle, and Rectangle. Square, Rhombus, Trapezoid, etc.

Distance between Two Lines

Cyclic Quadrilateral (Properties and Formulas)

Line Equation and Circle Equation

Circumradius and Inradius

Angles (Supplementary, Complementary, Obtuse, Acute, and Right)

Similar and Congruent Triangle

Theorems (Pythagoras, Midpoint, Apollonius, Basic Proportionality, Internal and External Angular Bisector, etc.)

Volume, Total Surface Area, and Lateral Surface Area of Different Solids like Cubes, Cuboids, Cylinders, Pyramids, Cones, Spheres, Hemispheres, and Frustum

How to prepare geometry for the CAT Exam?

The preparation of geometry questions for the CAT exam must be done perfectly.

  • Never Skip any Topic 

  • Needs Consistence Practice

  • Prepare well with detailed study material

  • Try to solve more questions

  • Attempt more and more Mock Tests

Stay informed, Stay ahead and Stay inspired with MBA Rendezvous.