# CAT Previous Year Arithmetic & Geometry Questions and Answers: 2023, 2022, 2021, and 2020 [Download PDF]

The best way to prepare for any competitive exam in India is to understand its exam pattern and practice the previous year’s questions. Thus, aspirants must practice the Quant, VARC and DILR sections while preparing for the CAT exam. CAT Quantitative Aptitude questions entail problems related to profit and loss, geometry, arithmetic, ratio & proportion etc. You can find some relevant questions related to CAT’s previous year’s questions on arithmetic & geometry in the blog post below.

## CAT Previous Year Arithmetic & Geometry Questions 2023, 2022, 2021, and 2020

The following sections include CAT exam’s previous year arithmetic & geometry questions of the past 5 years (2023, 2022, 2021, 2020, and 2019). These questions are useful for CAT 2024 aspirants.

### CAT Arithmetic Questions 2023

Question: 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 ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, is

A) 3

B) 2

C) 4

D) 0

Question: Let both the series a1,a2,a3,…and b1,b2,b3…be in arithmetic progression such that the common differences of both the series are prime numbers. If a5=b9,a19=b19

and b2=0, then a11 equals

A) 43

B) 45

C) 79

D) 84

Question: Three positive integers x, y and z are in arithmetic progression. If y − x > 2 and xyz = 5(x + y + z), then z − x equals

A) 12

B) 23

C) 43

D) 14

### CAT Arithmetic Questions 2022

Question: The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new student is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students:

A) 2:1

B) 4:1
C) 4.5
D) 5:6

Question: The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is:

A) 2

B) 1

C) 5

D) 6

Question: In an examination, the average marks of students in sections A and B are 32 and 60 respectively. The number of students in Section A is 10 less than that in Section B. The average marks of all students across both sections are combined in an integer, then the difference between the maximum and minimum number of students possible.

A) 12

B) 20

C) 30

D) 40

Question: Consider six distinct natural numbers such that the average of the two smallest natural numbers is 14 and the average of the two largest natural numbers is 28. Then, the maximum possible value of the average of these six natural numbers is:

A) 23

B) 34

C)22.5

D) 23.5

Question: The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is

A) 31

B) 23

C) 92

D) 100

Question: A circle of diameter 8 inches is inscribed in a triangle ABC where∠ABC=90∘. If BC = 10 inches then the area of the triangle in square inches is

A) 4√6

B) 6√6

C) 2√6

D) √6

Question: Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. If T is the midpoint of CD, then the length of AT, in cm, is

A) 6√6

B) 2√6

C) √13

D) 6√6

Question: If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

A) 4√6

B) 2√6

C) 6√6

D) 2√6

### CAT Geometry Questions 2021

Question: If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

A)4√6

B)6√6

C)√6

D)2√6

### CAT Geometry Questions 2020

Question: Let C1 and C2 be concentric circles such that the diameter of C1 is 2cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm of C1 is

A) 12

B) 9

C) 8

D) 10

Question: Let C be a circle of radius 5 meters having centre at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

A) 12

B) 9.8

C) 5.5

D) 8.8

Also Read: CAT Exam: Date, Registration, Eligibility, Syllabus & More [Guide]

Candidates can download PDF for the CAT Previous Year Arithmetic & Geometry Questions given below:

## FAQs

Q1. How many questions of arithmetic are asked in CAT exam?

Ans: Around 11-14 questions are dominated by Arithmetic topic in the quant section of the CAT exam.

Q2. Is arithmetic important for CAT?

Ans: Arithmetic has a vast number of sub-topics. Algebra has been one of the most dominant topics in CAT so place extra emphasis on this topic and geometry has covered a portion in recent years.

Q3. Does CAT repeat last year’s questions?

Ans: Top MBA entrance tests including the CAT, SNAP, CMAT, and NMAT may not directly repeat problems from prior years. MBA test questions are renowned for constantly changing due to shifting economic conditions.

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