CAT Averages Questions with Solutions PDF; Complete Practice Test & Preparation Guide

Updated on Oct 9, 2026 10:49 IST

By Abhishek Dhawan, Deputy Manager - MBA & BBA Content

Averages questions account for nearly 4 per cent to 6 per cent of the entire CAT question paper directly, and up to 15 per cent indirectly. A good hold on Averages can help candidates obtain a good score in the Quantitative Aptitude as well as Data Interpretation and Logical Reasoning (DILR) sections. In each slot of the CAT exam, candidates can expect 1 to 2 direct questions.

In the CAT exam, apart from the direct Averages questions, candidates will find Averages as a foundation to assess data analysis skills and logical reasoning. Candidates find CAT Averages questions on Simple Averages, Weighted Averages, and Mixtures and Alligations. A good hold on Averages also helps in advanced CAT topics like Profit and Loss, Time and Work, and DILR Applications such as Data Interpretation growth rates, average sales calculation, and table-based missing data problems.

This article hosts some CAT Averages questions with solution PDFs. Candidates can practice these CAT Averages questions with varied difficulty levels for overall CAT 2026 preparation.

Table of contents

CAT Averages Sample Questions with Solutions
CAT Averages Weightage and Exam Trends
Different Types of Averages Questions in CAT Exam
Explore More CAT Exam Prep Content
FAQs on CAT Averages

CAT Averages Sample Questions with Solutions

Difficulty Level: Easy

Question 1: The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is

Options:

50000
45000
40000
54000

Difficulty Level: Medium

Question 2: 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 students 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 is

Options:

1 : 4
1 : 2
4 : 1
3 : 1

Question 3: The salaries of three friends Sita, Gita and Mita are initially in the ratio 5 : 6 : 7, respectively. In the first year, they get salary hikes of 20%, 25% and 20%, respectively. In the second year, Sita and Mita get salary hikes of 40% and 25%, respectively, and the salary of Gita becomes equal to the mean salary of the three friends. The salary hike of Gita in the second year is

Options:

Difficulty Level: Hard

Question 4: In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by Options:

Question 5: In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is

Options:

Read More:

CAT Averages Weightage and Exam Trends

Averages is a foundational topic in the Arithmetic section of the CAT exam. While direct questions on simple averages are limited to 1 or 2 per slot, the concept frequently appears within other areas of the Quant and DILR sections.

Past Trends for CAT Averages Questions:

Direct QA Questions: Usually 1 to 2 questions per exam slot, often carrying moderate difficulty.
Cross-Topic Questions: Used extensively in Mixtures & Alligations, Time-Speed-Distance (average speed), and Profit & Loss.
DILR Integration: DILR sets involving tables, bar charts, and missing data often require calculating moving averages, class averages, and percent deviations to find missing values.
Question Styles: Recent CAT papers focus on boundary conditions (maximum or minimum possible average), replacement cases, and algebraic formulation rather than long additions.

Different Types of Averages Questions in CAT Exam

Most CAT Averages problems fall into four major categories. Understanding the best method for each category saves valuable exam time.

Question Type	What It Involves
Inclusion, Exclusion & Replacement	A person joins a group, leaves a group, or is replaced by a new person, altering the overall average.
Weighted Average & Mixtures	Combining two or more classes, batches, or solutions with different scores or concentrations.
Average Speed (Rates)	Covering different legs of a journey at different speeds.
Max / Min & Boundary Limits	Finding the highest or lowest possible score of an individual given the average and constraints (e.g., non-negative, distinct integers).

Explore More CAT Exam Prep Content

Check topic-wise preparation for CAT exam:

CAT Topic-Wise Practice Questions

Practice by topic with questions and detailed solutions

📘 VARC Practice 7 Topics ▾

VARC → Para Summary → Verbal Ability → Para Jumbles → Odd One Out → Critical Reasoning → Vocabulary → Idioms →

📊 DILR Practice 5 Topics ▾

DILR→ DI→ LR→ Puzzles→ Seating Arrangement→

📐 Quant Practice 13 Topics ▾

Quant→ Arithmetic→ Algebra→ Geometry→ Number System→ Percentages→ Profit & Loss→ Time & Work→ Probability→ Logarithms→ Trigonometry→ Time, Speed & Distance→

Explore More CAT Preparation Resources →

FAQs on CAT Averages

Find some frequently asked questions related to Averages preparation for CAT exam:

Q: How many questions on Averages appear in the CAT Quantitative Aptitude section?

Direct questions on Averages typically range from 1 to 2 per slot in the CAT exam. However, the concept appears across several other topics, including Mixtures & Alligations, etc.

Q: Can I solve CAT Averages questions without long equations?

Yes. Most CAT-level problems involving replacements, group additions, or combinations are designed to test logical shortcuts rather than heavy calculations.

Q: What are the common traps in CAT Averages questions?

Some frequent traps in CAT exam are:

Confusing the counts of original and new members in replacement vs. inclusion problems.
Weighting by values instead of quantities or frequencies in weighted average setups.