CAT Averages Bible Top 10 Must Solve Averages Questions covering 90% of Syllabus

Every real CAT question on this chapter from the past papers we have, newest year first. Passages and data sets stay together on one page.

Tap Show answer, or open the detailed solution (free login). Page 1 of 5.

Start here: the repeating CAT PYQs

Study the average pattern in each CAT PYQ, then practise variations. The 13 selected families contain 24 of the 24 questions tagged Averages in the reviewed set.

CAT Averages Bible Top 10 PYQ Questions

Questions	CAT Area Covered
First 5 CAT Questions	58.33%
First 10 CAT Questions	87.50%
All 13 CAT Questions	100%

Importance of Averages each year of CAT exam

CAT year	Total Averages questions	First 6 examples	First 10 examples	All 13 examples	Outside these 13 families	Share of all Quant
2021	5	2	5	5	0	7.58%
2022	9	6	7	9	0	13.64%
2023	5	3	4	5	0	7.58%
2024	3	3	3	3	0	4.55%
2025	2	2	2	2	0	3.03%
Total	24	16	21	24	0	7.27%
Share of all 24	100%	66.67%	87.50%	100%	0%

Quick review for beginners and last day revision

Rule	Formula or what to do	Small example
Basic average	Average = total / number; total = average × number.	Five marks average 38 → total = 190.
Combined average	(n₁a₁ + n₂a₂)/(n₁ + n₂)	Weight each group average by its count.
One entry added	Added value = (n + 1) × new average − n × old average.	Three people average 50; four average 48 → new person weighs 42.
One entry replaced	New total − old total = new value − old value.	For fixed n, average rises by d → total rises by nd.
New entry from prefix averages	Nth value = n × average of first n − (n − 1) × previous average.	Day 8 = 8a₈ − 7a₇
Overlapping groups	Subtract totals for the shared group rather than subtracting averages directly.	Days 1–9 total minus days 2–9 total gives day 1.
Average of an AP	Average = (first + last)/2	AP 3, 8, 13, 18, 23 has average 13.
Unit price	Average unit price = total money spent / total quantity bought.	Do not average daily prices when quantities differ.
Bounds	Minimum value ≤ average ≤ maximum value.	The smallest of a group cannot exceed the group average.
Distinct integer extremes	Fix the total, minimise or maximise the other entries subject to all restrictions.	To maximise tied top scores, minimise the sum of the remaining scores.

10 Core CAT PYQ Questions

Study these first.

CAT PYQ 1: Weighted subgroup payroll or marks averages

Understand: Total = average × count for each group. Add the group totals, then use the limits given to bound the unknown.

CAT 2023 Slot 1 · Quant

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

CAT PYQ 2: Add a person or compare alternative final averages

Understand: Two final averages that differ by one extra goal differ by 1 over the new match count. Subtract them to find the count.

CAT 2021 Slot 2 · Quant

In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is

CAT PYQ 3: Maximise or minimise distinct scores with a fixed total

Understand: Fix the total marks. To make the toppers as high as possible, keep all the other scores as low as allowed.

CAT 2021 Slot 3 · Quant

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

CAT PYQ 4: Recover entries from overlapping or prefix totals

Understand: Write the total of the first 1, 2, 3 and 4 numbers from the averages. Each new number is the difference of two totals.

CAT 2024 Slot 1 · Quant

There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is

CAT PYQ 5: Change an entry and track the total difference

Understand: A change in one entry changes the total by the same amount. Divide by the count to get the change in average.

CAT 2022 Slot 2 · Quant

The average of a non-decreasing sequence of N numbers a1, a2, ..., aN is 300. If a1 is replaced by 6a1, the new average becomes 400. Then, the number of possible values of a1 is

CAT PYQ 6: Whole number averages impose divisibility

Understand: Fix the total, then make the new total divisible by the count. Pick the smallest value that works.

CAT 2022 Slot 1 · Quant

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

CAT PYQ 7: Weighted unit cost from total spending and quantity

Understand: Average price = total money spent divided by total quantity bought. Never average the prices.

CAT 2021 Slot 1 · Quant

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to

CAT PYQ 8: Fixed cost divided by changing headcount

Understand: Split the cost into a fixed part and a part per person. Two cases give both parts.

CAT 2021 Slot 3 · Quant

One part of a hostel's monthly expenses is fixed, and the other part is proportional to the number of its boarders. The hostel collects ₹ 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is ₹ 200 per boarder, and when the number of boarders is 75, the profit of the hostel is ₹ 250 per boarder. When the number of boarders is 80, the total profit of the hostel, in INR, will be

CAT PYQ 9: Unknown group counts produce rational average equations

Understand: Write each average as total divided by count, set up the difference and clear the fractions.

CAT 2021 Slot 1 · Quant

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

CAT PYQ 10: Savings target average converted to an annual total

Understand: Convert the yearly average into a yearly total. Then see how much the remaining months must supply.

CAT 2022 Slot 2 · Quant

Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

Variations

Same idea, extra twist.

CAT PYQ 11: Permutation symmetry gives an equal positional contribution

Understand: Every digit appears equally often in each place, so the average digit in each place is the same.

CAT 2022 Slot 3 · Quant

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

CAT PYQ 12: Mean of AP terms equals the endpoint mean

Understand: The average of an AP is the average of its first and last terms.

CAT 2022 Slot 3 · Quant

The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is

CAT PYQ 13: An arithmetic mean fixes a middle salary

Understand: Find every salary after each hike. If one equals the mean, the mean equation gives its value.

CAT 2023 Slot 1 · Quant

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

CAT 2025 Slot 2 · QuantEasy

The average number of copies of a book sold per day by a shopkeeper is 60 in the initial seven days and 63 in the initial eight days, after the book launch. On the ninth day, she sells 11 copies less than the eighth day, and the average number of copies sold per day from second day to ninth day becomes 66. The number of copies sold on the first day of the book launch is ____

CAT 2025 Slot 3 · QuantMedium

The average salary of 5 managers and 25 engineers in a company is Rs 60000. If each of the manager receive 20% hike in the salary while the salary of the engineer remains unchanged , the average salary of all 30 employees increased by 5%.The average salary, of engineer , in rs , is :

CAT 2024 Slot 2 · Quant

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

CAT 2024 Slot 3 · Quant

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is _____

CAT 2023 Slot 2 · Quant

Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is

Frequently asked questions

Where can I find CAT average questions with solutions?

Every Averages question on this page is a real CAT question from the CAT Actual Quant Papers. Tap Show answer for the answer; the detailed step-by-step solution opens after a free login. Start with the 13 CAT PYQs at the top, because they repeat the most.

Are there CAT average questions with answers?

Yes. Every question has its answer one tap away, free for everyone: pick an option and press Submit, or tap Show answer.

Is there a PDF of CAT average questions?

Yes. Tap Download PDF at the top of this page (free, after a quick OTP login) for the CAT Averages Bible Top 10 PYQ Questions, a free PDF of the 10 most repeated CAT average questions. All the CAT Averages questions are also on this page to read online, with answers and, after a free login, detailed solutions.

What are the CAT average previous year questions (PYQs)?

They are the real questions of the CAT Actual Quant Papers that are about averages: 24 questions, grouped into 13 repeating CAT PYQs, with the other questions listed after them in paper order.

Which average questions should I practise first for CAT?

Start with the first 6 CAT PYQs, which cover about 70% of the Averages questions. Then do the first 10 (about 90%) and finally all 13 (all of them).

How many Averages questions came in CAT papers?

10 Averages questions are on this page: 2 in CAT 2025, 2 in CAT 2024, 2 in CAT 2023, 4 in CAT 2022. The same real question is shown once.

How difficult are CAT Averages questions?

Of the 2 Averages questions that carry a difficulty rating, 1 are Easy, 1 Medium and 0 Hard; the other 8 are not rated yet.

Are the solutions free?

The question and its answer are free for everyone. The detailed Cetking solution opens after a free login with your mobile number (OTP).

How is a set shown on this page?

Each passage or data set gets one page with all its questions together (1 set here), so you never solve half of one. Questions that stand alone are shown five to a page.

Where can I practise more Averages?

Open all CAT papers and topics for every paper, or the Cetking Arena to practise.

Last day solving checklist

Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
Form the relationships. Translate each given condition into an equation or restriction.
Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.

All 13 repeating CAT PYQs and how much each adds

CAT PYQ	Repeating CAT PYQ	Questions	Representative	Cumulative questions	Cumulative share
1	Weighted subgroup payroll or marks averages	4	CAT 2023 S1 Q10	4	16.67%
2	Add a person or compare alternative final averages	3	CAT 2021 S2 Q14	7	29.17%
3	Maximise or minimise distinct scores with a fixed total	3	CAT 2021 S3 Q7	10	41.67%
4	Recover entries from overlapping or prefix totals	2	CAT 2024 S1 Q11	12	50.00%
5	Change an entry and track the total difference	2	CAT 2022 S2 Q8	14	58.33%
6	Whole number averages impose divisibility	2	CAT 2022 S1 Q7	16	66.67%
7	Weighted unit cost from total spending and quantity	2	CAT 2021 S1 Q7	18	75.00%
8	Fixed cost divided by changing headcount	1	CAT 2021 S3 Q8	19	79.17%
9	Unknown group counts produce rational average equations	1	CAT 2021 S1 Q16	20	83.33%
10	Savings target average converted to an annual total	1	CAT 2022 S2 Q5	21	87.50%
11	Permutation symmetry gives an equal positional contribution	1	CAT 2022 S3 Q8	22	91.67%
12	Mean of AP terms equals the endpoint mean	1	CAT 2022 S3 Q17	23	95.83%
13	An arithmetic mean fixes a middle salary	1	CAT 2023 S1 Q12	24	100%

Based on CAT Actual Quant Papers.

CAT Averages Bible Top 10 Must Solve Averages Questions covering 90% of Syllabus

Start here: the repeating CAT PYQs

10 Core CAT PYQ Questions

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Variations

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Frequently asked questions