CAT Maxima and Minima Bible Top 10 Must Solve Maxima and Minima 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 9.
Start here: the repeating CAT PYQs
Study the optimisation pattern in each CAT PYQ, then practise variations. The 15 selected families contain 53 of the 54 questions on Maxima and Minima in the reviewed set.
CAT Maxima and Minima Bible Top 10 PYQ Questions
| Questions | CAT Area Covered |
|---|---|
| First 5 CAT Questions | 62.96% |
| First 10 CAT Questions | 87.04% |
| All 15 CAT Questions | 98.15% |
Importance of Maxima and Minima each year of CAT exam
| CAT year | Total Maxima and Minima questions | First 6 examples | First 10 examples | All 15 examples | Outside these 15 families | Share of all Quant |
|---|---|---|---|---|---|---|
| 2021 | 5 | 3 | 5 | 5 | 0 | 7.58% |
| 2022 | 12 | 10 | 10 | 12 | 0 | 18.18% |
| 2023 | 21 | 13 | 19 | 20 | 1 | 31.82% |
| 2024 | 5 | 3 | 3 | 5 | 0 | 7.58% |
| 2025 | 11 | 8 | 10 | 11 | 0 | 16.67% |
| Total | 54 | 37 | 47 | 53 | 1 | 16.36% |
| Share of all 54 | 100% | 68.52% | 87.04% | 98.15% | 1.85% |
Quick review for beginners and last day revision
| Rule | Formula or what to do | Small example |
|---|---|---|
| State the objective | Write exactly what must be maximised or minimised. | Maximise a count, a sum, an area or a profit. |
| Use every constraint | An extreme is valid only within all given restrictions. | Counts may need to be distinct positive integers. |
| Linear expression on an interval | For a linear function, the extreme occurs at an endpoint. | For 0 ≤ x ≤ 5, 3x + 2 ranges from 2 to 17. |
| Quadratic vertex | ax² + bx + c = a(x + b/2a)² + c − b²/4a | If a > 0, the vertex gives the unrestricted minimum. |
| Nonnegative square | u² ≥ 0; equality holds when u = 0. | (x − 4)² + 7 ≥ 7 |
| AM GM | For nonnegative a,b: a + b ≥ 2√(ab). Equality requires a = b. | For t > 0, t + 1/t ≥ 2. |
| Balanced integers | For fixed total, squares are minimised by values as equal as the integer conditions allow. | Split 11 into two integers: 5 and 6 minimise the sum of squares. |
| Factor restrictions | List feasible factor pairs or divisors before comparing objectives. | A theoretical real optimum may not be an integer solution. |
| Threshold | For a smallest whole number time, test the candidate and the preceding integer. | If growth first exceeds the target at year 9, check year 8 fails. |
| Attainability | Construct a valid example reaching the proposed bound. | An upper bound alone does not prove the maximum. |
10 Core CAT PYQ Questions
Study these first.
CAT PYQ 1: Integer allocation from linear totals and bounds
Understand: Write the counts as multiples of one number k, apply the total limit, and take the largest whole k.
Answer: 111
Solution — first steps
Step 2. Including Pinky, total=8k+1<300.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 2: Divisibility and factor constraints with feasible candidates
Understand: List the factor pairs the equations allow, then compare the candidates for the smallest product.
Answer: 34
Solution — first steps
Step 2. The second gives z(x+1)=51.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 3: Ordered or balanced integer values with fixed totals
Understand: To make the top score as large as possible, keep all the other scores as small as the rules allow.
Answer: 92
Solution — first steps
Step 2. To maximize each of five equal toppers, minimize the other 20 distinct integer scores with smallest 30.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 6: Set overlap extrema with attainability
Understand: Add the set sizes to find the least and most overlap, and check both extremes can really happen.
Answer: A. 47
Solution — first steps
Step 2. Without triple overlap, 100 students can contribute at most 200 memberships; every triple student raises this cap by 1. Thus triple overlap≥5.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 7: Digit restrictions and positional extrema
Understand: Turn the digit conditions into equations, keep each digit between 0 and 9, and take the largest allowed first digit.
Answer: 4195
Solution — first steps
Step 2. Also c=d+4=a+5; hence b=9−2a.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 10: Extreme integer parameter from a discriminant
Understand: Factor out the known root, make the discriminant of the rest non-negative, then pick the smallest integer.
Answer: 2
Solution — first steps
Step 2. Factor the polynomial as (x+2)[x²+(2r−1)x+1].
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Variations
Same idea, extra twist.
CAT PYQ 11: Endpoint extrema of piecewise or linear expressions
Understand: On an interval, the largest value of a modulus sum sits at an endpoint, so test the ends.
Answer: C. 50
Solution — first steps
Step 2. Put t=x−a, so 0≤t≤100−a and f=100−a+
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 12: Largest common term of APs
Understand: Common terms of two APs form a new AP whose step is the LCM; take the largest one below 1000.
Answer: 967
Solution — first steps
Step 2. Common values N satisfy N≡1 modulo6 and modulo7, hence N≡1 modulo42.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 13: Bound a logarithmic condition and construct equality
Understand: Change all the logs to one base, combine them, and use the limits on the variables to bound the answer.
Answer: 14
Solution — first steps
Step 2. Combine logs to get log_c(a²−b²)=2, hence a²=b²+c².
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 14: Maximise an integer representation of a surd
Understand: Find the exact square root first, then list the integer forms that give the same value.
Answer: C. 18
Solution — first steps
Step 2. Any integer representation a+b√n must have a=−3: otherwise squaring b√n=(−3−a)+2√5 would leave an irrational part in the integer b²n.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Answer: 55
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
g(x) = –x² + 3cx – 2c, is
Answer: A. 1/2
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
then the maximum possible value of 2m − 3n is ___
Answer: 17
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
(a − b)² + (a − c)² + (a − d)² is ______
Answer: 2
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Then, the smallest possible value of 3a + 2b + c is _______
Answer: 12
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Frequently asked questions
Where can I find CAT maxima and minima questions with solutions?
Every Maxima and Minima 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 CAT PYQs at the top, because they repeat the most.
Are there CAT maxima and minima 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 maxima and minima questions?
Yes. Tap Download PDF at the top of this page (free, after a quick OTP login) for the CAT Maxima and Minima Bible Top 10 PYQ Questions, a free PDF of the 10 most repeated CAT maxima and minima questions. All the CAT Maxima and Minima questions are also on this page to read online, with answers and, after a free login, detailed solutions.
What are the CAT maxima and minima previous year questions (PYQs)?
They are the real questions of the CAT Actual Quant Papers that are about maxima and minima: 54 questions, grouped into 15 repeating CAT PYQs, with the other questions listed after them in paper order.
Which maxima and minima questions should I practise first for CAT?
Start with the first 6 CAT PYQs, which cover about 70% of the Maxima and Minima questions. Then do the first 10 (about 90%) and finally all 15 (almost all of them).
How many Maxima and Minima questions came in CAT papers?
40 Maxima and Minima questions are on this page: 10 in CAT 2025, 3 in CAT 2024, 19 in CAT 2023, 8 in CAT 2022. The same real question is shown once.
How difficult are CAT Maxima and Minima questions?
Of the 10 Maxima and Minima questions that carry a difficulty rating, 2 are Easy, 4 Medium and 4 Hard; the other 30 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 (2 sets here), so you never solve half of one. Questions that stand alone are shown five to a page.
Where can I practise more Maxima and Minima?
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 16 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Integer allocation from linear totals and bounds | 9 | CAT 2022 S1 Q8 | 9 | 16.67% |
| 2 | Divisibility and factor constraints with feasible candidates | 9 | CAT 2022 S1 Q4 | 18 | 33.33% |
| 3 | Ordered or balanced integer values with fixed totals | 6 | CAT 2021 S3 Q7 | 24 | 44.44% |
| 4 | Smallest integer crossing an exponential threshold | 6 | CAT 2021 S3 Q20 | 30 | 55.56% |
| 5 | AM GM minimum or maximum with equality | 4 | CAT 2021 S3 Q19 | 34 | 62.96% |
| 6 | Set overlap extrema with attainability | 3 | CAT 2022 S1 Q17 | 37 | 68.52% |
| 7 | Digit restrictions and positional extrema | 3 | CAT 2021 S2 Q12 | 40 | 74.07% |
| 8 | Compare finitely many algebraic parameter cases | 3 | CAT 2023 S2 Q21 | 43 | 79.63% |
| 9 | Quadratic vertex by completing the square | 2 | CAT 2021 S3 Q22 | 45 | 83.33% |
| 10 | Extreme integer parameter from a discriminant | 2 | CAT 2023 S1 Q7 | 47 | 87.04% |
| 11 | Endpoint extrema of piecewise or linear expressions | 2 | CAT 2022 S1 Q22 | 49 | 90.74% |
| 12 | Largest common term of APs | 1 | CAT 2023 S2 Q22 | 50 | 92.59% |
| 13 | Bound a logarithmic condition and construct equality | 1 | CAT 2024 S2 Q9 | 51 | 94.44% |
| 14 | Maximise an integer representation of a surd | 1 | CAT 2024 S1 Q2 | 52 | 96.30% |
| 15 | Minimum labour cost with integer paid days | 1 | CAT 2025 S1 Q18 | 53 | 98.15% |
| 16 | Maximum admissible percentage decline | 1 | CAT 2023 S3 Q10 | 54 | 100% |
Based on CAT Actual Quant Papers.