CAT Maxima and Minima Bible Top 10 Must Solve Maxima and Minima Questions covering 90% of Syllabus – Page 3
All 40 Maxima and Minima questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 3 of 9.
A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is
Answer: 340
Solution — first steps
Step 1. Let total fruit count be T; mangoes=2T/5. Write apples A and bananas B, so A+B=3T/5.
Step 2. Total sold is T/5+96+2A/5=T/2. Therefore A=3T/4−240 and B=240−3T/20.
Step 2. Total sold is T/5+96+2A/5=T/2. Therefore A=3T/4−240 and B=240−3T/20.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value after 5 years is 25:36, then the minimum number of years required for the value to exceed Rs 20000 is _____
Answer: 9
Solution — first steps
16 → n=9
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
Answer: 72 and 80
Solution — first steps
Step 1. Let G be girls and B=250−G be boys. The bounds give 110≤G≤150.
Step 2. Because every student chooses at least one activity, inclusion–exclusion fixes the overlap: both=0.2B+0.4G.
Step 2. Because every student chooses at least one activity, inclusion–exclusion fixes the overlap: both=0.2B+0.4G.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
If \( n \) is the least positive integer such that \( 168 \) is a factor of \( 1134^n \), and \( m \) is the least positive integer such that \( 1134^m \) is a factor of \( 168^n \), then \( m + n \) equals:
Answer: C. 15
Solution — first steps
Answer: C. 15 Detailed Solution: 1.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Let n be the least positive integer such that 168 is a factor of 1134n. If m is the least positive integer such that 1134n is a factor of 168m, then m + n equals:
Answer: C. 15
Solution — first steps
Given 1134n and 168m conditions, solving for n and m, we get m+n = 15.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
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.