CAT Quadratic Equations Bible Top 10 Must Solve Quadratic Equations Questions covering 90% of Syllabus – Page 11
All 38 Quadratic Equations questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 11 of 11.
Refer to the passage above ↑
A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is
Answer: C. 200
Solution — first steps
Step 1. Let large price p>50 and small price p−50.
Step 2. Counts 5000/p and 1800/(p−50) sum 64.
Step 2. Counts 5000/p and 1800/(p−50) sum 64.
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Refer to the passage above ↑
A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is
Answer: 34
Solution — first steps
Step 1. Let small 2k, medium 5k, large L. Product 10k²L800.
Step 2. New product(2k+6)(5k+6)L = 3200 is four times the original.
Step 2. New product(2k+6)(5k+6)L = 3200 is four times the original.
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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 15 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Quadratic modelling of counts journeys and work rates | 9 | CAT 2021 S1 Q16 | 9 | 17.65% |
| 2 | Root sums products and conjugate roots | 7 | CAT 2021 S2 Q19 | 16 | 31.37% |
| 3 | Successive percentages replacement and price changes | 6 | CAT 2021 S2 Q4 | 22 | 43.14% |
| 4 | Discriminant conditions and integer parameters | 4 | CAT 2022 S1 Q5 | 26 | 50.98% |
| 5 | Modulus or square root branches producing quadratics | 4 | CAT 2021 S1 Q8 | 30 | 58.82% |
| 6 | Exponential substitutions and quadratic exponents | 4 | CAT 2023 S2 Q2 | 34 | 66.67% |
| 7 | Vertex repeated root and perfect square forms | 3 | CAT 2021 S3 Q22 | 37 | 72.55% |
| 8 | Logarithms converted to quadratic equations | 3 | CAT 2023 S1 Q1 | 40 | 78.43% |
| 9 | Shared roots eliminated between equations | 2 | CAT 2024 S1 Q20 | 42 | 82.35% |
| 10 | Rational expression range through a discriminant | 2 | CAT 2022 S3 Q15 | 44 | 86.27% |
| 11 | Grouped identities reduce coupled equations | 2 | CAT 2021 S2 Q3 | 46 | 90.20% |
| 12 | Geometric length constraints producing quadratics | 2 | CAT 2021 S3 Q11 | 48 | 94.12% |
| 13 | Balanced AP totals producing a quadratic index | 1 | CAT 2025 S1 Q4 | 49 | 96.08% |
| 14 | GP terms related by a quadratic product | 1 | CAT 2025 S2 Q8 | 50 | 98.04% |
| 15 | Consistency of a linear system gives a quadratic parameter | 1 | CAT 2023 S3 Q3 | 51 | 100% |
Based on CAT Actual Quant Papers.