CAT Algebra Bible Top 10 Must Solve Algebra Questions covering 100% of Syllabus – Page 4
All 21 Algebra questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 4 of 7.
Refer to the passage above ↑
All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is
Answer: B. \(\dfrac{P^{2}}{8} - 2R^{2}\)
Solution — first steps
Step 1. Let sides be u, v. The diagonal is 2R, so u²+v²=4R².
Step 2. The perimeter gives u+v=P/2.
Step 2. The perimeter gives u+v=P/2.
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Refer to the passage above ↑
Let a and b be natural numbers. If \(a^{2} + ab + a = 14\) and \(b^{2} + ab + b = 28\), then \((2a + b)\) equals
Answer: A. 8
Solution — first steps
Step 1. Factor the equations: a(a+b+1)=14 and b(a+b+1)=28.
Step 2. Their common positive factor gives b=2a.
Step 2. Their common positive factor gives b=2a.
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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 10 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Conjugate surds and difference of squares | 7 | CAT 2021 S1 Q4 | 7 | 21.21% |
| 2 | Symmetric sums products and reciprocal powers | 7 | CAT 2022 S3 Q14 | 14 | 42.42% |
| 3 | Square sum product identities in diagonal geometry | 5 | CAT 2021 S2 Q9 | 19 | 57.58% |
| 4 | Complete squares and use sign or equality conditions | 4 | CAT 2023 S1 Q2 | 23 | 69.70% |
| 5 | Group common expressions and factor product constraints | 4 | CAT 2021 S2 Q3 | 27 | 81.82% |
| 6 | Difference or sum formulas for sequence totals | 2 | CAT 2021 S2 Q20 | 29 | 87.88% |
| 7 | Add and subtract values at opposite polynomial roots | 1 | CAT 2022 S2 Q9 | 30 | 90.91% |
| 8 | Common base exponent identity for all parameter values | 1 | CAT 2022 S3 Q11 | 31 | 93.94% |
| 9 | Square and factor an absolute value inequality | 1 | CAT 2021 S3 Q18 | 32 | 96.97% |
| 10 | Expand a nested GP into simpler series | 1 | CAT 2023 S3 Q20 | 33 | 100% |
Based on CAT Actual Quant Papers.