CAT Algebra Bible Top 10 Must Solve Algebra Questions covering 100% of Syllabus – Page 7
All 21 Algebra questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 7 of 7.
Refer to the passage above ↑
A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is
Answer: 3500
Solution — first steps
Step 1. Each rhombus side 40/4=10.
Step 2. For diagonals p, q, pq 192 and p²+q²400.
Step 2. For diagonals p, q, pq 192 and p²+q²400.
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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 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.