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CAT Algebra Questions
Practise algebra (mathematics) for the Common Admission Test: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Algebra practice
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Q1.Solve: 4x + 5y = 10 and 4x + 2y = 16
Show answer & explanation
Answer: C — x = 5, y = -2
Elimination/substitution gives x = 5, y = -2. Check: 4(5) + 5(-2) = 10 ✓ and 4(5) + 2(-2) = 16 ✓.
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Q2.Find log₃ 9.
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Answer: C — 2
log_3(9) asks “3 to what power gives 9?” → 3^2 = 9, so the answer is 2.
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Q3.Solve: 5x + 5y = 100 and 5x + y = 52
Show answer & explanation
Answer: C — x = 8, y = 12
Elimination/substitution gives x = 8, y = 12. Check: 5(8) + 5(12) = 100 ✓ and 5(8) + 1(12) = 52 ✓.
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Q4.Find the sum of the first 27 terms of the AP 10, 19, 28, …
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Answer: A — 3429
Sₙ = n/2 × [2a + (n − 1)d] = 27/2 × [20 + 234] = 3,429.
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Q5.Solve: x² + 12x + 35 = 0
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Answer: C — -7, -5
Find two roots with sum -12 and product 35: -5 and -7. So x² + 12x + 35 = (x + 5)(x + 7) = 0.
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Q6.Solve: x² + x − 30 = 0
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Answer: C — -6, 5
Find two roots with sum -1 and product -30: 5 and -6. So x² + x − 30 = (x − 5)(x + 6) = 0.
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Q7.Find log₂ 16.
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Answer: A — 4
log_2(16) asks “2 to what power gives 16?” → 2^4 = 16, so the answer is 4.
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Q8.Find log₂ 4.
Show answer & explanation
Answer: D — 2
log_2(4) asks “2 to what power gives 4?” → 2^2 = 4, so the answer is 2.
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Q9.Solve: x² − 9 = 0
Show answer & explanation
Answer: C — -3, 3
Find two roots with sum 0 and product -9: 3 and -3. So x² − 9 = (x − 3)(x + 3) = 0.
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Q10.Find the sum of the first 9 terms of the AP 2, 5, 8, …
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Answer: D — 126
Sₙ = n/2 × [2a + (n − 1)d] = 9/2 × [4 + 24] = 126.
How to approach algebra questions
Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution. For simultaneous equations, elimination is usually faster than substitution under time pressure.
About CAT
Common Admission Test — conducted by Indian Institutes of Management (convening IIM rotates). The entrance exam for IIM MBA programmes, with VARC, DILR and Quantitative Ability sections.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
CAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Ratio, Ages & Mixtures | Quantitative aptitude | Calculated (new numbers every set) |
| Time, Work & Pipes | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Data Interpretation | Data interpretation | Calculated (new numbers every set) |
| Verbal Reasoning & Analogies | Reasoning | Calculated + question bank |