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IPMAT Algebra Questions
Practise algebra (mathematics) for the Integrated Programme in Management Aptitude 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: x² + 3x − 28 = 0
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Answer: B — -7, 4
Find two roots with sum -3 and product -28: 4 and -7. So x² + 3x − 28 = (x − 4)(x + 7) = 0.
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Q2.Solve: x² − 8x + 12 = 0
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Answer: D — 2, 6
Find two roots with sum 8 and product 12: 2 and 6. So x² − 8x + 12 = (x − 2)(x − 6) = 0.
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Q3.Find log₅ 3,125.
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Answer: A — 5
log_5(3125) asks “5 to what power gives 3125?” → 5^5 = 3125, so the answer is 5.
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Q4.Solve: x² + 10x + 21 = 0
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Answer: B — -7, -3
Find two roots with sum -10 and product 21: -7 and -3. So x² + 10x + 21 = (x + 7)(x + 3) = 0.
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Q5.Find log₅ 25.
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Answer: B — 2
log_5(25) asks “5 to what power gives 25?” → 5^2 = 25, so the answer is 2.
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Q6.Solve: x² − 6x + 8 = 0
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Answer: D — 2, 4
Find two roots with sum 6 and product 8: 2 and 4. So x² − 6x + 8 = (x − 2)(x − 4) = 0.
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Q7.Find the sum of the first 16 terms of the AP 1, 4, 7, …
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Answer: D — 376
Sₙ = n/2 × [2a + (n − 1)d] = 16/2 × [2 + 45] = 376.
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Q8.Find the sum of the first 20 terms of the AP 3, 5, 7, …
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Answer: B — 440
Sₙ = n/2 × [2a + (n − 1)d] = 20/2 × [6 + 38] = 440.
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Q9.Find log₃ 243.
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Answer: C — 5
log_3(243) asks “3 to what power gives 243?” → 3^5 = 243, so the answer is 5.
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Q10.Solve: x² + 10x + 9 = 0
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Answer: B — -9, -1
Find two roots with sum -10 and product 9: -9 and -1. So x² + 10x + 9 = (x + 9)(x + 1) = 0.
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 IPMAT
Integrated Programme in Management Aptitude Test — conducted by IIM Indore. Entrance for the five-year integrated management programme after Class 12.
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.
IPMAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| English Grammar | English | Question bank |
| Vocabulary & Idioms | English | Question bank |