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XAT Algebra Questions
Practise algebra (mathematics) for the Xavier 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.Find log 10,000 (base 10).
Show answer & explanation
Answer: C — 4
log_10(10000) asks “10 to what power gives 10000?” → 10^4 = 10000, so the answer is 4.
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Q2.Find the sum of the first 25 terms of the AP 2, 3, 4, …
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Answer: D — 350
Sₙ = n/2 × [2a + (n − 1)d] = 25/2 × [4 + 24] = 350.
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Q3.Find log₅ 625.
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Answer: C — 4
log_5(625) asks “5 to what power gives 625?” → 5^4 = 625, so the answer is 4.
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Q4.Solve: x² − 14x + 49 = 0
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Answer: C — 7, 7
Find two roots with sum 14 and product 49: 7 and 7. So x² − 14x + 49 = (x − 7)(x − 7) = 0.
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Q5.Find the sum of the first 28 terms of the AP 10, 17, 24, …
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Answer: B — 2926
Sₙ = n/2 × [2a + (n − 1)d] = 28/2 × [20 + 189] = 2,926.
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Q6.Solve: x + 3y = 42 and 5x + 5y = 90
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Answer: D — x = 6, y = 12
Elimination/substitution gives x = 6, y = 12. Check: 1(6) + 3(12) = 42 ✓ and 5(6) + 5(12) = 90 ✓.
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Q7.Solve: x + 3y = -8 and 4x + y = -10
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Answer: A — x = -2, y = -2
Elimination/substitution gives x = -2, y = -2. Check: 1(-2) + 3(-2) = -8 ✓ and 4(-2) + 1(-2) = -10 ✓.
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Q8.Solve: 4x + y = 46 and x + 2y = 15
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Answer: D — x = 11, y = 2
Elimination/substitution gives x = 11, y = 2. Check: 4(11) + 1(2) = 46 ✓ and 1(11) + 2(2) = 15 ✓.
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Q9.Find log 1,000,000 (base 10).
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Answer: A — 6
log_10(1000000) asks “10 to what power gives 1000000?” → 10^6 = 1000000, so the answer is 6.
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Q10.Find the sum of the first 12 terms of the AP 15, 16, 17, …
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Answer: A — 246
Sₙ = n/2 × [2a + (n − 1)d] = 12/2 × [30 + 11] = 246.
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 XAT
Xavier Aptitude Test — conducted by XLRI Jamshedpur. MBA entrance used by XLRI and many other business schools, known for decision-making questions.
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.
XAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Data Interpretation | Data interpretation | Calculated (new numbers every set) |
| Verbal Reasoning & Analogies | Reasoning | Calculated + question bank |
| Vocabulary & Idioms | English | Question bank |