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GRE Algebra Questions
Practise algebra (mathematics) for the GRE General 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 − 4 = 0
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Answer: B — -2, 2
Find two roots with sum 0 and product -4: -2 and 2. So x² − 4 = (x + 2)(x − 2) = 0.
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Q2.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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Q3.Find the sum of the first 29 terms of the AP 3, 10, 17, …
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Answer: D — 2929
Sₙ = n/2 × [2a + (n − 1)d] = 29/2 × [6 + 196] = 2,929.
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Q4.Find log₃ 243.
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Answer: A — 5
log_3(243) asks “3 to what power gives 243?” → 3^5 = 243, so the answer is 5.
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Q5.Find the sum of the first 10 terms of the AP 13, 16, 19, …
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Answer: B — 265
Sₙ = n/2 × [2a + (n − 1)d] = 10/2 × [26 + 27] = 265.
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Q6.Solve: x² − 7x + 10 = 0
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Answer: D — 2, 5
Find two roots with sum 7 and product 10: 5 and 2. So x² − 7x + 10 = (x − 5)(x − 2) = 0.
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Q7.Find log 100 (base 10).
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Answer: B — 2
log_10(100) asks “10 to what power gives 100?” → 10^2 = 100, so the answer is 2.
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Q8.Solve: x² − 2x − 15 = 0
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Answer: C — -3, 5
Find two roots with sum 2 and product -15: -3 and 5. So x² − 2x − 15 = (x + 3)(x − 5) = 0.
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Q9.Find the sum of the first 9 terms of the AP 20, 23, 26, …
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Answer: A — 288
Sₙ = n/2 × [2a + (n − 1)d] = 9/2 × [40 + 24] = 288.
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Q10.Solve: x² + 10x + 21 = 0
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Answer: A — -7, -3
Find two roots with sum -10 and product 21: -7 and -3. So x² + 10x + 21 = (x + 7)(x + 3) = 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 GRE
GRE General Test — conducted by Educational Testing Service (ETS). Graduate admission test with Verbal Reasoning, Quantitative Reasoning and Analytical Writing.
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.
GRE practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | 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) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Vocabulary & Idioms | English | Question bank |