If there’s one topic that consistently shapes performance in the CAT Quant section, it’s Algebra. Year after year, Algebra contributes a significant share of questions across all exam slots, making it one of the most dependable scoring areas alongside Arithmetic. A strong command of Algebra not only improves your accuracy but also helps you solve a large portion of the Quant section with confidence.
This guide brings together the most important Algebra questions to practice for CAT 2026, along with recent weightage trends, topic-wise insights, a quick formula revision section, and practical preparation tips. Whether you’re building your fundamentals or revising before mock tests, this resource is designed to help you practice the concepts that matter most for the exam.
Since CAT does not publish an official syllabus or topic-wise weightage, the distribution and trends discussed here are based on an analysis of recent CAT papers across multiple slots. These estimates are intended to help you prioritize your preparation—not to predict the exact paper pattern.
Why Algebra Should Be a Priority for CAT 2026
Algebra is one of the few CAT Quant topics where consistent practice translates directly into better scores. Most Algebra questions are concept-driven and revolve around a limited set of principles, formulas, and problem-solving techniques. Once you develop clarity in these fundamentals, solving new questions becomes a matter of applying familiar ideas rather than learning entirely new concepts.
Unlike topics that rely heavily on interpretation or experimentation, Algebra rewards candidates who practice systematically. That’s why it deserves a place at the core of every CAT aspirant’s preparation strategy.
| QA Topic Cluster | Approx. Questions* | Approx. Weightage* |
|---|---|---|
| Arithmetic | 8–10 | 35–40% |
| Algebra | 6–8 | 25–35% |
| Geometry & Mensuration | 3–5 | ~15% |
| Number Systems | 1–2 | 5–8% |
| Modern Math (P&C, Probability, Sets) | 1–2 | ~5% |
Estimated ranges based on analysis of CAT 2020–2025 papers across all slots. CAT does not release an official topic-wise syllabus or weightage.
Taken together, Arithmetic and Algebra generally account for nearly two-thirds of the Quantitative Aptitude section, making them the two most important areas to master. If your goal is to maximize your CAT Quant score, investing time in these topics early in your preparation will deliver the highest return. Within Algebra, the sub-topics that show up most consistently are Equations, Inequalities, and progressions—which is exactly where this guide’s practice questions are concentrated.
CAT Algebra Weightage Trends: Topic-Wise Breakdown
Recent CAT papers show a fairly consistent split across Algebra subtopics, though the exact counts shift slightly by slot and year. Inequalities, in particular, have trended upward in recent attempts, so they’re worth extra practice time even if they feel less familiar than quadratic equations.
| Algebra Sub-Topic | Typical Q. Count | Difficulty Tier |
| Linear Equations & Word Problems | 1–2 | Easy–Moderate |
| Quadratic Equations | 1–2 | Moderate |
| Inequalities | 1–2 | Moderate–Difficult |
| Logarithms | 1 | Easy–Moderate |
| Functions & Modulus | 1–2 | Moderate–Difficult |
| Progressions (AP/GP/HP) | 1–2 | Moderate |
| Surds & Indices | 0–1 | Easy |
| Polynomials & Remainder Theorem | 0–1 | Moderate |
*Ranges reflect recurring patterns across recent CAT slots and are meant to guide prioritisation, not to be read as a guaranteed question count.
Top Algebra Questions to Practice for CAT 2026
These questions cover the algebra concepts that show up most often in CAT — equations, inequalities, logarithms, functions, and progressions. Solve each one without a calculator, then check your method against the solution.
Q1. If 3x + 2y = 12 and 5x − y = 7, find x + y.
y = 5x−7 from eq. 2; substituting gives 13x = 26, so x = 2, y = 3, and x+y = 5.
Q2. Solve for x: 2ˣ × 2^(x+1) = 128.
Combine powers: 2^(2x+1) = 2⁷, so 2x+1 = 7 and x = 3.
Q3. If the roots of x² − 7x + k = 0 differ by 3, find k.
(root₁−root₂)² = 49−4k = 9, so k = 10.
Q4. Solve for x: |2x − 5| ≤ 7.
−7 ≤ 2x−5 ≤ 7 gives −1 ≤ x ≤ 6.
Q5. If log₂x + log₄x + log₈x = 11, find x.
log₂x × (11/6) = 11 gives log₂x = 6, so x = 64.
Q6. If f(x+1) = 2f(x) − 3 and f(1) = 5, find f(4).
f(2)=7, f(3)=11, f(4) = 2(11)−3 = 19.
Q7. In an AP, the 5th term is 17, and the 9th term is 33. Find the first term and common difference.
4d = 16 gives d = 4; a = 17−4d = 1.
Q8. The sum of three terms in a GP is 21, and their product is 216. Find the terms.
With terms a/r, a, ar: a³ = 216 gives a = 6; solving 2/r+2r = 5 gives r = 2 or 1/2, so terms are 3, 6, 12.
Q9. When x³ − 3x² + kx − 8 is divided by (x−2), the remainder is 6. Find k.
By the Remainder Theorem, f(2) = 2k−12 = 6, so k = 9.
Q10. If α and β are roots of x² − 5x + 6 = 0, find α² + β².
α+β = 5, αβ = 6, so α²+β² = 25−12 = 13.
Quick Formula Cheat-Sheet for CAT Algebra
Keep this as a one-page reference rather than a full formula book—most CAT Algebra questions draw from a surprisingly small core set of identities.
| Topic | Key Formula / Identity |
| Squares & Cubes | (a+b)² = a²+2ab+b² | a³+b³ = (a+b)(a²−ab+b²) |
| Quadratic Roots | Sum = −b/a, Product = c/a | Roots equal when b²−4ac = 0 |
| Logarithms | logₐx + logₐy = logₐ(xy) | logₐxⁿ = n·logₐx |
| AP | nth term = a+(n−1)d | Sum = n/2 [2a+(n−1)d] |
| GP | nth term = ar^(n−1) | Sum = a(rⁿ−1)/(r−1) |
| HP | Reciprocals of terms form an AP |
| Modulus Inequality | |x−a| ≤ b → a−b ≤ x ≤ a+b |
Common Mistakes CAT 2026 Aspirants Make in Algebra
Most Algebra marks are lost to avoidable habits rather than a lack of ability. Watch out for these patterns as you work through your practice sets:
- Jumping straight to mixed practice sets before any single sub-topic—Equations, Inequalities, Progressions—feels solid on its own.
- Memorising a formula without understanding why it works, which falls apart the moment a question phrases it differently than expected.
- Skipping sign checks in Inequalities, especially when multiplying or dividing by a negative or unknown-sign quantity.
- Treating Functions and Modulus questions as plug-and-chug instead of sketching the behaviour of the function first.
- Ignoring the time cost of a question—spending four minutes on a two-mark Algebra question that could have been skipped and revisited later.
Fixing these habits usually improves accuracy faster than learning new formulas, since most CAT Algebra questions test careful execution more than advanced theory.
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Algebra can single-handedly lift your Quant percentile—but only if you stop treating it as an afterthought. Linear Equations, Quadratic Equations, Inequalities, Logarithms, and Progressions show up in CAT every single year, without fail. The aspirants who prepare this topic with real structure, not scattered PDFs and random YouTube videos, are the ones walking into results day with the strongest QA scores.
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How to Practice CAT 2026 Algebra Questions the Right Way
- Practice topic-wise before mixing: 20–30 questions on one sub-topic build pattern recognition faster than jumping between topics.
- Maintain a formula sheet and revise it weekly instead of rewriting it from scratch each time.
- Redo every incorrect question after 3–4 days without checking the solution first — spaced revisits are where retention actually happens.
- Once individual sub-topics feel steady, move to sectional tests that mix Algebra with Arithmetic and Geometry, since CAT rarely isolates a single topic in a paper.
For a broader view of how Algebra fits into the rest of the section, it’s worth cross-checking this against our CAT 2026 Quant weightage guide, and pairing topic practice with CAT previous year question papers to see how these concepts appear under real exam phrasing.
For the exam’s official pattern and any policy updates, the IIM CAT website remains the authoritative source to check closer to the exam date.
Summary: Algebra Prep Snapshot for CAT 2026
If you’re short on time, this is the condensed version of everything above.
| Metric | Detail |
| Total QA Questions | 22 (per recent CAT papers) |
| Algebra Questions (est.) | 6–8, ~25–35% of QA |
| High-Frequency Sub-Topics | Equations, Inequalities, Progressions |
| Recommended Practice Volume | 150–200 questions across sub-topics before mocks |
| Best Time to Start | 8–10 weeks before CAT 2026, alongside Arithmetic |
Conclusion
Algebra is one of the few CAT Quant clusters where structured practice pays off almost linearly — the more correctly-solved questions you accumulate across equations, inequalities, and progressions, the more predictable this section becomes on exam day. Start with the easy set above to confirm your fundamentals, move through the moderate and difficult questions as your accuracy improves, and revisit the formula cheat-sheet weekly rather than once. Once Algebra feels steady on its own, folding it into full-length sectional and mock tests — including CATMock’s quant sectionals — is the most reliable way to check whether that practice holds up under real exam timing.
Frequently Asked Questions
Based on recent papers, Algebra typically contributes around 6–8 questions out of 22 in Quantitative Aptitude — this varies slightly by slot and isn’t officially confirmed by the exam conducting body.
Linear and Quadratic Equations, Inequalities, and Progressions have appeared most consistently in recent papers, making them a sensible starting point before moving to Functions and Logarithms.
The underlying concepts are largely the same, but CAT questions are designed to be solved quickly using shortcuts and elimination rather than long-form algebraic manipulation, which is usually what makes them feel harder.
Aiming for 150–200 solved questions spread across all Algebra sub-topics, before moving to full sectional mocks, gives most aspirants a reasonable base of pattern exposure.
A core set — squares and cubes of sums, quadratic root relationships, AP/GP/HP formulas, and basic log rules — covers most questions. Memorising rarely-used identities has limited returns given prep time constraints. Data note: CAT does not publish an official syllabus or topic-wise weightage. Figures in this article are estimates based on analysis of CAT 2020–2025 papers and are meant to guide prioritization, not to be read as guaranteed exam composition.
