{"id":3355,"date":"2026-07-14T11:20:53","date_gmt":"2026-07-14T05:50:53","guid":{"rendered":"https:\/\/www.catmock.com\/blog\/?p=3355"},"modified":"2026-07-14T11:20:54","modified_gmt":"2026-07-14T05:50:54","slug":"top-algebra-questions-to-practice-for-cat-2026","status":"publish","type":"post","link":"https:\/\/www.catmock.com\/blog\/top-algebra-questions-to-practice-for-cat-2026\/","title":{"rendered":"Top Algebra Questions to Practice for CAT 2026"},"content":{"rendered":"\n

If there’s one topic that consistently shapes performance in the CAT Quant section, it’s Algebra<\/strong>. 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.<\/p>\n\n\n\n

This guide brings together the most important Algebra questions to practice for CAT 2026<\/strong>, 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.<\/p>\n\n\n\n

Since CAT does not publish an official syllabus or topic-wise weightage<\/strong>, 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\u2014not to predict the exact paper pattern.<\/p>\n\n\n\n

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Why Algebra Should Be a Priority for CAT 2026<\/h1>\n\n\n\n

Algebra is one of the few CAT Quant topics where consistent practice translates directly into better scores<\/strong>. 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.<\/p>\n\n\n\n

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.<\/p>\n\n\n\n

QA Topic Cluster<\/strong><\/th>Approx. Questions<\/strong>*<\/th>Approx. Weightage<\/strong>*<\/th><\/tr><\/thead>
Arithmetic<\/td>8\u201310<\/td>35\u201340%<\/td><\/tr>
Algebra<\/td>6\u20138<\/td>25\u201335%<\/td><\/tr>
Geometry & Mensuration<\/td>3\u20135<\/td>~15%<\/td><\/tr>
Number Systems<\/td>1\u20132<\/td>5\u20138%<\/td><\/tr>
Modern Math (P&C, Probability, Sets)<\/td>1\u20132<\/td>~5%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Estimated ranges based on analysis of CAT 2020\u20132025 papers across all slots. CAT does not release an official topic-wise syllabus or weightage.<\/strong><\/em><\/p>\n\n\n\n

Taken together, Arithmetic and Algebra generally account for nearly two-thirds of the Quantitative Aptitude section<\/strong>, 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\u2014which is exactly where this guide’s practice questions are concentrated.<\/p>\n\n\n\n

CAT Algebra Weightage Trends: Topic-Wise Breakdown<\/strong><\/h1>\n\n\n\n

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.<\/p>\n\n\n\n

Algebra Sub-Topic<\/strong><\/td>Typical Q. Count<\/strong><\/td>Difficulty Tier<\/strong><\/td><\/tr><\/thead>
Linear Equations & Word Problems<\/td>1\u20132<\/td>Easy\u2013Moderate<\/td><\/tr>
Quadratic Equations<\/td>1\u20132<\/td>Moderate<\/td><\/tr>
Inequalities<\/td>1\u20132<\/td>Moderate\u2013Difficult<\/td><\/tr>
Logarithms<\/td>1<\/td>Easy\u2013Moderate<\/td><\/tr>
Functions & Modulus<\/td>1\u20132<\/td>Moderate\u2013Difficult<\/td><\/tr>
Progressions (AP\/GP\/HP)<\/td>1\u20132<\/td>Moderate<\/td><\/tr>
Surds & Indices<\/td>0\u20131<\/td>Easy<\/td><\/tr>
Polynomials & Remainder Theorem<\/td>0\u20131<\/td>Moderate<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

*Ranges reflect recurring patterns across recent CAT slots and are meant to guide prioritisation, not to be read as a guaranteed question count.<\/strong><\/em><\/p>\n\n\n\n

Top Algebra Questions to Practice for CAT 2026<\/strong><\/h1>\n\n\n\n

These questions cover the algebra concepts that show up most often in CAT \u2014 equations, inequalities, logarithms, functions, and progressions. Solve each one without a calculator, then check your method against the solution.<\/p>\n\n\n\n

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Q1. If 3x + 2y = 12 and 5x \u2212 y = 7, find x + y.<\/strong>
y = 5x\u22127 from eq. 2; substituting gives 13x = 26, so x = 2, y = 3, and x+y = 5.<\/p>\n\n\n\n

Q2. Solve for x: 2\u02e3 \u00d7 2^(x+1) = 128.<\/strong>
Combine powers: 2^(2x+1) = 2\u2077, so 2x+1 = 7 and x = 3.<\/p>\n\n\n\n

Q3. If the roots of x\u00b2 \u2212 7x + k = 0 differ by 3, find k.<\/strong>
(root\u2081\u2212root\u2082)\u00b2 = 49\u22124k = 9, so k = 10.<\/p>\n\n\n\n

Q4. Solve for x: |2x \u2212 5| \u2264 7.<\/strong>
\u22127 \u2264 2x\u22125 \u2264 7 gives \u22121 \u2264 x \u2264 6.<\/p>\n\n\n\n

Q5. If log\u2082x + log\u2084x + log\u2088x = 11, find x.<\/strong>
log\u2082x \u00d7 (11\/6) = 11 gives log\u2082x = 6, so x = 64.<\/p>\n\n\n\n

Q6. If f(x+1) = 2f(x) \u2212 3 and f(1) = 5, find f(4).<\/strong>
f(2)=7, f(3)=11, f(4) = 2(11)\u22123 = 19.<\/p>\n\n\n\n

Q7. In an AP, the 5th term is 17, and the 9th term is 33. Find the first term and common difference.<\/strong>
4d = 16 gives d = 4; a = 17\u22124d = 1.<\/p>\n\n\n\n

Q8. The sum of three terms in a GP is 21, and their product is 216. Find the terms.<\/strong>
With terms a\/r, a, ar: a\u00b3 = 216 gives a = 6; solving 2\/r+2r = 5 gives r = 2 or 1\/2, so terms are 3, 6, 12.<\/p>\n\n\n\n

Q9. When x\u00b3 \u2212 3x\u00b2 + kx \u2212 8 is divided by (x\u22122), the remainder is 6. Find k.<\/strong>
By the Remainder Theorem, f(2) = 2k\u221212 = 6, so k = 9.<\/p>\n\n\n\n

Q10. If \u03b1 and \u03b2 are roots of x\u00b2 \u2212 5x + 6 = 0, find \u03b1\u00b2 + \u03b2\u00b2.<\/strong>
\u03b1+\u03b2 = 5, \u03b1\u03b2 = 6, so \u03b1\u00b2+\u03b2\u00b2 = 25\u221212 = 13.<\/p>\n<\/div><\/div>\n\n\n\n

Quick Formula Cheat-Sheet for CAT Algebra<\/strong><\/h2>\n\n\n\n

Keep this as a one-page reference rather than a full formula book\u2014most CAT Algebra questions draw from a surprisingly small core set of identities.<\/p>\n\n\n\n

Topic<\/strong><\/td>Key Formula \/ Identity<\/strong><\/td><\/tr><\/thead>
Squares & Cubes<\/td>(a+b)\u00b2 = a\u00b2+2ab+b\u00b2  |  a\u00b3+b\u00b3 = (a+b)(a\u00b2\u2212ab+b\u00b2)<\/td><\/tr>
Quadratic Roots<\/td>Sum = \u2212b\/a, Product = c\/a  |  Roots equal when b\u00b2\u22124ac = 0<\/td><\/tr>
Logarithms<\/td>log\u2090x + log\u2090y = log\u2090(xy)  |  log\u2090x\u207f = n\u00b7log\u2090x<\/td><\/tr>
AP<\/td>nth term = a+(n\u22121)d  |  Sum = n\/2 [2a+(n\u22121)d]<\/td><\/tr>
GP<\/td>nth term = ar^(n\u22121)  |  Sum = a(r\u207f\u22121)\/(r\u22121)<\/td><\/tr>
HP<\/td>Reciprocals of terms form an AP<\/td><\/tr>
Modulus Inequality<\/td>|x\u2212a| \u2264 b  \u2192  a\u2212b \u2264 x \u2264 a+b<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Common Mistakes CAT 2026 Aspirants Make in Algebra<\/strong><\/h1>\n\n\n\n

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:<\/p>\n\n\n\n