CAT Algebra Questions with Solutions PDF

Common Admission Test 2026 ( CAT )

Abhishek Dhawan
Updated on Jul 30, 2026 00:33 IST

By Abhishek Dhawan, Deputy Manager - MBA & BBA Content

CAT Algebra questions are usually moderate to tough. Sometimes, they can be tricky. It is the second most dominant section of CAT Quantitative Aptitude section after Arithmetic. Questions are asked from Linear Equation, Quadratic Equation, Higher Degree Equation, Inequalities, Logarithms, Progression and Series, Functions and Graphs, Maxima and Minima and Modulus.

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CAT 2026 aspirants must be thorough with Algebraic formulae to solve questions in least time. Sum of series, telescoping sums, GP properties shifting graphs, composite functions, periodic functions, number of integral solutions, nature of roots, intervals Multi-layered log equations, properties simplification, and such topics should be in focus

CAT Quantitative Aptitude section has about 6 to 9 Algebra questions in. To score 99 percentile, attempt 5 to 8 CAT Algebra questions.

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  • Sample CAT Algebra Questions with Solutions
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Sample CAT Algebra Questions with Solutions

Question 1: Find the value of x if log3x + log9x + log27x + log81x = 25/4
(a) 9
(b) 27
(c) 81
(d) 243

Question 2: If log2[log3(log4x)] = 0 and log3[log4(log2y)] = 0, find x + y.
Options:
(a) 80
(b) 72
(c) 68
(d) 144

Question 3: Determine the number of real roots for the given equation: log2(x2 – 7x + 12) = log2{2} (x - 3) + 1.
Options:
(a) 0
(b) 1
(c) 2
(d) Infinity

Question 4: Find out the number of positive integer solutions (x, y) of the linear equation 3x + 5y = 105
a) 6
(b) 7
(c) 8
(d) 21 

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DEEPANKAR BEHERA

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Dedicate one focused hour in the morning to QA formulas or an RC passage, one hour in the evening to DILR sets, and reserve weekends for full-length mocks and thorough review.

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Loveleen Sharma

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It is not too late, provided you adjust your scope. Focus directly on core topics, start taking sectional tests immediately, and spend time learning through mock test analysis.

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Rohini Bisht

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Focus on formula sheets, mental math tables, grammar pointers, and your accumulated test error log. Avoid attempting full-length tests during the final three days before the exam.

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Dhanya Shekhar

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A beginner can build a respectable attempt by focusing strictly on high-yield areas such as Arithmetic, Algebra, core DI arrangements, and Reading Comprehension, rather than attempting the entire syllabus.

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Bhumika Sharma

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Yes, 60 days is adequate if you have a basic understanding of mathematics and reading skills. It provides sufficient time to revise concepts, complete timed sectional practice, and take 12 to 15 full mocks.

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Shruti Shukla

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