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.

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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CAT coaching institutes in Vadodara that offer weekend batches IMS Vadodara, Career Launcher (CL) Baroda and Endeavor Vadodara.

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Sayeba Naushad

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Answered Yesterday

To choose the best CAT Coaching institute in Vadodara, candidates must consider the following points:

  • Compare classroom vs. online/hybrid formats
  • Success Rate of the centre
  • Ask about batch size, number of full-length mocks, recorded sessions/notes
  • Final fee structure and refund/installment policy.

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Sayeba Naushad

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Answered Yesterday

The average fee in Vadodara ranges from ₹50,000 to ₹85,000 for offline classroom courses and ₹25,000 to ₹35,000 for online courses.

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Sayeba Naushad

Contributor-Level 10

Answered 2 days ago

CAT coaching institute in Cuttack that offers weekend batches is Career Launcher Cuttack. TIME and Samantaray Academy also offer weekend batches, but candidates need to contact them for more information. 

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Sayeba Naushad

Contributor-Level 10

Answered 2 days ago

To choose the best CAT Coaching institute in Cuttack, candidates must consider the following points:

  • Compare classroom vs. online/hybrid formats
  • Success Rate of the centre
  • Ask about batch size, number of full-length mocks, recorded sessions/notes
  •  Final fee structure and refund/installment policy

S

Sayeba Naushad

Contributor-Level 10

Answered 2 days ago

The average fee ranges in Cuttack from ₹50,000 to ₹85,000 for offline classroom courses and ₹25,000 to ₹45,000 for online courses.

S

Sayeba Naushad

Contributor-Level 10

Answered 3 days ago

CAT sectional cutoff is the minimum percentile score required in each individual section (VARC, DILR, and QA) to qualify for an institute's selection process. All IIMs have a distinct admission policy, including the sectional cutoffs and overall cutoff scores.

A

Akansha Goyal

Contributor-Level 7

Answered 3 days ago

IIM exam score remains valid a period of one year for admissions. However, IIM Ahmedabad has a deferred admission policy for its flagship PGP course, allowing selected candidates to postpone joining by up to two years to gain work experience.

Some other IIMs like IIM Trichy and IIM Sirmaur have known

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Loveleen Sharma

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The CAT exam pattern and difficulty levels do not change drastically. The core syllabus of Quant, VARC, and DILR typically remains the same.

CAT exam pattern saw a major change in 2020 as the COVID-19 pandemic demanded a reduction in the exam duration. The exam sections remained the same, while the q

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Vikram Tyagi

Contributor-Level 7

Answered 5 days ago

Career Launcher (Rajkot) and TIME are CAT coaching Institutes in Rajkot that offer weekend batches.

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Sayeba Naushad

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