CAT Algebra PYQs with Video Solutions & Formulas PDF

CAT Algebra PYQs

Algebra is an important part of CAT Quantitative Aptitude because it tests much more than the ability to remember formulas. CAT Algebra questions often require aspirants to translate conditions into equations, identify useful relationships between variables and choose the shortest possible route to the answer.

Practising CAT Algebra PYQs is one of the most effective ways to understand this difference. CAT Algebra previous year questions reveal how familiar concepts such as equations, inequalities, functions, logarithms and progressions are converted into aptitude-based problems that test reasoning rather than mechanical calculation.

Download CAT Algebra PYQ PDF

A CAT Previous Year Algebra Questions PDF allows aspirants to practise previous year questions without searching through complete CAT papers individually. A topic-wise CAT Algebra Questions PDF is especially useful during revision because students can quickly identify concepts where they are consistently losing marks or spending too much time.

However, simply completing the PDF should not be the target. The objective should be to identify recurring concepts, improve question selection and understand why certain approaches work better than others.

While solving the CAT Algebra PYQ PDF, maintain three categories:

This classification is more useful than simply recording whether an answer was correct or incorrect. A question that takes six minutes but is eventually solved correctly can still indicate a preparation gap because CAT Quant also tests question selection and speed.

Students can therefore use CAT Algebra PYQs as both a practice resource and a diagnostic tool.

CAT Algebra Formulas PDF

A CAT Formulas PDF should be used as a quick revision resource rather than as the primary method of learning Algebra. Unlike some calculation-heavy topics, CAT Algebra frequently requires students to understand when and how a mathematical relationship can be applied.

The formula sheet covers important CAT Algebra topics related to:

• Linear and quadratic equations
• Roots and coefficients of quadratic equations
• Algebraic identities
• Inequalities and modulus
• Logarithms
• Surds and indices
• Arithmetic and geometric progressions
• Functions
• Maximum and minimum value concepts

For example, remembering the relationship between the roots and coefficients of a quadratic equation is useful. The bigger skill is recognising when a CAT Algebra question can be simplified using that relationship without explicitly calculating both roots.

An effective revision technique is to annotate your formula PDF with trigger conditions. Instead of writing only the formula, add a short note explaining when you would consider using it. This makes formula revision more closely connected to actual Algebra practice questions and improves concept recall during timed tests.

Also Read: CAT Quants PYQ Analysis 2026, Difficulty, Repeated Topics

CAT Algebra PYQ Questions 

Not every Algebra topic appears in exactly the same form across CAT papers. Topic-wise practice helps students understand the different reasoning patterns that can appear within Algebra. It also makes it easier to identify which CAT Algebra topics require additional practice before moving to mixed Quant sets.

Question 1

A value of $$c$$ for which the minimum value of $$f(x)=x^{2}-4cx+8c$$ is greater than the maximum value of $$g(x)=-x^{2}+3cx-2c$$, is

A

$$2$$

B

$$\dfrac{1}{2}$$

C

$$-\dfrac{1}{2}$$

D

$$-2$$

Show Answer Explanation Video Solution

correct answer:- 2

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Question 2

Let $$3\leq x\leq6$$ and $$\left[x^{2}\right] =\left[x\right]^{2}$$ , where $$[x]$$ is the greatest integer not exceeding $$x$$ . If set $$S$$ represents all feasible values of $$x$$, then a possible subset of $$S$$ is

A

$$\left(3,\sqrt{10}\right)\cup \left[5,\sqrt{26}\right)\cup \left\{6\right\}$$

B

$$\left[3,\sqrt{10}\right] \cup \left[5,\sqrt{26}\right]$$

C

$$\left[3,\sqrt{10}\right]\cup \left[4,\sqrt{17}\right]\cup \left\{6\right\}$$

D

$$\left(4,\sqrt{18}\right)\cup\left[5,\sqrt{27}\right)\cup\left\{6\right\}$$

Show Answer Explanation Video Solution

correct answer:- 1

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Question 3

Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is

Show Answer Explanation Video Solution

correct answer:- 15

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Question 4

If a, b and c are positive real numbers such that $$a > 10 \geq b \geq c$$ and $$\cfrac{\log_8 (a + b)}{\log_2c} + \cfrac{\log_{27} (a - b)}{\log_3c} = \cfrac{2}{3}$$, then the greatest possible integer value of a is

Show Answer Explanation Video Solution

correct answer:- 14

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Question 5

A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

A

4095

B

8191

C

2047

D

1023

Show Answer Explanation Video Solution

correct answer:- 1

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Question 6

The roots $$\alpha, \beta$$ of the equation $$3x^2 + \lambda x - 1 = 0$$, satisfy $$\cfrac{1}{\alpha^2} + \cfrac{1}{\beta^2} = 15$$.
The value of $$(\alpha^3 + \beta^3)^2$$, is

A

16

B

4

C

1

D

9

Show Answer Explanation Video Solution

correct answer:- 2

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Question 7

If $$x$$ and $$y$$ are positive real numbers such that $$\log_{x}(x^2 + 12) = 4$$ and $$3 \log_{y} x = 1$$, then $$x + y $$ equals

A

20

B

68

C

10

D

11

Show Answer Explanation Video Solution

correct answer:- 3

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Question 8

If $$\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$$, then $$\sqrt{10x+9}$$ is equal to

A

$$3\sqrt{31}$$

B

$$4\sqrt{5}$$

C

$$3\sqrt{7}$$

D

$$2\sqrt{7}$$

Show Answer Explanation Video Solution

correct answer:- 3

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Question 9

If $$x$$ and $$y$$ are real numbers such that $$x^{2} + (x - 2y - 1)^{2} = -4y(x + y)$$, then the value $$x - 2y$$ is

A

0

B

1

C

-1

D

2

Show Answer Explanation Video Solution

correct answer:- 2

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Question 10

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is $$(n + 2n^2)$$. If the $$n^{th}$$ term of the progression is divisible by 9, then the smallest possible value of n is

A

9

B

4

C

7

D

8

Show Answer Explanation Video Solution

correct answer:- 3

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Question 11

Let $$0 \leq a \leq x \leq 100$$ and $$f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$$. Then the maximum value of f(x) becomes 100 when a is equal to

A

25

B

100

C

50

D

0

Show Answer Explanation Video Solution

correct answer:- 3

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Question 12

Let a, b, c be non-zero real numbers such that $$b^2 < 4ac$$, and $$f(x) = ax^2 + bx + c$$. If the set S consists of all integers m such that f(m) < 0, then the set S must necessarily be

A

the set of al!I positive integers

B

the set of all integers

C

either the empty set or the set of all integers

D

the empty set

Show Answer Explanation Video Solution

correct answer:- 3

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Question 13

A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

A

11

B

13

C

10

D

12

Show Answer Explanation Video Solution

correct answer:- 2

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Question 14

The number of integers n that satisfy the inequalities $$\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid$$ is

A

21

B

19

C

18

D

20

Show Answer Explanation Video Solution

correct answer:- 2

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Question 15

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

Show Answer Explanation Video Solution

correct answer:- 35

Classification of CAT Algebra PYQ questions by topic is:

Do not treat these Algebra topics for CAT as completely isolated chapters. CAT can combine multiple concepts within the same question. For instance, a question may initially appear to test quadratic equations but ultimately require an inequality to determine the possible range of a variable.

This is why topic-wise CAT Algebra questions should eventually be followed by mixed Algebra practice. Topic-wise practice develops concept recognition, while mixed practice develops the ability to independently identify which concept or method a question requires.

An Algebra Questions with Solutions PDF can also be useful at this stage, provided students study the method after attempting each problem independently rather than immediately reading the solution.

CAT Algebra Topic-Wise Weightage

There is no officially fixed topic-wise weightage for Algebra in CAT. The number and type of CAT Quant Algebra questions can vary by year and across different slots of the examination. Aspirants should therefore avoid preparing Algebra based on an assumed fixed number of questions.

A better approach is to use historical question patterns to determine preparation priority rather than treating past frequency as a prediction of the next CAT paper.

The exact number of questions should never determine whether you completely skip a topic. CAT papers can vary considerably, so over-optimising preparation around historical weightage can be risky.

Instead, use topic-wise trends to decide how much practice time each area deserves after ensuring that the fundamental CAT Algebra topics have been covered.

How to Prepare for CAT Algebra Using PYQs?

The biggest mistake students make with CAT Algebra previous year questions is solving them once and immediately moving on. PYQs become far more valuable when they are used to improve concept recognition, approach selection and solving speed.

Start by learning the basic concept and solving a small number of straightforward Algebra questions for CAT. Then attempt CAT PYQs from the same topic without looking at solutions.

For every difficult CAT Algebra PYQ, identify exactly where you got stuck. Was the formula unknown? Did you fail to form the equation? Did you choose an unnecessarily lengthy method? Or did you understand the solution afterwards but fail to recognise the required idea yourself?

A useful preparation cycle is:

Learn Concept → Solve Topic-Wise Questions → Attempt PYQs → Analyse Approach → Reattempt Difficult PYQs → Practise Mixed Questions

Reattempting is particularly important. Mark CAT Previous Year Algebra Questions that you could not solve or that took considerably longer than expected and return to them after a week. If you can now solve the question quickly without remembering the exact solution, your understanding has improved.

Also Read: CAT Mock Taking Strategies for Quant, Check Details Below

CAT Algebra PYQs: Conclusion

CAT Algebra PYQs are valuable not simply because they provide more questions to solve, but because they show how Algebra concepts are actually tested in CAT. Regular practice with previous year questions can help aspirants improve concept recognition, identify weaker topics and develop faster approaches for equations, inequalities, functions, logarithms and progressions.

Combine CAT Algebra PYQs with formula revision, topic-wise practice and mixed Quant sets rather than relying on any one resource alone. Analyse questions you solve slowly or incorrectly and reattempt them after revision. The key takeaway is simple: use CAT Algebra PYQs to improve your approach, not merely to increase your question count.