50+ CAT Linear Equations Questions With Video Solutions

CAT Linear Equations is a key topic in the  Quant section. Make sure you are aware of all the Important Concepts in CAT Quant (Linear Equation). One must not miss out on the questions on linear equations in the QA section. Linear Equations fall under the category of Algebra in the CAT Quants; You can also check out these CAT Linear Equation questions from the CAT Previous year papers. These are good sources of practice linear equations topic questions for CAT preparation. Keep practising free CAT mocks where you'll get a fair idea of how questions are asked, and type of questions asked. If you want to practice these questions, you can download these Important CAT Linear Equation Questions PDF (with detailed answers) and the video solutions below, which are completely Free.

Practice a good number of problems to improve your problem-solving skills and develop a strategic approach to solve the question from this topic quickly.

CAT Linear Equations Questions Weightage














Tips To Solve CAT Linear Equation Questions

Fundamentals of this concept are useful in solving the questions of the other topics by assuming the unknown values as variables.

Be careful of silly mistakes in this topic, as that is how students generally lose marks here.

The number of equations needed to solve the given problem equals the number of variables.

A linear equation is an equation which gives a straight line when plotted on a graph.

Linear equations can be of one variable or two variables, or three variables.

Let a, b, c and d be constants, and x, y and z are variables. A general form of a single variable linear equation is ax+b = 0.

A general form of two variable linear equation is ax+by = c.

A general form of three variable linear equation is ax+by+cz = d.

CAT Linear Equations Formulas PDF

To help CAT aspirants in their preparation, we have made a comprehensive formula PDF containing all the important linear equations that are essential. This PDF includes all the necessary formulas, techniques, and examples required to solve linear equations efficiently. Click on the link below to download the Linear equations formula PDF.

1. Linear Equations Formulae: Solving Linear Equations

    For equations of the form ax+by = c and mx+ny = p, find the LCM of b and n.

      Multiply each equation with a constant to make the y term coefficient equal to the LCM. Then subtract equation 2 from equation 1.

      2. Linear Equations Formulae:  Straight Lines

      Equations with 2 variables: Consider two equations ax+by=c and mx+ny=p. Each of these equations represent two lines on the x-y coordinate plane. The solution of these equations is the point of intersection.

      If $$ \frac{a}{m}=\frac{b}{n}\neq\frac{c}{p}$$: This means that both the equations have the same slope but different intersect and hence are parallel to each. Hence, there is no point of intersection and no solution.

      If $$ \frac{a}{m}\neq\frac{b}{n}$$: They have different slopes and hence must intersect at some point. This results in a Unique solution.

      $$ \frac{a}{m}=\frac{b}{n}=\frac{c}{p}$$: The two lines have the same slope and intercept. Hence they are the same lines. As they have infinite points common between them, there are infinite many solutions possible.

          CAT 2023 Linear Equations questions

          Question 1

          For some real numbers a and b, the system of equations $$x + y = 4$$ and $$(a+5)x+(b^2-15)y=8b$$ has infinitely many solutions for x and y. Then, the maximum possible value of ab is

          Question 2

          A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

          CAT 2022 Linear Equations questions

          Question 1

          If $$c=\frac{16x}{y}+\frac{49y}{x}$$ for some non-zero real numbers x and y, then c cannot take the value

          Question 2

          In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is

          Question 3

          Let a and b be natural numbers. If $$a^2 + ab + a = 14$$ and $$b^2 + ab + b = 28$$, then $$(2a + b)$$ equals

          Question 4

          The largest real value of a for which the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for x is

          Question 5

          A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained, is

          Question 6

          For natural numbers x, y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is

          CAT 2021 Linear Equations questions

          Question 1

          A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is

          Question 2

          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

          Question 3

          If $$3x+2\mid y\mid+y=7$$ and $$x+\mid x \mid+3y=1$$ then $$x+2y$$ is:

          CAT 2020 Linear Equations questions

          Question 1

          A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

          Question 2

          Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

          Question 3

          Let k be a constant. The equations $$kx + y = 3$$ and $$4x + ky = 4$$ have a unique solution if and only if

          Question 4

          In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹ 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent ₹ 450 on rice in April, then how much did he spend on wheat in May?

          Question 5

          If x and y are non-negative integers such that $$x + 9 = z$$, $$y + 1 = z$$ and $$x + y < z + 5$$, then the maximum possible value of $$2x + y$$ equals

          Question 6

          Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

          Question 7

          Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

          CAT 2019 Linear Equations questions

          Question 1

          If $$5^x - 3^y = 13438$$ and $$5^{x - 1} + 3^{y + 1} = 9686$$, then x + y equals

          Question 2

          In 2010, a library contained a total of 11500 books in two categories - fiction and nonfiction. In 2015, the library contained a total of 12760 books in these two categories. During this period, there was 10% increase in the fiction category while there was 12% increase in the non-fiction category. How many fiction books were in the library in 2015?

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