CAT Quantitative Aptitude Linear Equation: Check Fundamental Concept, Key Formulas, Previous Year’s Sample Question

CAT Linear Equations section is the part of algebra and candidates can expect around 1-2 questions from this topic. As per the previous year's analysis of CAT question paper, the difficulty level of questions asked from the algebra had been rated moderate. With regular practice and right knowledge of basic concepts of linear equations i.e. 1-Variable, 2-Variable and 3-Variable equations etc you can easily solve the questions based on this concept. Also Check CAT QA Syllabus

In CAT 2021, candidates can expect the questions from Linear Equations to be merged with other concepts or topics like Maximum, Minimum, Roots of Equation, Real and Imaginary Roots. Therefore the in depth preparation of the topic is required. In the article below, we have provided the basic concepts of linear equation along with important formulas and solved sample questions.

Basic Concept of Linear Equation

Linear equations is a mathematical statement that has an equal to the symbol of "=". In linear equations where each term contains an exponent of one. Also, after the graphing of the equation, a straight line can be seen. It is an equation where the equation of degree is 1. And it can be written for two different variables. Also, it is a combination of two variables.

• On the basis of the number of variables along with the variables used with themselves, the formula of CAT Linear Equations is set.

• At first, all the variables must be independent of each other.

• {y= a x + b [here both x and y are variables and both a and b are constants]}

Types of Linear Equations:

• Standard Form of Linear Equations
• Slope Intercept Form of Linear Equations
• Point Slope Form of Linear Equations

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CAT Quantitative Aptitude: Formulas for Linear Equations

In the below section, some of the basic and important formulas of CAT Linear Equations are mentioned.

CAT Linear Equations Previous Year’s Solved Question

In the section below, some solved questions of CAT Linear Equations of the previous year are mentioned below.

Ques. 3x + 4|y| = 33. What is the number of integer values of (x, y) possible?

1. 6
2. 3
3. 4
4. More than 6

Correct Answer: ( 4 )

Ques. (|x| - 3) (|y| + 4) = 12. What is the number of pairs of integers (x, y) that proves this equation?

1. 4
2. 6
3. 10
4. 8

Correct Answer: ( 3 )

Ques. x + |y| = 8, |x| + y = 6. What is the number of pairs of x, y that proves these two equations?

1. 2
2. 4
3. 0
4. 1

Correct Answer: ( 4 )

Ques. How many real solutions of the equation are there in x2 - 7|x| - 18 = 0 ?

1. 2
2. 4
3. 3
4. 1

Correct Answer: ( 1 )

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Ques. x2 - 9x + |k| = 0 has real roots. What are the number of integer values can 'k' take?

1. 40
2. 21
3. 20
4. 41

Correct Answer: ( 4 )

Ques. x2 - 11x + |p| = 0 has integer roots. What are the number of integer values can 'p' take?

1. 6
2. 4
3. 8
4. More than 8

Correct Answer: ( 4 )

Ques. 2x + 5y = 103. How many pairs of positive integers x and y that satisfy the equation?

1. 9
2. 10
3. 12
4. 20

Correct Answer: ( 2 )

Ques. Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Where Median (a,b,c) - Mean (a,b,c) = 2. What will be the median of a, b, and c?

1. 11.5
2. 9
3. 9.5
4. 12

Correct Answer: ( 3 )

Ques. Equation x2 + 5x – 7 = 0 contains roots both a and b and Equation 2x2 + px + q = 0 has roots a + 1 and b + 1. What will be the outcome of p + q?

1. 6
2. 0
3. -16
4. 2

Correct Answer: ( 3 )

Ques. What number of real solutions are there for the equation x2 – 7|x| - 30 = 0?

1. 3
2. 1
3. 2
4. None

Correct Answer: ( 3 )

CAT Linear Equations Preparation Tips

A list of important tips for the preparation of CAT Linear Equations are mentioned below.

• Note down all the terms and important formulas.
• Practice all the important formulas by solving topic wise question
• Use various methods like graphical, elimination, substitution method along with Factor Theorem while solving any questions
• Read different types of books and practice sample questions and previous year's question paper
• Try to give a mock test at least twice or thrice in a week.
• Start Linear Equation Preparation by starting with simple equations like
  • 6(2x – 5) = 4(8x + 7)
  • After that you can move for graphical linear equations or 3 variable linear equations.

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