Inequalities are one of the important topic in the quantitative part of the CAT exam that can present tricky questions. These questions are often integrated with other sections like ratio and proportion, and progressions. Without a solid understanding of the concepts, candidates may find these questions time-consuming. Mastery of algebraic expressions and equations is crucial.
Practicing with CAT previous years' question papers is an excellent way to become familiar with the exam pattern. Additionally, taking free CAT mock tests can help you understand the types of questions that are likely to appear on the exam.
We have compiled all the inequality questions from past CAT exams. You can download these questions in a PDF format, which includes detailed solutions explained by CAT experts. Click the link below to download the CAT linear equation questions PDF with detailed video solutions
Question 1
Let a, b, c, d be four integers such that a+b+c+d = 4m+1 where m is a positive integer. Given m, which one of the following is necessarily true?
correct answer:-2
Question 2
Given that $$-1 \leq v \leq 1, -2 \leq u \leq -0.5$$ and $$-2 \leq z \leq -0.5$$ and $$w = vz /u$$ , then which of the following is necessarily true?
correct answer:-2
Question 3
If x, y, z are distinct positive real numbers the $$(x^2(y+z) + y^2(x+z) + z^2(x+y))/xyz$$ would always be
correct answer:-3
Question 4
The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x <= y is:
correct answer:-2
Question 5
What values of x satisfy $$x^{2/3} + x^{1/3} - 2 <= 0$$?
correct answer:-1
Question 6
If x > 5 and y < -1, then which of the following statements is true?
correct answer:-4
Question 7
x and y are real numbers satisfying the conditions 2 < x < 3 and - 8 < y < -7. Which of the following expressions will have the least value?
correct answer:-3
Question 8
$$m$$ is the smallest positive integer such that for any integer $$n \geq m$$, the quantity $$n^3 - 7n^2 + 11n - 5$$ is positive. What is the value of $$m$$?
correct answer:-4
Question 9
If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a)(1+b)(1+c)(1+d)?
correct answer:-3
Question 10
Let x and y be two positive numbers such that $$x + y = 1.$$
Then the minimum value of $$(x+\frac{1}{x})^2+(y+\frac{1}{y})^2$$ is
correct answer:-3
Question 11
If x>2 and y>-1,then which of the following statements is necessarily true?
correct answer:-2
Question 12
If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have?
correct answer:-3
Question 13
If $$x^2 + 5y^2 + z^2 = 2y(2x+z)$$, then which of the following statements is(are) necessarily true?
A. x = 2y B. x = 2z C. 2x = z
correct answer:-3
Question 14
If u, v, w and m are natural numbers such that $$u^m + v^m = w^m$$, then which one of the following is true?
correct answer:-4
Question 15
If pqr = 1, the value of the expression $$1/(1+p+q^{-1}) + 1/(1+q+r^{-1}) + 1/(1+r+p^{-1})$$
correct answer:-3
Question 16
From any two numbers $$x$$ and $$y$$, we define $$x* y = x + 0.5y - xy$$ . Suppose that both $$x$$ and $$y$$ are greater than 0.5. Then
$$x* x < y* y$$ if
correct answer:-2
Question 17
The number of integers n satisfying -n+2 ≥ 0 and 2n ≥ 4 is
correct answer:-2
Question 18
x, y and z are three positive integers such that x > y > z. Which of the following is closest to the product xyz?
correct answer:-1
Question 19
Which of the following values of x do not satisfy the inequality $$(x^2 - 3x + 2 > 0)$$ at all?
correct answer:-1
Instruction for set :
For these questions the following functions have been defined.
$$la(x, y, z) = min (x+y, y+z)$$
$$le(x, y, z) = max(x -y, y-z)$$
$$ma (x, y, z) = \frac{1}{2} (le (x, y, z) + la (x, y, z))$$
Question 20
Given that $$x >y> z> 0$$. Which of the following is necessarily true?
correct answer:-4