Solving Inequalities — CAT Previous-Year Questions
11 previous-year questions on Solving Inequalities from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Solving Inequalities · CAT PYQs
The value of x satisfying the inequality ≤ are
Any non-zero real numbers x, y such that y ≠ 3 and < , will satisfy the condition
For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?
If f(x) = x3 – 4x + p, and f(0) and f(1) are of opposite signs, then which of the following is necessarily true?
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Given that −1 ≤ v ≤ 1, −2 ≤ u ≤ −0.5 and −2 ≤ z ≤ −0.5 and w = vz/u, then which of the following is necessarily true?
Answer the following question based on the information given below.
Consider three circular parks of equal size with centres at A1, A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3 and C1C2C3, as shown. Three sprinters A, B, and C begin running from points A1, B1 and C1 respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.
A real number x satisfying for every positive integer n, is best described by:
If x > 5 and y < −1, then which of the following statements is true?
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?
If x > 2 and y > – 1, Then which of the following statements is necessarily true?
Answer the questions based on the following information.
A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series S2, the nth term defined as the difference between the (n + 1)th term and the nth term of series S1, is an arithmetic progression with a common difference of 30.
Which of the following values of x do not satisfy the inequality (x2 – 3x + 2 > 0) at all?
Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.
What is the value of m which satisfies 3m2 – 21m + 30 < 0?