Inequalities & Modulus — CAT Previous-Year Questions
31 previous-year questions on Inequalities & Modulus from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.
Inequalities & Modulus · CAT PYQs
The value of x satisfying the inequality ≤ are
If x and y satisfy the equations |x| + x + y = 15 and x + |y| - y = 20, then (x - y) equals
The number of distinct real values of x, satisfying the equation
max{x, 2} - min{x, 2} = |x + 2| - |x - 2|, is
The number of distinct integer solutions (x, y) of the equation |x + y| + |x - y| = 2, is
Any non-zero real numbers x, y such that y ≠ 3 and < , will satisfy the condition
The largest real value of a for which the equation |x + a| + |x - 1| = 2 has an infinite number of solutions for x is
Let 0 ≤ a ≤ x ≤ 100 and f(x) = |x - a| + |x - 100| + |x - a - 50|. Then the maximum value of f(x) becomes 100 when a is equal to
The minimum possibe value of , for x < 3, is
If c = + for some non-zero real numbers x and y, then c cannot take the value
The number of integers n that satisfy the inequalities |n - 60| < |n - 100| < |n - 20| is
For a real number x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if
If 3x + 2|y| + y = 7 and x + |x| + 3y = 1, then x + 2y is
The number of distinct pairs of integers (m, n) satisfying |1 + mn| < |m + n| < 5 is
If the sum of squares of two numbers is 97, then which one of the following cannot be their product?
For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied?
If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a - b)2 + (a - c)2 + (a - d)2 is
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.
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?
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?
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.
If x, y, z are distinct positive real numbers, then would be
If |b| ≥ 1 and x = –|a|b, then which one 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 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)?
Let x, y be two positive numbers such that x + y = 1. Then, the minimum value of is ______.
If x > 2 and y > – 1, Then which of the following statements is necessarily true?
Answer the following question based on the information given below.
Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.
The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.
If x2 + y2 = 0.1 and |x – y| = 0.2, then |x| + |y| is equal to
If |r − 6| = 11 and |2q − 12| = 8,what is the minimum possible value of ?
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?