CAT Inequalities & Modulus questions 49 since 2017

Across the 24 CAT papers from 2017 to 2025, Inequalities & Modulus was asked 49 times, in 21 of the 24 papers. CAT asks about 2.0 Inequalities & Modulus questions per paper on average; in 2022–2025 it was 1.8 per paper, against 2.2 in the four years before (steady). Below is how often it appeared each year, the ideas CAT keeps reusing, and every question with its answer.

How many Inequalities & Modulus questions come in CAT each year?

Inequalities & Modulus ideas CAT has repeated

• AM–GM bound on a sum of reciprocal-type terms 5 questions, 2020–2023
• Polynomial or rational inequalities by the sign of factors 4 questions, 2017–2024
• Equations with |x|: split into sign cases and count roots 4 questions, 2019–2023
• Sums of |x − a|: distance on the number line 5 questions, 2017–2022

All Inequalities & Modulus questions, newest first

CAT 2025

• CAT 2025 Slot 3 · QA Q13 In a school with 1500 students, each student chooses any one…
• CAT 2025 Slot 3 · QA Q21 Let p, q and r be three natural numbers such that their sum…
• CAT 2025 Slot 2 · QA Q7 If a , b , c and d are integers such that their sum is 46…
• CAT 2025 Slot 2 · QA Q14 The set of all real values of x for which ( x ^ 2 - | x + 9…
• CAT 2025 Slot 1 · QA Q8 A value of c for which the minimum value of f(x)=x^2-4 c x+8…
• CAT 2025 Slot 1 · QA Q17 The number of distinct pairs of integers (x, y) satisfying…
• CAT 2025 Slot 1 · QA Q22 Let 3 ≤ x ≤ 6 and [x^2]=[x]^2 , where [x] is the greatest…

CAT 2024

• CAT 2024 Slot 3 · QA Q1 The number of distinct integer solutions (x, y) of the…
• CAT 2024 Slot 3 · QA Q18 The number of distinct real values of x , satisfying the…
• CAT 2024 Slot 2 · QA Q2 If x and y satisfy the equations |x|+x+y=15 and x+|y|-y=20…
• CAT 2024 Slot 2 · QA Q20 All the values of x satisfying the inequality 1/(x+5) ≤ 1/(2… answer only

CAT 2023

• CAT 2023 Slot 2 · QA Q4 Any non-zero real numbers x, y such that y ≠ 3 and x/y…
• CAT 2023 Slot 2 · QA Q7 Let k be the largest integer such that the equation…
• CAT 2023 Slot 2 · QA Q13 The price of a precious stone is directly proportional to…
• CAT 2023 Slot 2 · QA Q16 If a certain amount of money is divided equally among n…
• CAT 2023 Slot 1 · QA Q5 The number of integer solutions of equation 2|x|(x^2+1)=5…

CAT 2022

• CAT 2022 Slot 3 · QA Q2 The minimum possible value of (x^2-6 x+10)/(3-x) , for x3…
• CAT 2022 Slot 3 · QA Q15 If c=(16 x)/y+(49 y)/x for some non-zero real numbers x and…
• CAT 2022 Slot 2 · QA Q4 If a and b are non-negative real numbers such that a+2 b=6…
• CAT 2022 Slot 2 · QA Q16 Five students, including Amit, appear for an examination in…
• CAT 2022 Slot 1 · QA Q10 The largest real value of a for which the equation…
• CAT 2022 Slot 1 · QA Q22 Let 0 ≤ a ≤ x ≤ 100 and f(x)=|x-a|+|x-100|+|x-a-50| . Then…

CAT 2021

• CAT 2021 Slot 3 · QA Q13 If 3 x+2|y|+y=7 and x+|x|+3 y=1 , then x+2 y is
• CAT 2021 Slot 3 · QA Q18 The number of distinct pairs of integers (m, n) satisfying…
• CAT 2021 Slot 3 · QA Q19 The cost of fencing a rectangular plot is ₹ 200 per ft along…
• CAT 2021 Slot 2 · QA Q15 For all possible integers n satisfying 2.25 ≤ 2 + 2^n + 2 ≤… answer only
• CAT 2021 Slot 2 · QA Q16 For all real numbers x the condition |3x - 20| + |3x - 40| =… answer only
• CAT 2021 Slot 1 · QA Q1 f(x) = x^2+2 x-15x^2-7 x-18 is negative if and only if answer only
• CAT 2021 Slot 1 · QA Q2 The number of integers n that satisfy the inequalities |n… answer only
• CAT 2021 Slot 1 · QA Q8 If r is a constant such that |x^2 - 4 x - 13| = r has… answer only

CAT 2020

• CAT 2020 Slot 3 · QA Q12 Let m and n be natural numbers such that n is even and 0.2 <… answer only
• CAT 2020 Slot 2 · QA Q7 If x and y are positive real numbers satisfying x + y = 102… answer only
• CAT 2020 Slot 2 · QA Q10 For real x, the maximum possible value of x√(1 + x^4) is answer only
• CAT 2020 Slot 2 · QA Q12 If x and y are non-negative integers such that x + 9 = z, y… answer only
• CAT 2020 Slot 2 · QA Q18 In how many ways can a pair of integers (x , a) be chosen… answer only
• CAT 2020 Slot 1 · QA Q13 Among 100 students, x_1 have birthdays in January, x_2 have…

CAT 2019

• CAT 2019 Slot 1 · QA Q29 The number of solutions of the equation |x|(6x^2 + 1) = 5x^2… answer only
• CAT 2019 Slot 1 · QA Q31 The product of the distinct roots of |x^2 - x - 6| = x + 2… answer only

CAT 2018

• CAT 2018 Slot 2 · QA Q2 Let a_1, a_2, ... , a_52 be positive integers such that a_1… answer only
• CAT 2018 Slot 2 · QA Q13 The smallest integer n for which 4^n ＞ 17^19 holds, is… answer only
• CAT 2018 Slot 2 · QA Q14 The smallest integer n such that n^3 - 11n^2 + 32n - 28 ＞ 0… answer only
• CAT 2018 Slot 2 · QA Q18 If the sum of squares of two numbers is 97, then which one… answer only
• CAT 2018 Slot 2 · QA Q23 If a and b are integers such that 2x^2 − ax + 2 ＞ 0 and x^2… answer only
• CAT 2018 Slot 1 · QA Q10 While multiplying three real numbers, Ashok took one of the… answer only

CAT 2017

• CAT 2017 Slot 2 · QA Q19 If three sides of a rectangular park have a total length 400… answer only
• CAT 2017 Slot 2 · QA Q32 Let f(x) = 2x – 5 and g(x) = 7 – 2x. Then |f(x) + g(x)| =… answer only
• CAT 2017 Slot 1 · QA Q3 An elevator has a weight limit of 630 kg. It is carrying a… answer only
• CAT 2017 Slot 1 · QA Q26 For how many integers n, will the inequality (n – 5) (n –… answer only
• CAT 2017 Slot 1 · QA Q28 If a, b, c, and d are integers such that a + b + c + d = 30… answer only

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