CAT Inequalities & Modulus previous year questions

19 Inequalities & Modulus questions from CAT 2021–2025 (Quant), each with its answer and a step-by-step solution.

• Q17The number of distinct pairs of integers ( x,y ) satisfying the inequalities x>y≥ 3 and x+y<14 isCAT 2025 Slot 1 · Quant · Inequalities & Modulus
• Q14The set of all real values of x for which (x²- | x+9 |+x )>0 , isCAT 2025 Slot 2 · Quant · Inequalities & Modulus
• Q2If x and y satisfy the equations | x |+x+y=15 and x+ | y |-y=20 , then ( x-y ) equalsCAT 2024 Slot 2 · Quant · Inequalities & Modulus
• Q20All the values of x satisfying the inequality (1)/(x+5)≤ (1)/(2x-3) areCAT 2024 Slot 2 · Quant · Inequalities & Modulus
• Q1The number of distinct integer solutions ( x,y ) of the equation | x+y |+ | x-y |=2 , isCAT 2024 Slot 3 · Quant · Inequalities & Modulus
• Q18The number of distinct real values of x , satisfying the equation max x,2\-min x,2\= | x+2 |- | x-2 | , isCAT 2024 Slot 3 · Quant · Inequalities & Modulus
• Q5The number of integer solutions of equation 2 | x | (x²+1 )=5x² isCAT 2023 Slot 1 · Quant · Inequalities & Modulus
• Q4Any non-zero real numbers x , y such that y≠ 3 and (x)/(y)<(x+3)/(y-3) , will satisfy the conditionCAT 2023 Slot 2 · Quant · Inequalities & Modulus
• Q7Let n be any natural number such that 5^(n-1)<3^(n+1) . Then, the least integer value of m that satisfies…CAT 2023 Slot 3 · Quant · Inequalities & Modulus
• Q10The largest real value of a for which the equation | x+a |+ | x-1 |=2 has an infinite number of solutions for x isCAT 2022 Slot 1 · Quant · Inequalities & Modulus
• Q22Let 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…CAT 2022 Slot 1 · Quant · Inequalities & Modulus
• Q4If a and b are non-negative real numbers such that a+2b=6 , then the average of the maximum and minimum possible…CAT 2022 Slot 2 · Quant · Inequalities & Modulus
• Q2The minimum possible value of (x²-6x+10)/(3-x) , for x<3 , isCAT 2022 Slot 3 · Quant · Inequalities & Modulus
• Q15If c=(16x)/(y)+(49y)/(x) for some non-zero real numbers x and y , then c cannot take the valueCAT 2022 Slot 3 · Quant · Inequalities & Modulus
• Q2f ( x )=(x²+2x-15)/(x²-7x-18) is negative if and only ifCAT 2021 Slot 1 · Quant · Inequalities & Modulus
• Q20The number of integers n that satisfy the inequalities | n-60 |< | n-100 |< | n-20 | isCAT 2021 Slot 1 · Quant · Inequalities & Modulus
• Q16For all real numbers x the condition | 3x-20 |+ | 3x-40 |=20 necessarily holds ifCAT 2021 Slot 2 · Quant · Inequalities & Modulus
• Q13If 3x+2 | y |+y=7 and x+ | x |+3y=1 , then x+2y isCAT 2021 Slot 3 · Quant · Inequalities & Modulus
• Q18The number of distinct pairs of integers ( m,n ) satisfying | 1+mn |< | m+n |<5 isCAT 2021 Slot 3 · Quant · Inequalities & Modulus