CAT Equations questions 52 since 2017

Across the 24 CAT papers from 2017 to 2025, Equations was asked 52 times, in 23 of the 24 papers. CAT asks about 2.2 Equations questions per paper on average; in 2022–2025 it was 2.1 per paper, against 2.3 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 Equations questions come in CAT each year?

Equations ideas CAT has repeated

• Integer solutions of a linear equation with count and range constraints 5 questions, 2020–2025
• Rearrange into a sum of squares equal to zero, so each square is zero 4 questions, 2018–2024
• Symmetric functions of roots via sum and product (Vieta) 5 questions, 2017–2024
• Discriminant conditions for real, distinct or no real roots 6 questions, 2017–2022
• Unique, none or infinitely many solutions of a 2×2 linear system 3 questions, 2020–2024

All Equations questions, newest first

CAT 2025

• CAT 2025 Slot 3 · QA Q11 If f ( x ) = ( x ^ 2 + 3 x ) ( x ^ 2 + 3 x + 2 ) , then the…
• CAT 2025 Slot 2 · QA Q16 The equations 3 x ^ 2 - 5 x + p = 0 and 2 x ^ 2 - 2 x + q =…
• CAT 2025 Slot 1 · QA Q1 If a-6 b+6 c=4 and 6 a+3 b-3 c=50 , where a, b and c are…
• CAT 2025 Slot 1 · QA Q7 The number of non-negative integer values of k for which the…
• CAT 2025 Slot 1 · QA Q20 Stocks A, B and C are priced at rupees 120, 90 and 150 per…
• CAT 2025 Slot 1 · QA Q21 Kamala divided her investment of Rs 100000 between stocks…

CAT 2024

• CAT 2024 Slot 3 · QA Q2 For some constant real numbers p, k and a , consider the…
• CAT 2024 Slot 2 · QA Q16 The roots α, β of the equation 3 x^2+ x-1=0 , satisfy…
• CAT 2024 Slot 2 · QA Q21 If x and y are real numbers such that 4 x^2+4 y^2-4 x y-6…
• CAT 2024 Slot 1 · QA Q8 Let x, y , and z be real numbers satisfying aligned &…
• CAT 2024 Slot 1 · QA Q13 A shop wants to sell a certain quantity (in kg) of grains…
• CAT 2024 Slot 1 · QA Q20 If the equations x^2+m x+9=0, x^2+n x+17=0 and x^2+(m+n)…

CAT 2023

• CAT 2023 Slot 3 · QA Q3 For some real numbers a and b , the system of equations…
• CAT 2023 Slot 3 · QA Q5 A quadratic equation x^2+b x+c=0 has two real roots. If the…
• CAT 2023 Slot 2 · QA Q21 If p^2+q^2-29=2 p q-20=52-2 p q , then the difference…
• CAT 2023 Slot 1 · QA Q2 If x and y are real numbers such that x^2+(x-2 y-1)^2=-4…
• CAT 2023 Slot 1 · QA Q6 Let α and β be the two distinct roots of the equation 2…
• CAT 2023 Slot 1 · QA Q7 The equation x^3+(2 r+1) x^2+(4 r-1) x+2=0 has -2 as one of…

CAT 2022

• CAT 2022 Slot 3 · QA Q1 Suppose k is any integer such that the equation 2 x^2+k…
• CAT 2022 Slot 3 · QA Q14 If (3+2 √(2)) is a root of the equation a x^2+b x+c=0 , and…
• CAT 2022 Slot 3 · QA Q20 A donation box can receive only cheques of ₹100, ₹250, and…
• CAT 2022 Slot 2 · QA Q9 Let r and c be real numbers. If r and -r are roots of 5…
• CAT 2022 Slot 2 · QA Q15 In an examination, there were 75 questions. 3 marks were…
• CAT 2022 Slot 1 · QA Q5 Let a, b, c be non-zero real numbers such that b^2 4 a c…
• CAT 2022 Slot 1 · QA Q15 Let a and b be natural numbers. If a^2+a b+a=14 and b^2+a…

CAT 2021

• CAT 2021 Slot 3 · QA Q8 One part of a hostel's monthly expenses is fixed, and the…
• CAT 2021 Slot 3 · QA Q15 A shop owner bought a total of 64 shirts from a wholesale…
• CAT 2021 Slot 3 · QA Q17 A tea shop offers tea in cups of three different sizes. The…
• CAT 2021 Slot 2 · QA Q3 Consider the pair of equations: x^2 - xy - x = 22 and y^2… answer only
• CAT 2021 Slot 2 · QA Q19 Suppose one of the roots of the equation a x^2 - b x + c = 0… answer only
• CAT 2021 Slot 1 · QA Q5 A basket of 2 apples, 4 oranges and 6 mangoes costs the same… answer only
• CAT 2021 Slot 1 · QA Q16 Suppose hospital A admitted 21 less Covid infected patients… answer only

CAT 2020

• CAT 2020 Slot 3 · QA Q15 Let k be a constant. The equations kx + y = 3 and 4x + ky =… answer only
• CAT 2020 Slot 3 · QA Q23 Let m and n be positive integers, If x^2+ mx + 2n = 0 and… answer only
• CAT 2020 Slot 2 · QA Q17 The number of integers that satisfy the equality (x^2 - 5x +… answer only
• CAT 2020 Slot 2 · QA Q24 Aron bought some pencils and sharpeners. Spending the same… answer only
• CAT 2020 Slot 1 · QA Q8 Let A, B and C be three positive integers such that the sum…
• CAT 2020 Slot 1 · QA Q11 The number of distinct real roots of the equation (x + 1/x…
• CAT 2020 Slot 1 · QA Q15 How many distinct positive integer-valued solutions exist to…
• CAT 2020 Slot 1 · QA Q25 A gentleman decided to treat a few children in the following…

CAT 2019

• CAT 2019 Slot 2 · QA Q3 Let a, b, x, y be real numbers such that a^2 + b^2 = 25… answer only
• CAT 2019 Slot 2 · QA Q13 Let A be a real number. Then the roots of the equation x^2… answer only
• CAT 2019 Slot 2 · QA Q25 The quadratic equation x^2 + bx + c = 0 has two roots 4a and… answer only
• CAT 2019 Slot 2 · QA Q31 If 5^x - 3^y = 13438 and 5^x-1 + 3^y+1 = 9686 , then x+y… answer only
• CAT 2019 Slot 2 · QA Q34 John gets Rs 57 per hour of regular work and Rs 114 per hour… answer only
• CAT 2019 Slot 1 · QA Q2 If (5.55)^x = (0.555)^y = 1000, then the value of 1/x - 1/y… answer only
• CAT 2019 Slot 1 · QA Q12 The product of two positive numbers is 616. If the ratio of… answer only

CAT 2018

• CAT 2018 Slot 1 · QA Q16 If u^2 + (u−2v−1)^2 = −4v(u + v), then what is the value of… answer only

CAT 2017

• CAT 2017 Slot 2 · QA Q24 The minimum possible value of the sum of the squares of the… answer only
• CAT 2017 Slot 1 · QA Q13 If a and b are integers of opposite signs such that (a +… answer only
• CAT 2017 Slot 1 · QA Q22 If x + 1 = x^2 and x > 0, then 2x^4 is answer only
• CAT 2017 Slot 1 · QA Q27 If f_1(x) = x^2 + 11x + n and f_2(x) = x, then the largest… answer only

More QA: all Quantitative Ability topics · CAT topic weightage, every section