CAT Linear Equations Questions & Solutions

A sample of real CAT Linear Equations past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 65 Linear Equations questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is

   Answer: 15

2. Q2.CAT 2024

   For some constant real numbers p, k and a, consider the following system of linear equations in x and y:
   px - 4y = 2
   3x + ky= a
   A necessary condition for the system to have no solution for (x, y ), is

   • $ap + 6 = 0$

   • $2a + k \neq 0$

   • $ap - 6 = 0$

   • $kp + 12 \neq 0$

3. Q3.CAT 2022

   For natural numbers x, y, and z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is

   Answer: 34

4. Q4.CAT 2021

   If $3x+2\mid y\mid+y=7$ and $x+\mid x \mid+3y=1$ then $x+2y$ is:

   • $-\frac{4}{3}$

   • $\frac{8}{3}$

   • $0$

   • $1$

5. Q5.CAT 2020

   In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹ 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent ₹ 450 on rice in April, then how much did he spend on wheat in May?

   • Rs.560

   • Rs.570

   • Rs.590

   • Rs.580

6. Q6.CAT 2017

   The number of solutions $(x, y, z)$ to the equation $x - y - z = 25$, where x, y, and z are positive integers such that $x\leq40,y\leq12$, and $z\leq12$ is

   • 101

   • 99

   • 87

   • 105

7. Q7.CAT 2006

   When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

   • 5

   • 6

   • 7

   • 8

   • 10

8. Q8.CAT 2004

   In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts.

   Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

   • 130 minutes

   • 135 minutes

   • 170 minutes

   • 180 minutes

9. Q9.CAT 2003

   A test has 50 questions. A student scores 1 mark for a correct answer, $\frac{-1}{3}$ for a wrong answer, and $\frac{-1}{6}$ for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

   • 6

   • 12

   • 3

   • 9

10. Q10.CAT 2002

    A car rental agency has the following terms. If a car is rented for 5 hr or less, then, the charge is Rs. 60 per hour or Rs. 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hr, the charge is Rs. 50 per hour or Rs. 7.50 per kilometre whichever is more. Akil rented a car from this agency, drove it for 30 km and ended up playing Rs. 300. For how many hours did he rent the car?

    • 4 hr

    • 5 hr

    • 6 hr

    • None of these

11. Q11.CAT 2001

    A change-making machine contains one-rupee, two-rupee and five-rupee coins. The total number of coins is 300. The amount is Rs. 960. If the numbers of one-rupee coins and two-rupee coins are interchanged, the value comes down by Rs. 40. The total number of five-rupee coins is

    • 100

    • 140

    • 60

    • 150

12. Q12.CAT 1996

    The points of intersection of three lines $2x+3y-5=0, 5x-7y+2=0$ and $9x-5y-4=0$

    • form a triangle

    • are on lines perpendicular to each other

    • are on lines parallel to each other

    • are coincident

CAT Linear Equations previous year questions with solutions — AthenaPrep