Mastering Linear Equations for CAT: Your Essential Practice Sheet 3

Welcome, fellow CAT aspirants!

Linear equations are a cornerstone of the Quantitative Aptitude section of the CAT exam. While they might seem simple, the exam often presents them in complex word problems that test your logical reasoning as much as your mathematical skills. A strong grasp of this topic can significantly boost your score and save you precious time on test day. This blog post provides a comprehensive practice sheet designed to help you tackle these questions with confidence. Inside, you'll find a curated set of problems ranging in difficulty, along with detailed, step-by-step solutions to guide you. Let's get started on building a solid foundation for your CAT preparation!

Q.1 The graphs of the linear equations 4x – 2y = 10 and 4x + ky = 2 intersect at a point (a, 4). The value of k is equal to:

a.4

b.-4

c.3

d.-3

Q.2 What is the value of k for which the following system of equations has no solution: 2x - 8y = 3 and kx + 4y = 10?

a.-2

b.1

c.-1

d.2

Q.3 A test has 175 questions. A candidate gets 4 marks for each correct answer and loses 2 marks for each wrong answer and loses 1 mark for each unanswered question. A student scored 405. On analyzing his performance he concluded that he had not attempted 35 questions. How many questions did he answer wrongly?  

a.30

b.25

c.20

d.Cannot be delermined

Q.4 If the system of equations below has infinite solutions, find the value of k, 4x + ky = 2 + 10y and kx + 24y = 8.

a.-10

b.16

c.-16

d.Cannot be determined

Q.5 Madhav started playing a card game. In the first round he doubled his amount and he gave away p rupees to his friend. In the second round he tripled the amount left with him after the first round and gave away 2p rupees to his friend. In the third round he quadrupled the amount left with him after the second round and gave away p rupees to his friend and was finally left with no money. If he gave away a total of 160 to his friend, then what was the amount that he started with?  

a.Rs. 21

b.Rs. 40

c.Rs. 24

d.Rs. 35

Q.6 Radha takes some flowers in a basket and visit three temples one by one. At each temple, she offers one half of the flowers from the basket. If she is left with 3 flowers at the end, find the number of flowers she had in the beginning.

a.8

b.16

c.20

d.24

Q.7 Amla purchased 3 apples, 5 mangoes and 10 oranges for Rs. 50 from the shopkeeper. Amit purchased  6 apples, 5 oranges and 10 mangoes for Rs. 70 from the shopkeeper.  The cost of 5 oranges, 5 mangoes and 3 apples, in INR, will be ……….

a.70

b.60

c.40

d.30

Q.8 Total cost of 7 pens, 8 pencils and 3 erasers is equal to the total cost of 3 pens, 4 pencils and 8 erasers, which is also equal to the total cost of 11 pens and 4 erasers. If the cost of ‘n’ pens is equal to the cost of 6 erasers, then the value of ‘n’ is ……….

a.7

b.8

c.9

d.12

Q.9 Which of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution such that p + q + r ≠ 0 ?

(i). x + 2y – 3z = p (ii). 2x + 6y – 11z = q   (iii). x – 2y + 7z = r

a.5p – 2q – r = 0

b.5p + 2q + r = 0

c.5p + 2q – r = 0

d.5p – 2q + r = 0

Q.10 When a two-digit number is reversed and added to the original number, the result is divisible by 13. How many such numbers are possible?

Q.11 Find a three digit number which, when reversed, becomes equal to 17 times the square of its cube root?

Q.12 Nargis takes a 3-digit number N and reverses it. She then subtracts the original number from the new number obtained, getting an answer of 594. How many possible values of N could exist?

Q.13 A string of length 40 metres is divided into three parts of different lengths. The first part is three times the second part, and the last part is 23 metres smaller than the first part. Find the length of the largest part.

a.27

b.18

c.9

d.15

Q.14In how many ways can 38 be divided into three positive parts, such that the first part is divisible by 8, the second part is divisible by 7 and the third part is divisible by 3? 

a.1

b.2

c.3

d.4

Q.15 Cost of 2 apples, 3 oranges and 5 bananas is 15 rupees. Cost of 4 apples, 2 oranges and 10 bananas is 26 rupees. Find cost of 1 orange.

a.1

b.3

c.2

d.4

Q.16 A sum of money was distributed equally among a certain number of children. If there were 5 children less, each would have received a rupee more. But if there were 15 children more, each would have received Rs.2 less. Find the sum of money distributed.

a.Rs.120

b.Rs.125

c.Rs.100

d.Rs.360

Q.17 When a number is divided into two unequal parts, the difference of the squares of the two unequal parts is 48 times the difference of the two unequal parts.  What is the number ?

a.96

b.72

c.120

d.48

Q.18 Katrina wants to buy 6 kg of tomatoes and 7 kg of potatoes which together would cost her Rs. 190. In the market as tomatoes were very good, she decided to buy 2 kg more tomatoes and 6 kg less potatoes and spent only Rs. 170. What is  the price of 1 kg of tomatoes? 

a.Rs.10

b.Rs.15

c.Rs.20

d.Rs.25

Q.19 An examination (3/5)th of the students who appeared failed by 10 marks and (1/5)th of the students got 10 marks above the pass mark. Each of the remaining students got 20 marks above the pass mark. Students who gave the exam scored 62 marks on an average. The pass mark is?

a.64

b.66

c.62

d.56

1	2	3	4	5	6	7	8	9	10
B	C	C	B	D	D	C	B	A	6
11	12	13	14	15	16	17	18	19
216	30	A	B	A	D	D	C	C