# Top CAT Quant Linear Equations Questions PDF

by Naveen Neredimalli Mon 15 Apr 2024 05:33 PM 287

Check out the top 20 CAT Quant Linear Equations questions. These linear equations, fundamental in maths, are frequently tested in CAT to evaluate your understanding of algebraic concepts and your ability to solve real-world problems efficiently. You can download these questions in PDF, which provides detailed solutions and questions, offering valuable practice and insight into the types of questions you may encounter on test day. Whether you're a CAT aspirant preparing for the exam or aiming to enhance your mathematical skills, these questions will help you strengthen your problem-solving abilities and improve your performance in the Quant section.

#### Question 1

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 yearÂ less than the average age of all three, then Harry's age, in years, is

#### Question 2

Let k be a constant. The equations $$kx + y = 3$$ and $$4x + ky = 4$$ have a unique solution ifÂ and only if

#### Question 3

In May, John bought the same amount of rice and the same amount of wheat as he hadÂ bought in April, but spent â‚¹ 150 more due to price increase of rice and wheat by 20%Â and 12%, respectively. If John had spent â‚¹ 450 on rice in April, then how much did heÂ spend on wheat in May?

#### Question 4

If x and y are non-negative integers such that $$x + 9 = z$$, $$y + 1 = z$$ and $$x + y < z + 5$$, then the maximum possible value of $$2x + y$$ equals

#### Question 5

Aron bought some pencils and sharpeners. Spending the same amount of money asÂ Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of oneÂ sharpener is â‚¹ 2 more than the cost of a pencil, then the minimum possible number ofÂ pencils bought by Aron and Aditya together is

#### Question 6

Rahul has just made a $$3 \times 3$$ magic square, in which, the sum of the cells along any row, column or diagonal, is the same number N. The entries in the cells are given as expressions in x, y, and Z. Find N?

#### Question 7

A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

#### Question 8

A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is

#### Question 9

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

#### Question 10

Let a and b be natural numbers. If $$a^2 + ab + a = 14$$ and $$b^2 + ab + b = 28$$, then $$(2a + b)$$ equals

#### Question 11

The largest real value of a for which the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for x is

#### Question 12

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

#### Question 13

In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is

#### Question 14

If $$c=\frac{16x}{y}+\frac{49y}{x}$$ for some non-zero real numbers x and y, then c cannot take the value

#### Question 15

A donation box can receive only cheques of â‚¹100, â‚¹250, and â‚¹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of â‚¹15250. Then, the maximum possible number of cheques of â‚¹500 that the donation box may have contained, is

#### Question 16

The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible.

#### Question 17

Let x and y be two positive integers and p be a prime number. If x (x - p) - y (y + p) = 7p, what will be the minimum value of x - y?

#### Question 18

For some real numbers a and b, the system of equations $$x + y = 4$$ and $$(a+5)x+(b^2-15)y=8b$$ has infinitely many solutions for x and y. Then, the maximum possible value of ab is

#### Question 19

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

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