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Linear Equations

Q.No: 1
Test Name : CAT 2017 Actual Paper Slot 1

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 ≤ 40, y ≤ 12,and z ≤ 12 is

A
101
B
99
C
87
D
103
Answer key/Solution
Solution:
Q.No: 2
Test Name : CAT 2018 Actual Paper Slot 2

In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is

Answer key/Solution
Solution:
Q.No: 3
Test Name : CAT 2019 Actual Paper Slot 1


A
1
B
2/3
C
1/3
D
3
Answer key/Solution
Solution:
Q.No: 4
Test Name : CAT 2019 Actual Paper Slot 2

Let a, b, x, y be real numbers such that a2 + b2 = 25, x2 + y2 = 169, and ax + by = 65. If k = ay – bx, then

A
B
C
k = 0
D
Answer key/Solution
Solution:
Q.No: 5
Test Name : CAT Actual Paper 2020 Slot-1

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

Answer key/Solution
Solution:
Q.No: 6
Test Name : CAT Actual Paper 2020 Slot-2


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Solution:
Q.No: 7
Test Name : CAT Actual Paper 2020 Slot-2


A
30
B
27
C
33
D
36
Answer key/Solution
Solution:
Q.No: 8
Test Name : CAT Actual Paper 2020 Slot-3

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

A
|k| ≠ 2
B
k = 2
C
k ≠ 2
D
|k| = 2
Answer key/Solution
Solution:
Q.No: 9
Test Name : CAT Actual Paper 2022 Slot-1


A
0
B
2
C
–1
D
1
Answer key/Solution
Solution:
Q.No: 10
Test Name : CAT Actual Paper 2022 Slot-2

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

Answer key/Solution
Solution:
Q.No: 11
Test Name : CAT Actual Paper 2023 Slot 3

For some real numbers a and b, the system of equations x + y = 4 and (a + 5) x + (b2 – 15)y = 8b has infinitely many solutions for x and y. Then, the maximum possible value of ab is

A
15
B
33
C
55
D
25
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