Answer:
Since we have cancelled y in our first step, x = 0 is also a solution
So, Number of possible solutions = 4 + 1 = 5
Hence, the answer is 5
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CAT 2019 Quant Question: Work, time
Three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job. If two machines can finish the job in 13 days, then how many men can finish the job in 13 days? [TITA]
Answer:
Let Machines be referred as R and men be referred as M
It is given that, three men and eight machines can finish a job in half the time taken by three machines and eight men to finish the same job.
From the given data,
3M + 8R = 2 x (3R + 8M)
2R = 13M
R = 
M
Therefore, if two machines can finish a job in 13 days, 2 Robos can finish the job in 13 days.
Hence, the answer is 13
CAT 2019 Quant Question: Quadratic equations
The product of the distinct roots of 
A. -4
B. -16
C. -8
D. -24
Answer:
Removing the modulus,
(x-4) (x+2) = 0
x = 4 or -2
For the solution to be valid, the value of the equation must be positive
When x = 4,
16 - 4 -6 = x + 2
6 - 2 = x
4 = x. Therefore, x = 4 works
For x = -2,
4 + 2 - 6 = x + 2
0 - 2 = x
-2 = x. Therefore, x = - 2 works
x = +2 or -2
-4 + 2 + 6 = x + 2
Therefore, Product of distinct roots = 2 x -2 x 4 = -16
Hence, the answer is -16
Choice B is the correct answer.
CAT 2019 Quant Question: Speed, time and distance
The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While traveling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B traveled this distance in 45 minutes, then its speed, in km per hour, was
A. 18π
B. 16π
C. 12π
D. 14π
Answer:
Circumference of A and B are in the ratio 3: 4
So, Ratio of Distance travelled in one revolution by A and B = 3: 4
Since they travel the same distance,
Ratio of number of revolutions of A and B = 4: 3 ----- (1)
We know that each wheel of A requires 5000 more revolutions than B
So, the Ratio of number of revolutions of A and B = (n + 5000): n ------(2)
So, comparing (1) and (2)
Number of revolutions of A and B are 20000 and 15000 respectively
So, we know Bike B does 15000 revolutions in 45 minutes
Distance travelled = 2 x π x r x Number of revolutions
Speed of Bike B = 
mph
Speed of Bike B = 2 x 
x 
x 5 x 4 Kmph
Speed of Bike B = 16 Kmph
Hence, the answer is 16π
Choice B is the correct answer.
CAT 2019 Quant Question: Functions
Consider a function f(x+y) = f(x) f(y) where x , y are positive integers, and f(1) = 2. If f (a+1) + f (a+2) + … + f(a+n) = 16
Answer:
We know that f(x+y) = f(x) f(y)
Let x = a and y = 1,
f (a + 1) = f(a). f (1)
f(a+1) = f(a). 2
f(a+2) = f(a+1) f(1)
which is an infinite GP series
On solving,
2 f(a) = 16
f(a) = 8
We know that, f (1) = 2 , f(2) = 4 and f(3) = 8
So, a = 3
Hence, the answer is ‘3’
CAT 2019 Quant Question: Averages
Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is
A. 51
B. 53
C. 49
D. 48
Answer:
It is given that, a1, a2, a3,… Ramesh, Gautham, …, a22 writes an examination
Given that, Average score of the 21 students other than Gautham = 62
So, Total Score - Gautham’s score = 62 x 21
Ramesh scored 82.5
It is given that, when Ramesh leaves, the average score drops down by 1 mark.
Which means that Ramesh scored more than the Overall class average.
Since his departure has resulted in the decrease of the overall class average by 1, his score is 21 more than the average.
Overall Class average = 82.5 - 21 = 61.5 marks
Total Score - Gautham’s score = 62 x 21
61.5 x 22 - 62 x 21 = Gautham’s score
1353 - 1302 = Gautham’s score
Gautham’s score = 51 marks
Hence, the answer is 51
Choice A is the correct answer.
CAT 2019 Quant Question: Logarithms
The real root of the equation 
is
Answer:
The idea is to convert the above equation to a quadratic one.
Solving the above quadratic equation,
(y + 7) (y - 3) = 0
So, y = -7 or +3
Hence, the answer is 
Choice A is the correct answer.
CAT 2019 Quant Question: Averages
The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers?
A. 4
B. 5
C. 4.5
D. 3.5
Answer:
We are told that exactly 20 of the 30 integers do not exceed 5…
That means exactly 10 of the 30 integers do exceed 5.
In order to keep the average of the 20 integers as high as possible, we need to keep the average of the 10 integers above 5 as low as possible. Since we are dealing with integers, the least value that the 10 integers above 5 can take is 6.
So, the sum of the 10 integers = 10 * 6 = 60
So the sum of the remaining 20 integers = Total sum - 60 = 5 * 50 - 60 = 90
Hence the average of the remaining 20 is 90/20 = 4.5
Hence, the answer is 4.5
Choice C is the correct answer.
CAT 2019 Quant Question: Number theory
Let a, b, x, y be real numbers such that 
and ax + by = 65. If k = ay - bx, then
Answer:
Expanding the equation,
Hence, the answer is k = 0
Choice A is the correct answer.
CAT 2019 Quant Question: Geometry
In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is
A. 80
B. 68
C. 72
D. 78
Answer:
We know that intersection of two medians is called a Centroid
We know, a Centroid divides the median in the ratio 2:1
AD = 12cms,
AG = 8cms, GD = 4cms
And similarly, BG = 6cms, GE = 3cms
Now, area (
ABE) can be easily found out
area (ABE) = 
x BE X AG
Hence, the answer is 72
Choice C is the correct answer.
CAT 2019 Quant Question: Sequence & series
A. -1
B. 1
C. 0
D. 10