CAT 2022 Question Paper Slot -2 | QA
CAT Quantitative Aptitude (QA) | CAT Previous Year Paper
Unlike previous years, the CAT 2022 Quant section was not dominated by Arithmetic, though it remained the most tested topic, followed by Algebra. Within Arithmetic, questions were primarily focused on Speed-Time-Distance, Mixture, and Alligations. The section included eight TITA (Type-in-the-answer) questions. Overall, the CAT 2022 Quantitative Aptitude Section was difficult paper compared to the previous years.
CAT 2022 Slot 2 - Quantitative Aptitude
CAT 2022 Slot 2 – QA
4. Manu earns Rs 4000 per month and wants to save an average of Rs 550 per month in a year. In the first nine months, his monthly expenses was Rs 3500, and he foresees that, tenth month onward, his monthly expense will increase to Rs 3700. In Order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be
A. 4400
B. 4200
C. 4300
D. 4350
CAT 2022 Slot 2 – QA
5. Mr. Pinto invests one fifth of his capital at 6%, one third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is
CAT 2022 Slot 2 – QA
6. Let f(x) be a quadratic polynomial in x such that f(x) ≥ 0 for all real numbers x. if f(2)=0 and f(4) =6 then f(-2) is equal to A. 12 B. 24 C. 6 D. 36CAT 2022 Slot 2 – QA
7. Let r and c be real numbers. If r and – r are roots 5x3 + 3x2 – 10x + 9 = 0, then c equals to
A. – 9/2
B. 9/2
C. – 4
D. 4
CAT 2022 Slot 2 – QA
8. Regular polygons A and B have number of sides in the ratio 1:2 and interior angles in the ratio 3:4. Then the numbers of sides of B equals
f(x) + f(x-1) – 1 = 0 and g(x) = x2 If f(x2 – x) = 5 then the value of the sum f(g(5) + g(f(5)) is
CAT 2022 Slot 2 – QA
10. Two ships meet mid-ocean and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is
A. 20
B. 12
C. 18
D. 24
CAT 2022 Slot 2 – QA
11. In an election there were four candidates and 80% of the registered voters casted their votes. One of the candidates received 30% of the casted votes while the other three candidates received the remaining casted votes in the proportion 1:2:3. If the winner of the election received 2512 votes more than the candidate with the second highest votes, then the number of registered voters was
A. 50240
B. 40192
C. 60288
D. 62800
CAT 2022 Slot 2 – QA
12. In an examination, there were 75 questions. 3 marks are awarded for each correct answer, 1 marks 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
CAT 2022 Slot 2 – QA
13. The number of integers greater than 2000 that can be formed with the digits 0, 1, 2, 3, 4, 5, using each digit at most once, is
A. 1440
B. 1200
C. 1480
D. 1420
CAT 2022 Slot 2 – QA
18. Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
CAT 2022 Slot 2 – QA
19. There are two containers of the same volume, first container half filled with sugar syrup and the second container half filled with milk. Half the content of the fist container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is
A. 4 : 5
B. 6 : 5
C. 5 : 4
D. 5 : 6
CAT 2022 Slot 2 – QA
20. The length of each side of the equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. The length of AD, in cm, is
A. √8
B. √6
C. √7
D. √5
CAT 2022 Slot 2 – QA
21. Five students, including Amit, appear for an examination in which possible marks are integer between 0 and 50, both inclusive. The average marks for all the students are 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, Then the difference between the highest and lowest possible marks of Amit is
A. 22
B. 21
C. 24
D. 20
The answer Option is D.
If 1/(√y+√z) is the arithmetic mean of 1/√x +1/√z & 1/(√x+√y)
Then = 2/(√y+√x) = 1/(√x+√z) + 1/(√x+√y)
Rationalizing,
(2 √y-√z)/(y-z) = (√x-√y)/(x-z) + (√x-√y)/(x-y) ———- (1)
So, starting with options
If y, x & z are in AP,
⇒x-y=z-x=d & z-y=2d
⇒from (1),
RHS,
= (√x-√z)/(-d) + (√x-√y)/d=(√x-√y+√z-√x)/d
= (√z-√y)/d
LHS =(2(√x-√(y)))/(-2d)=(√z-√y)/d= RHS.
Hence, LHS = RHS
So, ⇒(b)is true.
Using the examples of the circle L
x^2+y^2+4x-6y-3=0, we can find the point of center of the circle and the radius (x^2+4x+4)+(y^2-6y+9)-4-9-3=0
(〖x+2)]^2+(〖y-3)〗^2=16
So, radius (r) = 4, Centre = (-2, 3)
DIAGRAM
OP being the radius of bigger circle (L) with center at O.
We can find the measurement of OP using trigonometry.
Sin 30^0 =OQ/OP=1/2=4/OP
⇒OP=8=radius of bigger circle (L)
Therefore, Example of the bigger circle (L) with centre (-2, 3)
and radius 8 is 〖(x+2)〗^2+〖(y-3)〗^2=8^2
Substituting x=6,in the above circle equation we can find.
〖(6+2)〗^2+〖(y-3)〗^2=64
8^2+〖(y-3)〗^2=64
(y-3)^2=0
⇒ y = 3.
So, the solution of this question is (a) (6, 3).
CAT 2022 Slot 2 – QA
22. If a and b are non- negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a+b)
A. 3
B. 4
C. 3.5
D. 4.5