CAT 2024 Question Paper Slot -2 | QA
CAT Quantitative Aptitude (QA) | CAT Previous Year Paper
Unlike previous years, the CAT 2024 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 2024 Quantitative Aptitude Section was difficult paper compared to the previous years.
CAT 2024 Slot 2 - Quantitative Aptitude
CAT 2024 Slot 2 – QA
1. The sum of the infinite series 1/5 (1/5 – 1/7) + (1/5)2 ((1/5)2 – (1/7)2) + (1/5)3 ((1/5)3 – (1/7)3) +………. is equal to
A. 7/408
B. 5/408
C. 7/816
D. 5/816
CAT 2024 Slot 2 – QA
2. A company has 40 employees whose names are listed in a certain order. In the years 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs 60000, and of the first 10 and last 10 employees together was Rs 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in year 2023 was
A. 95000
B. 90000
C. 85000
D. 80000
CAT 2024 Slot 2 – QA
3. Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, the Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
CAT 2024 Slot 2 – QA
4. Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then re-invests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
A. 20640
B. 20480
C. 20808
D. 20860
CAT 2024 Slot 2 – QA
5. 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.
CAT 2024 Slot 2 – QA
6. ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at the point E. If AB= 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of △AEB is A. 10 B. 8 C. 7 D. 9CAT 2024 Slot 2 – QA
7. If m and n are natural numbers such that n greater than 1, and m = 225 x 340, then m – n equalsA. 209942
B. 209937
C. 209947
D. 209932
8. If a, b and c are positive real numbers such that a > 10 ≥ b ≥ c and log8(a+b)/log2 c + log27 (a – b)/log3 c = 2/3, then the greatest integer value of a is
CAT 2024 Slot 2 – QA
9. All the values of x satisfying the inequality 1/x+5 ≤ 1/2x-3 are
A. -5 < x < 3/2 or 3/2 < x ≤ 8
B. -5 < x < 3/2 or x > 3/2
C. x < -5 or 3/2 < x ≤ 8
D. x < -5 or x > 3/2
CAT 2024 Slot 2 – QA
10. If x and y satisfy the equation ∣x∣ + x + y = 15 and x + ∣y∣- y = 20, then (x-y) equals
A. 15
B. 20
C. 5
D. 10
CAT 2024 Slot 2 – QA
12. P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One can travel from P to S either via Q, or via R, or Via Q followed by R, Respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R
A. 5 : 4
B. 3 : 2
C. 4 : 3
D. 2 : 1
CAT 2024 Slot 2 – QA
14. The roots α, β of the equation 3x2+ λx-1=0, satisfy 1/α2 +1/β2 = 15. The value of (α3+β3)2 is
A. 16
B. 4
C. 1
D. 9
CAT 2024 Slot 2 – QA
16. A vessel contains a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to his new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was
A. 5 : 4
A. 4 : 5
A. 3 : 5
A. 5 : 3
CAT 2024 Slot 2 – QA
17. The coordinates of the three vertices of a triangle are: (1, 2), (7,2) and (1,10). Then the radius of the incircle of a triangle is
CAT 2024 Slot 2 – QA
18. A bus starts at 9 am and follows a fixed route every day. One day, it travelled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than it scheduled arrival time. Next day, it travelled two thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is
A. 9:00 pm
B. 7:30 pm
C. 10:30 pm
D. 7:00 pm
CAT 2024 Slot 2 – QA
19. When 3333 is divided by 11, the remainder is
A. 6
B. 1
C. 10
D. 5
CAT 2024 Slot 2 – QA
20. A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x) f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is
A. 8191
B. 2047
C. 1023
D. 4095
CAT 2024 Slot 2 – QA
21. Three circles of radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is
A. 4+√3 : 1
B. 7+4√3 : 1
C. 2+√3 : 1
D. 4+2√3 : 1
The answer option is B.
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 2024 Slot 2 – QA
22. Bina incurs 19% loss when she sells a product at Rs.4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then the profit, in rupees, made by Shyam is