top of page
CAT 2024 Slot 3 - QUANTS
Q.1
The number of distinct integer solutions (x,y) of the equations | x + y | + | x - y | = 2, is
8
Answer
CAT 2024 Slot 3 - QUANTS
Q.2
For some constant real numbers p, k and a, consider the following system of linear equations x and y:
px - 4y = 2
3x + ky = a
A necessary condition for the system to have no solutions (x,y), is :
-
2a + k
-
ap - 6 = 0
-
ap + 6 = 0
-
kp + 12
Option 1
Answer
CAT 2024 Slot 3 - QUANTS
Q.3
-
7
-
10
-
8
-
9
Option 3
Answer
CAT 2024 Slot 3 - QUANTS
Q.4
A circular plot of land is divided into two region by a chord of length 10√3 meters such that the chord subtends and angle of 120 at the center. Then, the area , in square meters , of the smaller region is
-
25(
Option 1
Answer
CAT 2024 Slot 3 - QUANTS
Q.5
In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
-
72 and 80, respectively
-
75 and 90, respectively
-
72 and 88, respectively
-
75 and 96, respectively
Option 1
Answer
CAT 2024 Slot 3 - QUANTS
Q.6
-
8
-
9
-
4
-
5
Option 2
Answer
CAT 2024 Slot 3 - QUANTS
Q.7
The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is
90
Answer
CAT 2024 Slot 3 - QUANTS
Q.8
In a group of 250 students, the percentage of girls was at least 44% and at most 60%. The rest of the students were boys. Each student opted for either swimming or running or both. If 50% of the boys and 80% of the girls opted for swimming while 70% of the boys and 60% of the girls opted for running, then the minimum and maximum possible number of students who opted for both swimming and running, are
-
27.5
-
30
-
25
-
20
Option 3
Answer
CAT 2024 Slot 3 - QUANTS
Q.9
Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayna in the sam job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Anya on the second day, Mohit and Anya on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
-
3/20
-
3/10
-
1/20
-
1/5
Option 2
Answer
CAT 2024 Slot 3 - QUANTS
Q.10
A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was
30
Answer
CAT 2024 Slot 3 - QUANTS
Q.11
Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is
9
Answer
CAT 2024 Slot 3 - QUANTS
Q.12
Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
-
25
-
10
-
15
-
20
Option 2
Answer
CAT 2024 Slot 3 - QUANTS
Q.13
The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is
70
Answer
CAT 2024 Slot 3 - QUANTS
Q.14
The number of all positive integers up to 500 with non-repeating digits is
378
Answer
CAT 2024 Slot 3 - QUANTS
Q.15
A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is
-
780
-
720
-
640
-
800
Option 2
Answer
CAT 2024 Slot 3 - QUANTS
Q.16
2
Answer
CAT 2024 Slot 3 - QUANTS
Q.17
-
-1023132
-
-1022121
-
-1024144
-
-1026169
Option 3
Answer
CAT 2024 Slot 3 - QUANTS
Q.18
The number of distinct real values of x, satisfying the equation
max{x,2} - min{x,2} = | x + 2 | - | x - 2 |, is
2
Answer
CAT 2024 Slot 3 - QUANTS
Q.19
Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is
-
1 : 1
-
7 : 9
-
4 : 3
-
3 : 7
Option 2
Answer
CAT 2024 Slot 3 - QUANTS
Q.20
-
2
-
-3
-
-2
-
3
Option 2
Answer
CAT 2024 Slot 3 - QUANTS
Q.21
A Regular octagon ABCDEFGH has sides of lenght 6 cm each. Then the area, in sq.cm, of the square ACEG is
-
36(1 + √2)
-
72(1 + √2)
-
36(2 + √2)
-
72(2 + √2)
Option 3
Answer
CAT 2024 Slot 3 - QUANTS
Q.22
-
2log 2
-
3log 2
-
4log 2
-
log 2
Option 1
Answer
bottom of page