CAT 2021 Question Paper Slot -3 | QA
CAT Quantitative Aptitude (QA) | CAT Previous Year Paper
The CAT 2021 Question Paper Slot 3 QA (Quantitative Ability) section was primarily focused on Arithmetic, followed by Algebra. Within Arithmetic, topics like Speed-Time-Distance, Mixture, and Alligations were heavily represented. However, this year brought a surprise with fewer questions from Geometry compared to previous years. There were 8 TITA questions in total. Overall, the difficulty level of this section was moderate.
CAT 2021 Question Paper - Slot - 3 (Quantitative Aptitude)
CAT 2021 Slot 3 – QA
1. If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then the weight of the initial alloy, in Kg, is
A. 3
B. 3.5
C. 4
D. 4.5
CAT 2021 Slot 3 – QA
2. The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is
CAT 2021 Slot 3 – QA
3. A tea shop offers tea in cups of three different sies. The product of the prices, In INR, of three different sizes is equals to 800. The prices of the smallest size and the medium size are in the ratio 2:5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR. is
CAT 2021 Slot 3 – QA
4. In a tournament, a team has played 40 matches so far and won 30% of them. If they win 60% of the remaining matches, There overall win percentage will be 50%. Suppose they win 90% of the remaining matches, then the total number of matches won by the team in the tournament will be
A. 80
B. 84
C. 86
D. 78
CAT 2021 Slot 3 – QA
5. Anil can paint a house in 12 days while Barun can paint it in 16 days. Anil, Barun, and Chandu undertake to paint the house for INR 24000 and the three of them together complete the painting in 6 days. If Chandu is paid in proportion to the work done by him, then amount in INR received by him is
CAT 2021 Slot 3 – QA
6. If f(x) = x2 – 7x and g(x) = x + 3, then the minimum value of f(g(x)) – 3x is
A. – 20
B. – 12
C. – 16
D. – 15
CAT 2021 Question Paper - Slot - 3 (Quantitative Aptitude)
CAT 2021 Slot 3 – QA
7. In a triangle ABC, ∠BCA=50°. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then ∠FDE, in degrees, is equals to A. 72 B. 80 C. 100 D. 96
CAT 2021 Slot 3 – QA
8. Bank A offers 6% interest rate per annum compounded half yearly. Bank B & bank C offer simple interest, but the annual interest rate offered by bank C is twice that of bank B. Raju invests a certain amount in bank B for a certain period and Rupa invests INR 10,000 in bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in bank A for 1 year. The interest accrued, in INR, to Rupa is
A. 2436
B. 1436
C. 3436
D. 2346
CAT 2021 Slot 3 – QA
10. One part of hostel’s monthly expenses is fixed, and the other part is proportional to the number of it’s boarders. The hostel collects INR 1600 per month from each boarder. When the number of boarders is 50, the profit of the hostel is INR 200 per boarder, and when the number of boarders is 75, the profit of the hostel is INR 250 per boarder. When the number of boarders is 80, the total profit of hostel, in INR will be
A. 20200
B. 20500
C. 20000
D. 20800
CAT 2021 Slot 3 – QA
11. One day, Rahul started a work at 9 a.m. and Gautam joined him 2 hrs later. They then worked together and completed the work at 5 p.m. the same day. If both had started at 9 a.m. and worked together, the work would have been completed 30 min earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is
A. 11.5
B. 12
C. 10
D. 12.5
CAT 2021 Slot 3 – QA
12. Meera and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 min, Amal completes exactly 3 more rounds then Meera. If they walk in opposite directions, then they meet for the first time exactly after 3 min. The number of rounds Meera walks in 1 hr is
CAT 2021 Question Paper - Slot - 3 (Quantitative Aptitude)
CAT 2021 Slot 3 – QA
13.
CAT 2021 Slot 3 – QA
16. A 4 – digit number is formed by using only the digit 1, 2 and 3 such that both 2 & 3 appear at least once. The number of all such 4 – digit numbers is
CAT 2021 Slot 3 – QA
17. A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is
A. 175
B. 200
C. 150
D. 225
CAT 2021 Question Paper - Slot - 3 (Quantitative Aptitude)
CAT 2021 Slot 3 – QA
19. The total of Male and Female populations in a city increased by 25% from 1970 to 1980. During the same period, the male population increased by 40% while the female population increased by 20%. From 1980 to 1990, the female population increased by 25%. In 1990, if the female population is twice the male population, then the percentage increase in the total of male and female population in the city from 1970 to 1990 is
A. 68.25
B. 69.25
C. 68.50
D. 68.75
CAT 2021 Slot 3 – QA
20. A park is shaped like a rhombus and has area 96 Sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along it’s two diagonals, at the rate of INR 125 per m, is
CAT 2021 Slot 3 – QA
21. Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm & 20 cm, respectively. If the angle ADC is equals to 30°, then the area of the parallelogram in sq cm is
A. 25(√5 + √15) / 2
B. 25(√5 + √15)
C. 25(√3 + √15)
D. 25(√3 + √15) / 2
The answer Option is C.
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).