CAT 2022 Question Paper Slot -1 | 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 1 - Quantitative Aptitude
CAT 2022 Slot 1 – QA
1. Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3: 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is
CAT 2022 Slot 1 – QA
2. The largest real value of a for which the equation |x + a | + |x-1| = 2 has an infinite solution for x is
A. 2
B. -1
C. 0
D. 1
The answer is Option D.
x2+x2 + 4xy+ 4y2 =0
x2 + 4xy+ 4y2 + (x-2y-1)2 = 0
(x + y)2 + (x – 2y-1)2 = 0
We know that,
If a2 + b2 = 0, then a = b = 0
x + 2y = 0 and x-2y-1 = 0
Hence, x – 2y = 1
CAT 2022 Slot 1 – QA
3. The average of 3 integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is
A. 5
B. 1
C. 3
D. 4
CAT 2022 Slot 1 – QA
5. In a village, the ratio of number of males to females is 5: 4. The ratio of number of literate males to literate females is 2: 3. The ratio of the number of illiterate males to illiterate females is 4: 3. If 3600 males in the village are literate, then the total number of females in the village is
CAT 2022 Slot 1 – QA
6. Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (-2, 8), respectively. Then, the coordinates of the vertex D are A. (-4, 5) B. (-3, 4) C. (0, 11) D. (4, 5)CAT 2022 Slot 1 – QA
7. Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is A. 60% B. 62.5% C. 37.5% D. 40%CAT 2022 Slot 1 – QA
8. The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is
A. 1 : 2
B. 4 : 1
C. 1 : 4
D. 3 : 1
CAT 2022 Slot 1 – QA
9. A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1: 3, then the ratio of lemon juice and sugar syrup in the new mixture is
A. 1 : 7
B. 1 : 6
C. 1 : 5
D. 1 : 4
CAT 2022 Slot 1 – QA
10. Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at 308.32 per kg and makes an overall profit of 64%. Then, Amal’s cost price for syrup, in rupees per kg, is
CAT 2022 Slot 1 – QA
11. A trapezium ABCD has side AD parallel to BC, ∠ BAD = 90°, BC = 3cm and AD = 8cm. If the perimeter of this trapezium is 36cm, then the area, in Sq cm, is
CAT 2022 Slot 1 – QA
17. Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of 1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is
A. 2520
B. 1176
C. 1680
D. 1440
CAT 2022 Slot 1 – QA
18. For natural numbers x, y, and z, if xy + yz = 19 and yz + xz = 51 then the minimum possible value of xyz is
CAT 2022 Slot 1 – QA
19. The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
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).