All 22 Quant questions from the CAT 2022 · Slot 1 paper, with the correct answer for each.
In a village the ratio of males to females is 5 : 4, of literate males to literate females is 2 : 3, and of illiterate males to illiterate females is 4 : 3. If 3600 males are literate, then the total number of females in the village is (numerical value)
Correct answer: 43200
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
Correct answer: C · 4 : 1
For any natural number n, suppose the sum of the first n terms of an arithmetic progression is (n + 2n2). If the nth term of the
progression is divisible by 9, then the smallest possible value of n is
Correct answer: C · 7
Let $0 \le a \le x \le 100$ and $f(x) = |x - a| + |x - 100| + |x - a - 50|$. Then the maximum value of $f(x)$ becomes 100 when $a$ is equal to
Correct answer: C · 50
Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively.
Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time
taken, in minutes, by train B to travel from station Y to station X is
Correct answer: B · 15
A trapezium ABCD has AD parallel to BC, ∠BAD = 90°, BC = 3 cm and AD = 8 cm. If the perimeter is 36 cm, then its area in sq. cm is (numerical value)
Correct answer: 66
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 Rs.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
Rs. 744. Then the amount, in rupees, that she had spent in buying almonds is
Correct answer: A · 1680
Let $A$ be the largest positive integer that divides all numbers of the form $3^k + 4^k + 5^k$, and $B$ the largest positive integer that divides all numbers of the form $4^k + 3(4^k) + 4^{k+2}$, for any positive integer $k$. Then $(A + B)$ equals (numerical value)
Correct answer: 82
Let a, b, c be non-zero real numbers such that b2 < 4ac, and f(x) = ax2 + bx + c. If the set S consists of all integers m such that
f(m) < 0, then the set S must necessarily be
Correct answer: C · either the empty set or the set of all integers
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 (numerical value)
Correct answer: 84
Let a and b be natural numbers. If a² + ab + a = 14 and b² + ab + b = 28, then (2a + b) equals (numerical value)
Correct answer: A · 8
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 Rs. 308.32 per kg and
makes an overall profit of 64%. Then, Amal’s cost price for syrup, in rupees per kg, is
Correct answer: 160
All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is
Correct answer: B · P²/8 − 2R²
The average of three 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
Correct answer: C · 5
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
Correct answer: D · 1 : 7
The largest real value of a for which the equation |x + a| + |x - 1| = 2 has an infinite number of solutions for x is
Correct answer: C · 1
In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any
of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the
three drinks is
Correct answer: A · 47
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
Correct answer: D · (−4, 5)
For natural numbers x, y, z, if xy + yz = 19 and yz + xz = 51, then the minimum possible value of xyz is (numerical value)
Correct answer: 34
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
Correct answer: A · 37.5%
Pinky stands in a queue; the ratio of persons ahead of her to persons behind her is 3 : 5. If the total number in the queue is less than 300, the maximum possible number of persons ahead of Pinky is (numerical value)
Correct answer: 111
For any real number x, let [x] be the largest integer not exceeding x. If the floor-function sum (as printed) equals 25, then N equals (numerical value)
Correct answer: 44