All 26 Quant questions from the CAT 2020 · Slot 2 paper, with the correct answer for each.
The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of
train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by
train 1 to that taken by train 2 in travelling from A to C is
Correct answer: A · 5:7
John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than
John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them
working together. In how many days will Jim finish the job working alone?
Correct answer: 4
Let $f(x) = x^2 + ax + b$ and $g(x) = f(x + 1) - f(x - 1)$. If $f(x) \ge 0$ for all real $x$, and $g(20) = 72$, then the smallest possible value of $b$ is
Correct answer: B · 4
For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three
years at 3% per annum by Rs. 1125.Then the principal amount in rupees is
Correct answer: 90000
Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is
located 4 meters north of O and B is located3 meters east of O. Then, the length of PQ, in meters, is nearest to
Correct answer: A · 8.8
In a car race, car A beats car B by 45 km, car B beats car C by 50km, and car A beats C by 90 km. the distance (in km) over which
the race has been conducted is
Correct answer: B · 450
How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?
Correct answer: 315
The sum of the perimeters of an equlateral triangle and a rectangle is 90 cm the area, T, of the triangle and the area, R, of the
rectangle, both in sq cm, satisfy the relationship R = T2. If the sides of the rectangle are in the ratio 1:3, then the length, in cm,
of the longer side of the rectangle, is
Correct answer: A · 27
A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of
the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is Rs 400, then
Sunil’s share, in rupees, is
Correct answer: 800
The value of $\log_a(a/b) + \log_b(b/a)$, for $1 < a \le b$ cannot be equal to
Correct answer: C · 1
Students in a college have to choose at least two subjects from Chemistry, Mathematics and Physics. The number of students
choosing all three subjects is 18, choosing Mathematics as one of their subjects is 23 and choosing Physics as one of their
subjects is 25. The smallest possible number of students who could choose Chemistry as one of their subjects is
Correct answer: C · 20
In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire
group of 10 students, the maximum possible mean exceeds the minimum possible mean by
Correct answer: B · 4
A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram
and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of
Ram's speed to Rahim's speed is
Correct answer: C · 2
Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram
and Rahim are walking on track T1 and track T2at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that
Ram will make to meet Rahim again for the first time is
Correct answer: B · 3
Let C1and C2 be concentric circles such that the diameter of C1 is 2cm longer than that of C2. If a chord of C1 has length 6cm
and is a tangent of C2, then the diameter, in cm, of C1 is
Correct answer: 10
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then
he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes
a 10% profit. With no discounts, his percentage of profit would have been
Correct answer: A · 50
The number of integers that satisfy the equality (x2 - 5x + 7)x + 1 = 1 is
Correct answer: A · 3
The number of pairs of integers $(x, y)$ satisfy $x \ge y \ge -20$ and $2x + 5y = 99$ is
Correct answer: 17
From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three
perpendiculars is $s$. Then the area of triangle is
Correct answer: D · $\frac{s^2}{\sqrt{3}}$
Let the m-th and n-th terms of a geometric progression be 3/4 and 12, respectively, where m < n. If the common ratio of the
progression is an integer r, then the smallest possible value of r + n - m is
Correct answer: D · -2
In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent Rs. 150 more
due to price increase of rice and wheat by 20%and 12%, respectively. If John had spent Rs. 450 on rice in April, then how much
did he spend on wheat in May?
Correct answer: A · Rs. 560
If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5,then the maximum possible value of 2x + y
?
Correct answer: 23
Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils
and 10 less sharpeners. If the cost of one sharpener is Rs. 2 more than the cost of a pencil, then the minimum possible number
of pencils bought by Aron and Aditya together is
Correct answer: A · 33
For real $x$, the maximum possible value of $\frac{x}{\sqrt{1 + x^4}}$ is
Correct answer: D · $\frac{1}{\sqrt{2}}$
In how many ways can a pair of integers (x, a) be chosen such that x2 − 2 | x | + | a - 2 | = 0?
Correct answer: D · 7
If x and y are positive real numbers satisfying x + y = 102, then the minimum possible value of 2601(1 + 1/x)(1 + 1/y)
Correct answer: 2704