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Official CAT 2020 Paper – Questions, Answers, and Detailed Solutions

Official CAT 2020 Paper- Verbal Ability - Slot 1

Q.1- Q.5. The word ‘anarchy’ comes from the Greek anarkhia, meaning contrary to authority or without a ruler, and was used in a derogatory sense until 1840, when it was adopted by Pierre-Joseph Proudhon to describe his political and social ideology…

Q.6- Q.9. In the late 1960s, while studying the northern-elephant-seal population along the coasts of Mexico and California, Burney Le Boeuf and his colleagues couldn’t help but notice that the threat calls of males at some sites sounded different from those of males at other sites. . .

Q.10- Q.13. Few realise that the government of China, governing an empire of some 60 million people during the Tang dynasty (618–907), implemented a complex financial system that recognised grain, coins and textiles as money. . . 

Q.14- Q.18. Vocabulary used in speech or writing organizes itself in seven parts of speech (eight, if you count interjections such as Oh! and Gosh! and Fuhgeddaboudit!). Communication composed of these parts of speech must be organized by rules of grammar upon which we agree… 

Q.19. Tensions and sometimes conflict remain an issue in and between the 11 states in South East Asia (Brunei Darussalam, Cambodia, Indonesia, Laos, Malaysia, Myanmar, the Philippines, Singapore, Thailand, Timor-Leste and Vietnam).

Q.20. For nearly a century most psychologists have embraced one view of intelligence. Individuals are born with more or less intelligence potential (I.Q.); this potential is heavily in\xef\xac\x82uenced by heredity and difcult to alter;…

Q.21. Relying on narrative structure alone, indigenous significances of nineteenth century San folktales are hard to determine.

Q.22. For years, movies and television series like Crime Scene Investigation (CSI) paint an unrealistic picture of the “science of voices.” In the 1994 movie Clear and Present Danger an expert listens to a brief recorded utterance and declares that the speaker is “Cuban, aged 35 to 45…

Q.23. As Soviet power declined, the world became to some extent multipolar, and Europe strove to define an independent identity. What a journey Europe has undertaken to reach this point…

Q.24. Man has used poisons for assassination purposes ever since the dawn of civilization, against individual enemies but also occasionally against armies.

Q.25. For feminists, the question of how we read is inextricably linked with the question of what we read….

Q.26. Talk was the most common way for enslaved men and women to subvert the rules of their bondage, to gain more agency than they were supposed to have…

Official CAT 2020 Paper- Verbal Ability - Slot 2

Q.1- Q.5. The claims advanced here may be condensed into two assertions: [first, that visual] culture is what images, acts of seeing, and attendant intellectual, emotional, and perceptual sensibilities do to build, maintain, or transform the worlds in which people live…

Q.6- Q.9. 174 incidents of piracy were reported to the International Maritime Bureau last year, with Somali pirates responsible for only three. The rest ranged from the discreet theft of coils of rope in the Yellow Sea to the notoriously ferocious Nigerian gunmen attacking and hijacking oil tankers in the Gulf of Guinea, as well as armed robbery off Singapore and the Venezuelan coast and kidnapping in the Sundarbans in the Bay of Bengal. . .

Q.10- Q.14. In a low-carbon world, renewable energy technologies are hot business. For investors looking to redirect funds, wind turbines and solar panels, among other technologies, seem a straightforward choice. But renewables need to be further scrutinized before being championed as forging a path toward a low-carbon future.. . . 

Q.15- Q.18. Aggression is any behavior that is directed toward injuring, harming, or inflicting pain on another living being or group of beings. Generally, the victim(s) of aggression must wish to avoid such behavior in order for it to be considered true aggression… 

Q.19. But the attention of the layman, not surprisingly, has been captured by the atom bomb, although there is at least a chance that it may never be used again.

Q.20. While you might think that you see or are aware of all the changes that happen in your immediate environment, there is simply too much information for your brain to fully process everything.

Q.21. With the Treaty of Westphalia, the papacy had been confined to ecclesiastical functions, and the doctrine of sovereign equality reigned. What political theory could then explain the origin and justify the functions of secular political order?…

Q.22. All humans make decisions based on one or a combination of two factors. This is either intuition or information. Decisions made through intuition are usually fast, people don’t even think about the problem…

Q.23. The rural-urban continuum and the heterogeneity of urban settings pose an obvious challenge to identifying urban areas and measuring urbanization rates in a consistent way within and across countries…

Q.24. You can observe the truth of this in every e-business model ever constructed: monopolise and protect data..

Q.25. The victim’s trauma after assault rarely gets the attention that we lavish on the moment of damage that divided the survivor from a less encumbered past…

Q.26. It also has four movable auxiliary telescopes 1.8 m in diameter….

Official CAT 2020 Paper- Verbal Ability - Slot 3

Q.1- Q.5. Mode of transportation affects the travel experience and thus can produce new types of travel writing and perhaps even new “identities.” Modes of transportation determine the types and duration of social encounters;…

Q.6- Q.9. Although one of the most contested concepts in political philosophy, human nature is something on which most people seem to agree. By and large, according to Rutger Bregman in his new book Humankind. . .

Q.10- Q.13. [There is] a curious new reality: Human contact is becoming a luxury good. As more screens appear in the lives of the poor, screens are disappearing from the lives of the rich. The richer you are, the more you spend to be off-screen… 

Q.14- Q.18. I’ve been following the economic crisis for more than two years now. I began working on the subject as part of the background to a novel, and soon realized that I had stumbled across the most interesting story I’ve ever found…. 

Q.19. Brown et al. (2001) suggest that ‘metabolic theory may provide a conceptual foundation for much of ecology just as genetic theory provides a foundation for much of evolutionary biology’… 

Q.20. It advocated a conservative approach to antitrust enforcement that espouses faith in efficient markets and voiced suspicion regarding the merits of judicial intervention to correct anticompetitive practices…

Q.21. Aesthetic political representation urges us to realize that ‘the representative has autonomy with regard to the people represented’ but autonomy then is not an excuse to abandon one’s responsibility…

Q.22. Each one personified a different aspect of good fortune….

Q.23. The logic of displaying one’s inner qualities through outward appearance was based on a distinction between being a woman and being feminine…

Q.24. The dominant hypotheses in modern science believe that language evolved to allow humans to exchange factual information about the physical world. But an alternative view is that language evolved, in modern humans at least, to facilitate social bonding...

Q.25. Complex computational elements of the CNS are organized according to a “nested” hierarchic criterion; the organization is not permanent and can change dynamically from moment to moment as they carry out a computational task.

Q.26. Machine learning models are prone to learning human-like biases from the training data that feeds these algorithms.

Official CAT 2020 Paper- LR DI - Slot 1

Official CAT 2020 Paper- LR DI - Slot 2

Official CAT 2020 Paper- LR DI - Slot 3

Official CAT 2020 Paper- Quantitative Ability - Slot 1

Q.1. How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Q.2. If f(5 + x) = f(5 – x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

Q.3. Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Q.4. A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

Q.5. If log4 5 = (log4 y) (log6 √5),then y equals

Q.6. The number of real-valued solutions of the equation 2x + 2-x =2 – (x – 2)2 is

Q.7. A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

Q.8. Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

Q.9. If x = (4096)7+4√3, then which of the following equals 64?

Q.10. The mean of all 4 digit even natural numbers of the form ‘aabb’, where a>0, is

Q.11. The number of distinct real roots of the equation (x + 1/x)2 – 3 (x + 1/x) + 2 = 0 equals

Q.12. A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

Q.13. Among 100 students, x1 have birthdays in January, x2 have birthdays in February, and so on.
If x0 = max(x1, x2, . . ., x12), then the smallest possible value of x0 is

Q.14. Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

Q.15. How many distinct positive integer-valued solutions exist to the equation (x2 – 7x + 11)(x2 – 13x + 42)  = 1?

Q.16. The area of the region satisfying the inequalities |x| – y ≤ 1, y ≥ 0, and y ≤ 1 is

Q.17. A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it’s base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

Q.18. A circle is inscribed in a rhombus with diagonals 12 cm and 16 cm. The ratio of the area of the circle to the area of the rhombus is

Q.19. Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8kmph, and at 9:40 am if he travels at 15kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?

Q.20. If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

Q.21. If y is a negative number such that   then y equals

Q.22. On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches opposite two sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

Q.23. In a group of people, 28% of the members are young while the rest are old. If 65% of the members are literates, and 25% of the literates are young, then the percentage of old people among the illiterates is nearest to

Q.24. An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of metals A, B, C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, of the metal C is

Q.25. A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

Q.26. A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?

 

Official CAT 2020 Paper- Quantitative Ability - Slot 2

Q.1. In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

Q.2. From the interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the perpendiculars is ‘s’. Then the area of the triangle is

Q.3. 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

Q.4. The number of pairs of integers(x,y) satisfying x ≥ y ≥ -20 and 2x + 5y = 99 is

Q.5. The value of loga a/b + logb/a for 1 < a ≤ b cannot be equal to

Q.6. Let the m-th and n-th terms of a Geometric progression be 3/4 and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n – m is

Q.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) is

Q.8. 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

Q.9. 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 located 3 meters east of O. Then, the length of PQ, in meters, is nearest
to

Q.10. For real x, the maximum possible value of X/(√(1+ x4) ) is

Q.11. 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

Q.12. 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 equals

Q.13. 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

Q.14. Let f(x) = x2 + ax + b and g(x) = f(x + 1) – f(x – 1). If f(x) ≥ 0 for all real x, and g(20) = 72, then the smallest possible value of b is

Q.15. 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

Q.16. The sum of perimeters of an equilateral triangle and a rectanmgle 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

Q.17. The number of integers that satisfy the equality (x2 – 5x + 7)x + 1 = 1 is

Q.18. In how many ways can a pair of integers (x , a) be chosen such that x2 − 2 | x | + | a – 2 | = 0 ?

Q.19. 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 T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

Q.20. 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 minutes and four minutes, respectively. If they start at the same time, then the ratio of Ram’s speed to Rahim’s speed is

Q.21. Let C1 and C2 be concentric circles such that the diameter of C1 is 2cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm of C 

Q.22. 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?

Q.23. In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent 450 on rice in April, then how much did he spend on wheat in May?

Q.24. 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 2 more than the cost of a pencil, then the minimum
possible number of pencils bought by Aron and Aditya together is

Q.25. 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

Q.26. How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

Official CAT 2020 Paper- Quantitative Ability - Slot 3

Q.1. If x1 = -1 and xm = xm + 1 + (m + 1) for every positive integer m, then x100 equals

Q.2. Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

Q.3. Let loga30 = A, log5/3 = -B and log2a = 1/3 , then log3a equals

Q.4. A contractor agreed to construct a 6 km road in 200 days. He employed 140 persons for the work. After 60 days, he realized that only 1.5 km road has been completed. How many additional people would he need to employ in order to
finish the work exactly on time?

Q.5. The area, in sq. units, enclosed by the lines x = 2, y = |x – 2| + 4, the X-axis and the Y-axis is equal to

Q.6. Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is 1 year less than the average age of all three, then Harry’s age, in years, is

Q.7. How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

Q.8. In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

Q.9. If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) – f(-10) is equal to

Q.10. Equals

Q.11. If a,b,c are non-zero and 14a = 36b = 84c, then 6b (1/c – 1/a) is equal to

Q.12. Let m and n be natural numbers such that n is even and 0.2 < m/20, n/m, n/11 < 0.5. Then m – 2n equals

Q.13. Anil, Sunil, and Ravi run along a circular path of length 3 km, starting from the same point at the same time, and going in the clockwise direction. If they run at speeds of 15 km/hr, 10 km/hr, and 8 km/hr, respectively, how much distance in km will Ravi have run when Anil and Sunil meet again for the first time at the starting point?

Q.14. A man buys 35 kg of sugar and sets a marked price in order to make a 20% profit. He sells 5 kg at this price, and 15 kg at a 10% discount. Accidentally, 3 kg of sugar is wasted. He sells the remaining sugar by raising the marked price by p percent so as to make an overall profit of 15%. Then p is nearest to

Q.15. Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

Q.16. How many integers in the set {100, 101, 102, …, 999} have at least one digit repeated?

Q.17. A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is

Q.18. Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is

Q.19. The vertices of a triangle are (0,0), (4,0) and (3,9). The area of the circle passing through these three points is

Q.20. A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Q.21. A and B are two railway stations 90 km apart. A train leaves A at 9:00 am, heading towards B at a speed of 40 km/hr. Another train leaves B at 10:30 am, heading towards A at a speed of 20 km/hr. The trains meet each other at

Q.22. Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in
one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

Q.23. Let m and n be positive integers, If x+ mx + 2n = 0 and x+ nx + m = 0 have real roots, then the smallest possible value of m + n is

Q.24. In a trepezium ABCD, AB is parallel to DC, BC is perpendicular to DC and BAD = 45°. If DC = 5 cm, BC = 4 cm, the area of the trepezium in sq. cm is

Q.25. The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

Q.26. How many pairs (a,b) of positive integers are there such that a ≤ b and ab = 42017?

 

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