CAT Questions

What is the number of all possible positive integer values of n for which n^2 + 96 is a perfect square

Numbers

What is the number of all possible positive integer values of n for which n2 + 96 is a perfect square?

  1. 2
  2. 4
  3. 5
  4. Infinite

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How many times will the digit 5 come in counting from 1 to 99

Numbers

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

  1. 16
  2. 15
  3. 14
  4. 13

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It takes the pendulum of a clock 7 seconds to strike 4 o'clock

Clocks

It takes the pendulum of a clock 7 seconds to strike 4 o'clock. How much time will it take to strike 11 o'clock?

  1. 18 seconds
  2. 19.25 seconds
  3. 20 seconds
  4. 23.33 seconds

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Twenty four people are part of three committees

Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee.

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A company administers a written test comprising of three sections of 20 marks each

A company administers a written test comprising of three sections of 20 marks each - Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.

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Fuel contamination levels at each of 20 petrol pumps

Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.

  1. Contamination levels at three pumps among P1 – P5 were recorded as high.
  2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
  3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
  4. High contamination levels were not recorded at any of the pumps P16 – P20.
  5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.

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You are given an n×n square matrix to be filled with numerals

You are given an n×n square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

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Adriana, Bandita, Chitra, and Daisy are four female students

Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes - X, Y, and Z. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects.

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An ATM dispenses exactly Rs. 5000 per withdrawal using

An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.

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The multi-layered pie-chart below shows the sales of LED television

Pie Charts

The multi-layered pie-chart below shows the sales of LED television sets for a big retail electronics outlet during 2016 and 2017. The outer layer shows the monthly sales during this period, with each label showing the month followed by sales figure of that month. For some months, the sales figures are not given in the chart. The middle-layer shows quarter-wise aggregate sales figures (in some cases, aggregate quarter-wise sales numbers are not given next to the quarter).

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When they work alone, B needs 25% more time to finish a job than A does

Time Work

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

  1. 20
  2. 16
  3. 22
  4. 18

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Humans and robots can both perform a job but at different efficiencies

Time Work

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

  1. 36
  2. 32
  3. 45
  4. 40

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The distance from A to B is 60 km. Partha and Narayan start from A

Time Distance

The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the mid-point of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is

  1. 4
  2. 6
  3. 5
  4. 3

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Let f(x) = min{2x^2, 52 − 5x}, where x is any positive real number

Relations Functions

Let f(x) = min{2x2, 52 − 5x}, where x is any positive real number. Then the maximum possible value of f(x) is

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John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum

Interests

John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is

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Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg

Ratio Proportion

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

  1. 18 : 25
  2. 19 : 24
  3. 21 : 25
  4. 17 : 25

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In an examination, the maximum possible score is N

Percentages

In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?

  1. N ≤ 200
  2. 243 ≤ N ≤ 252
  3. N ≥ 253
  4. 201 ≤ N ≤ 242

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If f(x + 2) = f(x) + f(x + 1) for all positive integers x

Relations Functions

If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals

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The number of integers x such that 0.25 2^x 200, and 2^x + 2

Numbers

The number of integers x such that 0.25 < 2x < 200, and 2x + 2 is perfectly divisible by either 3 or 4, is

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How many numbers with two or more digits can be formed

Quant PnC

How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?

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In a circle with center O and radius 1 cm

Geometry

In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points
on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is

  1. (π/3√3)1/2
  2. (π/4)1/2
  3. (π/6)1/2
  4. (π/4√3)1/2

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In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm

Geometry

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

  1. 18√3
  2. 24√3
  3. 32√3
  4. 12√3

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Let ABCD be a rectangle inscribed in a circle of radius 13 cm

Geometry

Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?

  1. 24, 10
  2. 25, 9
  3. 24, 12
  4. 25, 10

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Raju and Lalitha originally had marbles in the ratio 4:9

Ratio Proportion

Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?

  1. 1/4
  2. 7/33
  3. 1/5
  4. 6/19

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A CAT aspirant appears for a certain number of tests

Averages

A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is

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A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice

Profit Loss

A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold 8 kg of peanuts at a profit of 10% and 16 kg of walnuts at a profit of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall profit of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?

  1. 98
  2. 96
  3. 84
  4. 86

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Each of 74 students in a class studies at least one of the three subjects

Quant Sets

Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is

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Train T leaves station X for station Y at 3 pm

Time Distance

Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y?

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log12 81 = p, then 3[(4-p)/(4+p)] is equal to

Logarithms

log12 81 = p, then 3[(4-p)/(4+p)] is equal to

  1. log4 16
  2. log6 8
  3. log6 16
  4. log2 8

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A right circular cone, of height 12 ft, stands on its base

Mensuration

A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is

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Points E, F, G, H lie on the sides AB, BC, CD, and DA

Geometry

Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is

  1. 2 : 5
  2. 4 : 9
  3. 3 : 8
  4. 1 : 3

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While multiplying three real numbers, Ashok took one of the numbers

Numbers

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

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If x is a positive quantity such that 2x = 3^log5 2, then x is equal to

Logarithms

If x is a positive quantity such that 2x = 3log5 2, then x is equal to

  1. 1 + log3 5/3
  2. log5 8
  3. 1 + log5 3/5
  4. log5 9

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If u^2 + (u − 2v − 1)^2 = −4v(u + v), then what is the value of u + 3v

Polynomials

If u2 + (u − 2v − 1)2 = −4v(u + v), then what is the value of u + 3v?

  1. 1/4
  2. 0
  3. 1/2
  4. -1/4

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Given an equilateral triangle T1 with side 24 cm

Progressions

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3, ... will be

  1. 164√3
  2. 188√3
  3. 248√3
  4. 192√3

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In an apartment complex, the number of people aged 51 years

Averages

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

  1. 27
  2. 28
  3. 26
  4. 25

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If among 200 students, 105 like pizza and 134 like burger

Quant Sets

If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be

  1. 93
  2. 26
  3. 23
  4. 96

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In a circle, two parallel chords on the same side of a diameter

Geometry

In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

  1. √12
  2. √14
  3. √13
  4. √11

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A trader sells 10 litres of a mixture of paints A and B

Mixtures Alligation

A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

  1. 26
  2. 16
  3. 20
  4. 22

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If log log2 (5 + log3 a) = 3 and log5 (4a + 12 + log2 b) = 3

Logarithms

If log log2 (5 + log3 a) = 3 and log5 (4a + 12 + log2 b) = 3, then a + b is equal to

  1. 67
  2. 40
  3. 32
  4. 59

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Point P lies between points A and B such that the length of BP

Time Distance

Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is

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Given that x^2018 y^2017 = 1/2 and x^2016 y^2019 = 8

Numbers

Given that x2018y2017 = 1/2 and x2016y2019 = 8, the value of x2 + y3 is

  1. 35/4
  2. 37/4
  3. 31/4
  4. 33/4

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A tank is fitted with pipes, some filling it and the rest draining it

Time Work

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

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Let x, y, z be three positive real numbers in a geometric progression

Progressions

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is:

  1. 3/6
  2. 3/2
  3. 5/2
  4. 1/6

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1600 satellites were sent up by a country for several purposes

CAT Logical Reasoning

1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.

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The eventual diagnosis was skin cancer and after treatment

Para Jumbles

The four sentences (labelled 1, 2, 3, and 4) given in this question, when properly sequenced, form a coherent paragraph. Decide on the proper order for the sentences and key in this sequence of four numbers as your answer.

  1. The eventual diagnosis was skin cancer and after treatment all seemed well.
  2. The viola player didn’t know what it was; nor did her GP.
  3. Then a routine scan showed it had come back and spread to her lungs.
  4. It started with a lump on Cathy Perkins’ index finger.

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Displacement in Bengal is thus not very significant

CAT Odd One Out

Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.

  1. Displacement in Bengal is thus not very significant in view of its magnitude.
  2. A factor of displacement in Bengal is the shifting course of the Ganges leading to erosion of river banks.
  3. The nature of displacement in Bengal makes it an interesting case study.
  4. Since displacement due to erosion is well spread over a long period of time, it remains invisible.
  5. Rapid displacement would have helped sanitize the public to its human costs.

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In many cases time inconsistency is what prevents our going

CAT Odd One Out

Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.

  1. In many cases time inconsistency is what prevents our going from intention to action.
  2. For people to continuously postpone getting their children immunized, they would need to be constantly fooled by themselves.
  3. In the specific case of immunization, however, it is hard to believe that time inconsistency by itself would be sufficient to make people permanently postpone the decision if they were fully cognizant of its benefits.
  4. In most cases, even a small cost of immunization was large enough to discourage most people.
  5. Not only do they have to think that they prefer to spend time going to the camp next month rather than today, they also have to believe that they will indeed go next month.

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But now we have another group: the unwitting enablers

Para Jumbles

The four sentences (labelled 1,2,3,4) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper sequence of order of the sentences and key in this sequence of four numbers as your answer:

  1. But now we have another group: the unwitting enablers.
  2. Democracy and high levels of inequality of the kind that have come to characterize the United States are simply incompatible.
  3. Believing these people are working for a better world, they are, actually, at most, chipping away at the margins, making slight course corrections, ensuring the system goes on as it is, uninterrupted.
  4. Very rich people will always use money to maintain their political and economic power.

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The conceptualization of landscape as a geometric object

Summary

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.

The conceptualization of landscape as a geometric object first occurred in Europe and is historically related to the European conceptualization of the organism, particularly the human body, as a geometric object with parts having a rational, three-dimensional organization and integration. The European idea of landscape appeared before the science of landscape emerged, and it is no coincidence that Renaissance artists such as Leonardo da Vinci, who studied the structure of the human body, also facilitated an understanding of the structure of landscape. Landscape which had been a subordinate background to religious or historical narratives, became an independent genre or subject of art by the end of sixteenth century or the beginning of the seventeenth century.

  1. Landscape became a major subject of art at the turn of the sixteenth century.
  2. The three-dimensional understanding of the organism in Europe led to a similar approach towards the understanding of landscape.
  3. The study of landscape as an independent genre was aided by the Renaissance artists.
  4. The Renaissance artists were responsible for the study of landscape as a subject of art.

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