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CAT 2017 Slot 1 Question Paper

CAT 2017 · Slot 1VARC · 34qDILR · 32qQA · 34q100 questions+3 / −1
Verbal Ability & RCQ1–Q34 · 34 questions
1
Reading ComprehensionHARD

Which one of the following best describes what the passage is trying to do?

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2
Reading ComprehensionMEDIUM

Early maps did NOT put north at the top for all the following reasons EXCEPT

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3
Reading ComprehensionEASY

According to the passage, early Chinese maps placed north at the top because

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4
Reading ComprehensionEASY

It can be inferred from the passage that European explorers like Columbus and Megellan

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5
Reading ComprehensionEASY

Which one of the following about the northern orientation of modern maps is asserted in the passage?

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6
Reading ComprehensionEASY

The role of natural phenomena in influencing map-making conventions is seen most clearly in

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7
Reading ComprehensionMEDIUM

The printing press has been likened to the Internet for which one of the following reasons?

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8
Reading ComprehensionEASY

According to the passage, the invention of the printing press did all of the following EXCEPT

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9
Reading ComprehensionEASY

Steve Jobs predicted which one of the following with the introduction of the iPhone?

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10
Reading ComprehensionMEDIUM

"I'm still waiting to see if the iPhone can do what the printing press did for religion and democracy." The author uses which one of the following to indicate his uncertainty?

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11
Reading ComprehensionEASY

The author attributes the French and American revolutions to the invention of the printing press because

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12
Reading ComprehensionEASY

The main conclusion of the passage is that the new technology has

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13
Reading ComprehensionMEDIUM

The central idea of this passage is that:

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14
Reading ComprehensionEASY

Why does the author say in paragraph 2, 'the massive distribution centers Amazon has opened across the country, often not too far from malls the company helped shutter'?

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15
Reading ComprehensionHARD

In the first paragraph, the phrase "real estate developers once stumbled over themselves to court..." suggests that they

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16
Reading ComprehensionEASY

The author calls the mall an ecosystem unto itself because

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17
Reading ComprehensionEASY

Why does the author say that the mall has been America's public square?

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18
Reading ComprehensionEASY

The author describes 'Perfume clouds in the department stores' in order to

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19
Reading ComprehensionMEDIUM

Which of the following best sums up Ehrlich and Raven's argument in their classic 1969 paper?

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20
Reading ComprehensionHARD

All of the following statements are true according to the passage EXCEPT

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21
Reading ComprehensionMEDIUM

The author discusses Mayr, Ehrlich and Raven to demonstrate that

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22
Reading ComprehensionMEDIUM

The central point in the first paragraph is that the economic benefits of the Olympic Games

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23
Reading ComprehensionMEDIUM

Sports facilities built for the Olympics are not fully utilised after the Games are over because

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24
Reading ComprehensionMEDIUM

The author feels that the Games place a burden on the host city for all of the following reasons EXCEPT that

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25
Para SummaryMEDIUM

The passage given below is followed by four summaries. Choose the option that best captures the author' s position.
To me, a "classic" means precisely the opposite of what my predecessors understood: a work is classical by reason of its resistance to contemporaneity and supposed universality, by reason of its capacity to indicate human particularity and difference in that past epoch. The classic is not what tells me about shared humanity — or, more truthfully put, what lets me recognize myself as already present in the past, what nourishes in me the illusion that everything has been like me and has existed only to prepare the way for me. Instead, the classic is what gives access to radically different forms of human consciousness for any given generation of readers, and thereby expands for them the range of possibilities of what it means to be a human being.

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26
Para SummaryMEDIUM

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

A translator of literary works needs a secure hold upon the two languages involved, supported by a good measure of familiarity with the two cultures. For an Indian translating works in an Indian language into English, finding satisfactory equivalents in a generalized western culture of practices and symbols in the original would be less difficult than gaining fluent control of contemporary English. When a westerner works on texts in Indian languages the interpretation of cultural elements will be the major challenge, rather than control over the grammar and essential vocabulary of the language concerned. It is much easier to remedy lapses in language in a text translated into English, than flaws of content. Since it is easier for an Indian to learn the English language than it is for a Briton or American to comprehend Indian culture, translations of Indian texts is better left to Indians.

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27
Para SummaryMEDIUM

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

For each of the past three years, temperatures have hit peaks not seen since the birth of meteorology, and probably not for more than 110,000 years. The amount of carbon dioxide in the air is at its highest level in 4 million years. This does not cause storms like Harvey — there have always been storms and hurricanes along the Gulf of Mexico — but it makes them wetter and more powerful. As the seas warm, they evaporate more easily and provide energy to storm fronts. As the air above them warms, it holds more water vapour. For every half a degree Celsius in warming, there is about a 3% increase in atmospheric moisture content. Scientists call this the Clausius-Clapeyron equation. This means the skies fill more quickly and have more to dump. The storm surge was greater because sea levels have risen 20 cm as a result of more than 100 years of human- related global warming which has melted glaciers and thermally expanded the volume of seawater.

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28
Para JumblesHARDTITA

The five sentences labelled 1, 2, 3, 4, 5) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on. the proper order for the sentences and key in this sequence of five numbers as your answer.
1. The process of handing down implies not a passive transfer, but some contestation in defining what exactly is to be handed down.
2. Wherever Western scholars have worked on the Indian past, the selection is even more apparent and the inventing of a tradition much more recognizable.
3. Every generation selects what it requires from the past and makes its innovations, some more than others.
4. It is now a truism to say that traditions are not handed down unchanged, but are invented.
5. Just as life has death as its opposite, so is tradition by default the opposite of innovation.

29
Para JumblesHARDTITA

The five sentences labelled (1, 2, 3, 4, 5) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper order for the sentences and key in this sequence of five numbers as your answer.

1. Scientists have for the first time managed to edit genes in a human embryo to repair a genetic mutation, fuelling hopes that such procedures may one day be available outside laboratory conditions.
2. The cardiac disease causes sudden death in otherwise healthy young athletes and affects about one in 500 people overall.
3. Correcting the mutation in the gene would not only ensure that the child is healthy but also prevents transmission of the mutation to future generations.
4. It is caused by a mutation in a particular gene and a child will suffer from the condition even if it inherits only one copy of the mutated gene.
5. In results announced in Nature this week, scientists fixed a mutation that thickens the heart muscle, a condition called hypertrophic cardiomyopathy.

30
Para JumblesHARDTITA

The five sentences labelled (1, 2, 3, 4, 5) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on. the proper order for the sentences and key in this sequence of five numbers as your answer.
1. The study suggests that the disease did not spread with such intensity, but that it may have driven human migrations across Europe and Asia.
2. The oldest sample came from an individual who lived in southeast Russia about 5,000 years ago.
3. The ages of the skeletons correspond to a time of mass exodus from today's Russia and Ukraine into western Europe and central Asia, suggesting that a pandemic could have driven these migrations.
4. In the analysis of fragments of DNA from 101 Bronze Age skeletons for sequences from Yersinia pestis, the bacterium that causes the disease, seven tested positive.
5. DNA from Bronze Age human skeletons indicate that the black plague could have emerged as early as 3,000 BCE, long before the epidemic that swept through Europe in the rnid-1300s.

31
Para JumblesHARDTITA

The five sentences labelled (1, 2, 3, 4, 5) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper order for the sentences and key in this sequence of five numbers as your answer.
1. This visual turn in social media has merely accentuated this announcing instinct of ours, enabling us with easy-to-create, easy-to-share, easy-to-store and easy-to-consume platforms, gadgets and apps.
2. There is absolutely nothing new about us framing the vision of who we are or what we want, visually or otherwise, in our Facebook page, for example.
3. Turning the pages of most family albums, which belong to a period well before the digital dissemination of self-created and self-curated moments and images, would reconfirm the basic instinct of documenting our presence in a particular space, on a significant occasion, with others who matter.
4. We are empowered to book our faces and act as celebrities within the confinement of our respective friend lists, and communicate our activities, companionship and locations with minimal clicks and touches.
5. What is unprecedented is not the desire to put out newsfeeds related to the self, but the ease with which this broadcast operation can now be executed, often provoking (un)anticipated responses from beyond one' s immediate location.

32
Odd one outMEDIUMTITA

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.

l. People who study children's language spend a lot of time watching how babies react to the speech they hear around them.
2. They make films of adults and babies interacting, and examine them very carefully to see whether the babies show any signs of understanding what the adults say.
3. They believe that babies begin to react to language from the very moment they are born.
4. Sometimes the signs are very subtle — slight movements of the baby's eyes or the head or the hands.
5. You'd never notice them if you were just sitting with the child, but by watching a recording over and over, you can spot them.

33
Odd one outMEDIUMTITA

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. Neuroscientists have just begun studying exercise's impact within brain cells — on the genes themselves.
2. Even there, in the roots of our biology, they' ve found signs of the body's influence on the mind.
3. It turns out that moving our muscles produces proteins that travel through the bloodstream and into the brain, where they play pivotal roles in the mechanisms of our highest thought processes.
4. In today's technology-driven, plasma-screened-in world, it's easy to forget that we are born movers-animals, in fact — because we' ve engineered movement right out of our lives.
5. It's only in the past few years that neuroscientists have begun to describe these factors and how they work, and each new discovery adds awe-inspiring depth to the picture.

34
Odd one outMEDIUMTITA

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. The water that made up ancient lakes and perhaps an ocean was lost.
2. Particles from the Sun collided with molecules in the atmosphere, knocking them into space or giving them an electric charge that caused them to be swept away by the solar wind.
3. Most of the planet's remaining water is now frozen or buried, but clues over the past decade suggested that some liquid water, a presumed necessity for life, might survive in underground aquifers.
4. Data from NASA's MAVEN orbiter show that solar storms stripped away most of Mars's once-thick atmosphere.
5. A recent study reveals how Mars lost much of its early water, while another indicates that some liquid water remains.

Data Interpretation & LRQ35–Q66 · 32 questions
35
SchedulingEASY

Assume that only one client's order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 1 completely served?

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36
SchedulingEASY

Assume that only one client's order can be processed at any given point of time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 3 completely served?

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37
SchedulingMEDIUM

Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
At what time is the order placed by Client 2 completely served?

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38
SchedulingMEDIUM

Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.
Also assume that the fourth client came in only at 10:35. Between 10:00 and 10:30, for how many minutes is exactly one of the employees idle?

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39
Quant Based DIMEDIUM

What percentage of kids from S were studying in P?

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40
Quant Based DIMEDIUM

Among the kids in W whose mothers had completed primary education, how many were not in school?

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41
Quant Based DIMEDIUM

In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools.
What number of the surveyed kids now were in G in W?

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42
Quant Based DIHARD

In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in on.e region, 25% were in G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools.
What percentage of the surveyed kids in S, whose mothers had dropped out before completing primary education, were in G now?

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43
Venn DiagramsHARD

What best can be concluded about the number of candidates sitting for the separate test for BIE who were at or above the 90th percentile overall in CET?

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44
Venn DiagramsHARDTITA

If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, what is the number of candidates who are at or above the 90th percentile overall and at or above the 80th percentile in both P and M in CET?

45
Venn DiagramsHARDTITA

If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, then how many candidates were shortlisted for the AET for AIE?

46
Venn DiagramsHARD

If the number of candidates who are at or above the 90th percentile overall and also are at or above the 80th percentile in P in CET, is more than 100, how many candidates had to sit for the separate test for BIE?

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47
ChartsMEDIUMTITA

What is Amda's score in F?

48
ChartsMEDIUMTITA

What is Zooma's score in S?

49
ChartsHARD

Benga and Delma, two countries categorized as happy, are tied with the same total score. What is the
maximum score they can have?

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50
ChartsHARD

If Benga scores 16 and Delma scores 15, then what is the maximum number of countries with a score of 13?

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51
Data change over a periodHARD

The number of times in which the composition of team T2 and the number of times in which composition of team T4 remained unchanged in two successive months are:

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52
Data change over a periodMEDIUM

The number of SE in T1 and T5 for the projects in the third month are, respectively:

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53
Data change over a periodHARD

Which of the following CANNOT be the total credit points earned by any employee from the projects?

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54
Data change over a periodHARD

One of the employees named Aneek scored 185 points. Which of the following CANNOT be true?

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55
Quant Based DIMEDIUM

How many individuals in this layout can be reached by just one individual?

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56
Quant Based DIMEDIUM

Which of the following is true for any individual at a platform of height 1 m in this layout?

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57
Quant Based DIMEDIUM

We can find two individuals who cannot be reached by anyone in

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58
Quant Based DIMEDIUM

Which of the following statements is true about this layout?

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59
2D & 3D LRHARD

If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is:

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60
2D & 3D LRHARD

Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and/or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is:

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61
2D & 3D LRHARDTITA

Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
1. Both cities are in G1
2. Between A and any city in G2
3. Between B and any city in G3
4. Between C and any city in G4
Then the minimum number of direct flights that satisfies the underlying principle of the airline is:

62
2D & 3D LRHARDTITA

Suppose the 10 cities are divided into 4 distinct groups Gl, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that Gl consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following:
1. Both cities are in G1
2. Between A and any city in G2
3. Between B and any city in G3
4. Between C and any city in G4
However, due to operational difficulties at A, it was later decided that the only flights that would operate at A would be those to and from B. Cities in G2 would have to be assigned to G3 or to G4.
What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose?

63
2D & 3D LRMEDIUMTITA

How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department?

64
2D & 3D LRMEDIUM

If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-N-B and a car that takes the route A-M-B?

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65
2D & 3D LRMEDIUMTITA

A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the
travel time per car by 1 minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.
How many cars would the police department order to take the A-M-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.)

66
2D & 3D LRHARD

A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-M-N-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by j. minute. Assume that any car taking the A-M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route.
If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.)

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Quantitative AbilityQ67–Q100 · 34 questions
67
Averages, Ratio and ProportionEASYTITA

Arun's present age in years is 40% of Barun's. In another few years, Arun's age will be half of Barun's. By what percentage will Barun's age increase during this period?

68
Time and WorkEASYTITA

A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?

69
Averages, Ratio and ProportionEASYTITA

An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?

70
Time, Speed and DistanceEASYTITA

A man leaves his home and walks at a speed of 12 km per hour, reaching the railway station 10 minutes after the train had departed. If instead he had walked at a speed of 15 km per hour, he would have reached the station 10 minutes before the train's departure. The distance (in km) from his home to the railway station is

71
Profit and LossMEDIUMTITA

Ravi invests 50% of his monthly savings in fixed deposits. Thirty percent of the rest of his savings is invested in stocks and the rest goes into Ravi's savings bank account. If the total amount deposited by him in the bank (for savings account and fixed deposits) is Rs 59500, then Ravi's total monthly savings (in Rs) is

72
Profit and LossEASY

If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?

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73
Time, Speed and DistanceMEDIUM

A man travels by a motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motor boat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is

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74
Profit and LossEASY

Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by Cl, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs 19 crore more than C1, then the total profit (in Rs) made by all five companies is

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75
Averages, Ratio and ProportionEASY

The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is

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76
Averages, Ratio and ProportionEASY

A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio

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77
Profit and LossEASY

In a market, the price of medium quality mangoes is half that of good mangoes. A shopkeeper buys 80 kg good mangoes and 40 kg medium quality mangoes from the market and then sells all these at a common price which is 10% less than the price at which he bought the good ones. His overall profit is

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78
Profit and LossMEDIUM

If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

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79
InequalitiesHARD

If a and b are integers of opposite signs such that (a+3)2:b2=9:1(a + 3)^{2} : b^{2} = 9 : 1(a+3)2:b2=9:1 and (a−1)2:(b−1)2=4:1(a -1)^{2}:(b - 1)^{2} = 4:1(a−1)2:(b−1)2=4:1, then the ratio a2:b2a^{2} : b^{2}a2:b2 is

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80
Averages, Ratio and ProportionMEDIUM

A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is

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81
GeometryMEDIUM

The area of the closed region bounded by the equation 

I x I + I y I = 2 in the two-dimensional plane is

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82
GeometryMEDIUM

From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is

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83
GeometryMEDIUM

Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is

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84
GeometryMEDIUM

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8 : 27 : 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to

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85
GeometryHARDTITA

A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9π9\pi9π cubic centimeters. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is

86
GeometryMEDIUMTITA

Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is

87
Logarithms, Surds and IndicesMEDIUM

Suppose, log⁡3x=log⁡12y=a\log_3 x = \log_{12} y = alog3​x=log12​y=a, where x,yx, yx,y are positive numbers. If GGG is the geometric mean of x and y, and log⁡6G\log_6 Glog6​G is equal to

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88
Quadratic EquationsMEDIUM

If x+1=x2x+1=x^{2}x+1=x2 and x>0, then 2x42x^{4}2x4  is

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89
Logarithms, Surds and IndicesMEDIUM

The value of log⁡0.0085+log⁡381−7\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7log0.008​5​+log3​​81−7 is equal to

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90
Logarithms, Surds and IndicesMEDIUM

If 92x−1−81x−1=19449^{2x-1}-81^{x-1}=194492x−1−81x−1=1944, then xxx is

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91
Linear EquationsHARD

The number of solutions (x,y,z)(x, y, z)(x,y,z) to the equation x−y−z=25x - y - z = 25x−y−z=25, where x, y, and z are positive integers such that x≤40,y≤12x\leq40,y\leq12x≤40,y≤12, and z≤12z\leq12z≤12 is

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92
InequalitiesMEDIUMTITA

For how many integers n, will the inequality (n−5)(n−10)−3(n−2)≤0(n - 5) (n - 10) - 3(n - 2)\leq0(n−5)(n−10)−3(n−2)≤0 be satisfied?

93
Functions, Graphs and StatisticsMEDIUMTITA

If f1(x)=x2+11x+nf_{1}(x)=x^{2}+11x+nf1​(x)=x2+11x+n and f2(x)=xf_{2}(x)=xf2​(x)=x, then the largest positive integer n for which the equation f1(x)=f2(x)f_{1}(x)=f_{2}(x)f1​(x)=f2​(x) has two distinct real roots is

94
Number SystemsMEDIUMTITA

If a,b,c,a, b, c,a,b,c, and ddd are integers such that a+b+c+d=30a+b+c+d=30a+b+c+d=30 then the minimum possible value of (a−b)2+(a−c)2+(a−d)2(a - b)^{2} + (a - c)^{2} + (a - d)^{2}(a−b)2+(a−c)2+(a−d)2  is

95
Probability, CombinatoricsHARDTITA

Let AB, CD, EF, GH, and JK be five diameters of a circle with center at 0. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

96
GeometryMEDIUM

The shortest distance of the point (12,1)(\frac{1}{2},1)(21​,1) from the curve y = I x -1I + I x + 1I is

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97
Progressions and SeriesMEDIUM

If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

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98
Probability, CombinatoricsMEDIUM

In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

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99
Functions, Graphs and StatisticsMEDIUM

f(x)=5x+23x−5f(x) = \frac{5x+2}{3x-5}f(x)=3x−55x+2​ and g(x)=x2−2x−1g(x) = x^2 - 2x - 1g(x)=x2−2x−1, then the value of g(f(f(3)))g(f(f(3)))g(f(f(3))) is

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100
Progressions and SeriesMEDIUM

Let a1a_1a1​, a2a_2a2​,.............,  a3na_{3n}a3n​ be an arithmetic progression with a1a_1a1​ = 3 and a2a_{2}a2​ = 7. If a1a_1a1​+ a2a_{2}a2​ +...+ a3na_{3n}a3n​= 1830, then what is the smallest positive integer m such that m(a1a_1a1​+ a2a_{2}a2​ +...+ ana_nan​) > 1830?

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