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HomeCAT PYQsCAT 2017 Slot 2 Question Paper

CAT 2017 Slot 2 Question Paper

CAT 2017 · Slot 2VARC · 34qDILR · 32qQA · 34q100 questions+3 / −1
Verbal Ability & RCQ1–Q34 · 34 questions
1
Reading ComprehensionEASY

In the author's view, cities promote human creativity for all the following reasons EXCEPT that they

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2
Reading ComprehensionEASY

The author uses 'ironic' in the third paragraph to point out that

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3
Reading ComprehensionMEDIUM

The central idea of this passage is that

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4
Reading ComprehensionEASY

Jane Jacobs believed that cities that are more creative

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5
Reading ComprehensionEASY

The 1968 study is used here to show that

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6
Reading ComprehensionHARD

The author's conclusions about the most 'creative cities' in the US (paragraph 6) are based on his assumption that

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7
Reading ComprehensionMEDIUM

The purpose of this passage is to

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8
Reading ComprehensionEASY

All of the following statements are true EXCEPT

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9
Reading ComprehensionMEDIUM

Based on this extract, the author would support which one of the following actions?

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10
Reading ComprehensionEASY

In paragraph 6, the author provides the examples of crowberry and alpine azalea to demonstrate that

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11
Reading ComprehensionEASY

Which one of the following statements can be inferred from the passage?

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12
Reading ComprehensionEASY

In paragraph 1, the author uses blankets as a device to

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13
Reading ComprehensionMEDIUM

Which of the following statements best reflects the author's argument?

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14
Reading ComprehensionMEDIUM

The author points out all of the following about electric cars EXCEPT

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15
Reading ComprehensionEASY

According to the author, the main reason for Tesla's remarkable sales is that

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16
Reading ComprehensionMEDIUM

The author comes to the conclusion that

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17
Reading ComprehensionEASY

In paragraphs 5 and 6, the author provides the example of Uber to argue that

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18
Reading ComprehensionEASY

In paragraph 6, the author mentions electrically powered bicycles to argue that

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19
Reading ComprehensionMEDIUM

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

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20
Reading ComprehensionEASY

According to the passage, some governments still use typewriters because:

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21
Reading ComprehensionMEDIUM

The writer praises typewriters for all the following reasons EXCEPT

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22
Reading ComprehensionMEDIUM

The primary purpose of the passage is:

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23
Reading ComprehensionMEDIUM

The evidence - "Most of the artifacts also date to the 780s, but some are as old as 725" — has been used in the passage to argue that:

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24
Reading ComprehensionMEDIUM

All of the following hold true for Vikings EXCEPT

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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.
North American walnut sphinx moth caterpillars (Amorpha juglandis) look like easy meals for birds, but they have a trick up their sleeves — they produce whistles that sound like bird alarm calls, scaring potential predators away. At first, scientists suspected birds were simply startled by the loud noise. But a new study suggests a more sophisticated mechanism: the caterpillar's whistle appears to mimic a bird alarm call, sending avian predators scrambling for cover. When pecked by a bird, the caterpillars whistle by compressing their bodies like an accordion and forcing air out through specialized holes in their sides. The whistles are impressively loud — they have been measured at over 80 dB from 5 cm away from the caterpillar — considering they are made by a two-inch long insect.

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26
Para SummaryHARD

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

Both Socrates and Bacon were very good at asking useful questions. In fact, Socrates is largely credited with coming up with a way of asking questions, 'the Socratic method,' which itself is at the core of the 'scientific method,' popularised by Bacon. The Socratic method disproves arguments by finding exceptions to them, and can therefore lead your opponent to a point where they admit something that contradicts their original position. In common with Socrates, Bacon stressed it was as important to disprove a theory as it was to prove one — and real-world observation and experimentation were key to achieving both aims. Bacon also saw science as a collaborative affair, with scientists working together, challenging each other.

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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.
A fundamental property of language is that it is slippery and messy and more liquid than solid, a gelatinous mass that changes shape to fit. As Wittgenstein would remind us, "usage has no sharp boundary." Oftentimes, the only way to determine the meaning of a word is to examine how it is used. This insight is often described as the "meaning is use" doctrine. There are differences between the "meaning is use" doctrine and a dictionary-first theory of meaning. "The dictionary's careful fixing of words to definitions, like butterflies pinned under glass, can suggest that this is how language works. The definitions can seem to ensure and fix the meaning of words, just as the gold standard can back a country's currency." What Wittgenstein found in the circulation of ordinary language, however, was a free-floating currency of meaning. The value of each word arises out of the exchange. The lexicographer abstracts a meaning from that exchange, which is then set within the conventions of the dictionary definition.

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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 implications of retelling of Indian stories, hence, takes on new meaning in a modern India.
2. The stories we tell reflect the world around us.
3. We cannot help but retell the stories that we value — after all, they are never quite right for us — in our time. 

4. And even if we manage to get them quite right, they are only right for us — other people living around us will have different reasons for telling similar stories.

5. As soon as we capture a story, the world we were trying to capture has changed.

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. Before plants can take life from atmosphere, nitrogen must undergo transformations similar to ones that food undergoes in our digestive machinery.
2. In its aerial form nitrogen is insoluble, unusable and is in need of transformation.
3. Lightning starts the series of chemical reactions that need to happen to nitrogen, ultimately helping it nourish our earth.
4. Nitrogen — an essential food for plants — is an abundant resource, with about 22 million tons of it floating over each square mile of earth.
5. One of the most dramatic examples in nature of ill wind that blows goodness is lightning.

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. This has huge implications for the health care system as it operates today, where depleted resources and time lead to patients rotating in and out of doctor's offices, oftentimes receiving minimal care or concern (what is commonly referred to as "bed side manner") from doctors.
2. The placebo effect is when an individual's medical condition or pain shows signs of improvement based on a fake intervention that has been presented to them as a real one and used to be regularly dismissed by researchers as a psychological effect.
3. The placebo effect is not solely based on believing in treatment, however, as the clinical setting in which treatments are administered is also paramount.
4. That the mind has the power to trigger biochemical changes because the individual believes that a given drug or intervention will be effective could empower chronic patients through the notion of our bodies' capacity for self-healing.
5. Placebo effects are now studied not just as foils for "real" interventions but as a potential portal into the self-healing powers of the body.

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. Johnson treated English very practically, as a living language, with many different shades of meaning and adopted his definitions on the principle of English common law — according to precedent.
2. Masking a profound inner torment, Johnson found solace in compiling the words of a language that was, in its coarse complexity and comprehensive genius, the precise analogue of his character.
3. Samuel Johnson was a pioneer who raised common sense to heights of genius, and a man of robust popular instincts whose watchwords were clarity, precision and simplicity.
4. The 18th century English reader, in the new world of global trade and global warfare, needed a dictionary with authoritative acts of definition of words of a language that was becoming seeded throughout the first British empire by a vigorous and practical champion.
5. The Johnson who challenged Bishop Berkeley's solipsist theory of the nonexistence of matter by kicking a large stone ("I refute it thus") is the same Johnson for whom language must have a daily practical use.

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.
1. Although we are born with the gift of language, research shows that we are surprisingly unskilled when it comes to communicating with others.
2. We must carefully orchestrate our speech if we want to achieve our goals and bring our dreams to fruition.
3. We often choose our words without thought, oblivious of the emotional effects they can have on others.
4. We talk more than we need to, ignoring the effect we are having on those listening to us.
5. We listen poorly, without realizing it, and we often fail to pay attention to the subtle meanings conveyed by facial expressions, body gestures, and the tone and cadence of our voice.

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: Over the past fortnight, one of its finest champions managed to pull off a similar impression.
2. Wimbledon's greatest illusion is the sense of timelessness it evokes.
3. At 35 years and 342 days, Roger Federer became the oldest man to win the singles title in the Open Era — a full 14 years after he first claimed the title as a scruffy, pony-tailed upstart.
4. Once he had survived the opening week, the second week witnessed the range of a rested Federer's genius.
5. Given that his method isn't reliant on explosive athleticism or muscular ball-striking, both vulnerable to decay, there is cause to believe that Federer will continue to enchant for a while longer.

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. Those geometric symbols and aerodynamic swooshes are more than just skin deep.
2. The Commonwealth Bank logo — a yellow diamond, with a black chunk sliced out in one corner — is so recognisable that the bank doesn't even use its full name in its advertising.
3. It's not just logos with hidden shapes; sometimes brands will have meanings or stories within them that are deliberately vague or lost in time, urging you to delve deeper to solve the riddle.
4. Graphic designers embed cryptic references because it adds a story to the brand; they want people to spend more time with a brand and have that idea that they are an insider if they can understand the hidden message.
5. But the CommBank logo has more to it than meets the eye, as squirrelled away in that diamond is the Southern Cross constellation.

Data Interpretation & LRQ35–Q66 · 32 questions
35
Table based DI SetsEASY

How many Thin Crust pizzas were to be delivered to Party 3?

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36
Table based DI SetsEASY

How many Normal Cheese pizzas were required to be delivered to Party 1?

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37
Table based DI SetsMEDIUM

For Party 2, if 50% of the Normal Cheese pizzas were of Thin Crust variety, what was the difference between the numbers of T-EC and D-EC pizzas to be delivered to Party 2?

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38
Table based DI SetsMEDIUM

Suppose that a T-NC pizza cost as much as a D-NC pizza, but 3/5th of the price of a D-EC pizza.A D-EC pizza costs Rs. 50 more than a T-EC pizza, and the latter costs Rs. 500.
If 25% of the Normal Cheese pizzas delivered to Party 1 were of Deep Dish variety, what was the total bill for Party 1?

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39
ArrangementMEDIUM

How many elective courses among E1 to E6 had a decrease in their enrollments after the change process?

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40
ArrangementMEDIUM

After the change process, which of the following is the correct sequence of number of students in the six electives E 1 to E6?

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41
ArrangementMEDIUM

After the change process, which course among E1 to E6 had the largest change in its enrollment as a percentage of its original enrollment?

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42
ArrangementHARD

Later, the college imposed a condition that if after the change of electives, the enrollment in any elective (other than E7) dropped to less than 20 students, all the students who had left that course will be required to re-enroll for that elective.
Which of the following is a correct sequence of electives in decreasing order of their final enrollments?

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43
Quant Based DIMEDIUM

Among the three, Neeta received the least amount in bank deposits, while Geeta received the highest. The value of the assets was distributed equally among the children, as were the gold coins.
How much did Seeta receive in bank deposits (in lakhs of rupees)?

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44
Quant Based DIMEDIUMTITA

Among the three, Neeta received the least amount in bank deposits, while Geeta received the highest. The value of the assets was distributed equally among the children, as were the gold coins.

How many flats did Neeta receive?

45
Quant Based DIMEDIUM

The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1:2:3, while the gold coins were distributed among them in the ratio of 2:3:4. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in bank deposits.
How many gold coins did the old woman have?

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46
Quant Based DIHARDTITA

The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1:2:3, while the gold coins were distributed among them in the ratio of 2:3:4. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in. bank deposits.
How much did Geeta get in bank deposits (in lakhs of rupees)?

47
ArrangementEASY

Which of the following is NOT necessarily true?

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48
ArrangementMEDIUMTITA

What is the total cost of repairing the odd-numbered dorms (in Rs. Crores)?

49
ArrangementMEDIUMTITA

Suppose further that:
1. 4 of the 10 dorms needing repair are women's dorms and need a total of Rs. 20 Crores for repair.
2. Only one of Dorms 1 to 5 is a women's dorm.
What is the cost for repairing Dorm 9 (in Rs. Crores)?

50
ArrangementMEDIUM

Suppose further that:
1. 4 of the 10 dorms needing repair are women's dorms and need a total of Rs. 20 Crores for repair.
2. Only one of Dorms 1 to 5 is a women's dorm.
Which of the following is a women's dorm?

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51
ArrangementMEDIUMTITA

What was the second highest rating given?

52
ArrangementEASYTITA

What was the number of the cup that contained tea from Ooty?

53
ArrangementMEDIUM

If the tea from Munnar did not get the minimum rating, what was the rating of the tea from Wayanad?

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54
ArrangementMEDIUM

If cups containing teas from Wayanad and Ooty had consecutive numbers, which of the following statements may be true?

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55
2D & 3D LRMEDIUM

If the queen is at c5, and the other pieces at positions c2, g1, g3, g5 and a3, how many are under attack by the queen? There are no other pieces on the board.

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56
2D & 3D LRMEDIUM

If the other pieces are only at positions a1, a3, b4, d7, h7 and h8, then which of the following positions of the queen results in the maximum number of pieces being under attack?

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57
2D & 3D LRMEDIUM

If the other pieces are only at positions a1, a3, b4, d7, h7 and h8, then from how many positions the queen cannot attack any of the pieces?

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58
2D & 3D LRMEDIUM

Suppose the queen is the only piece on the board and it is at position d5. In how many positions can another piece be placed on the board such that it is safe from attack from the queen?

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59
ArrangementMEDIUM

In which row was Manik sitting?

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60
ArrangementHARD

How much extra did Jayanta pay for his choice of seat?

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61
ArrangementHARD

How much extra did Gargi pay for her choice of seat?

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62
ArrangementHARD

Who among the following did not pay any extra amount for his his/her choice of seat?

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63
PuzzlesHARDTITA

The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not.
How many different sequences of scans are allowed for any given person's original scan?

64
PuzzlesHARD

The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is also allowed, but LIMRT is not.
How many different sequences are allowed for any given person's original scan?

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65
PuzzlesHARDTITA

The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.
Suppose the lab allows a variation of the original sequence (of six inputs) where at most two scans (out of six) are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
How many different sequences of scans are allowed for any given person's original scan?

66
PuzzlesHARD

The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.
Suppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
How many different sequences of scans are allowed if the original scan sequence is LRLTIM?

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Quantitative AbilityQ67–Q100 · 34 questions
67
Probability, CombinatoricsMEDIUMTITA

The numbers 1, 2, ..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value.

If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is

68
Time, Speed and DistanceMEDIUMTITA

In a 10 km race, A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. I f A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?

69
Mixtures and SolutionsEASY

Bottle 1 contains a mixture of milk and water in 7: 2 ratio and Bottle 2 contains a mixture of milk and water in 9: 4 ratio. In what ratio of volumes should the liquids in Bottle 1 and Bottle 2 be combined to obtain a mixture of milk and water in 3:1 ratio?

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70
Time, Speed and DistanceMEDIUM

Arun drove from home to his hostel at 60 miles per hour. While returning home he drove half way along the same route at a speed of 25 miles per hour and then took a bypass road which increased his driving distance by 5 miles, but allowed him to drive at 50 miles per hour along this bypass road. If his return journey took 30 minutes more than his onward journey, then the total distance traveled by him is

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71
Averages, Ratio and ProportionEASY

Out of the shirts produced in a factory, 15% are defective, while 20% of the rest are sold in the domestic market. If the remaining 8840 shirts are left for export, then the number of shirts produced in the factory is

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72
Averages, Ratio and ProportionMEDIUM

The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

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73
Profit and LossEASY

The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30% Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is

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74
Time and WorkEASY

A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

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75
Profit and LossMEDIUM

Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?

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76
Averages, Ratio and ProportionMEDIUM

In a village, the production of food grains increased by 40% and the per capita production of food grains increased by 27% during a certain period. The percentage by which the population of the village increased during the same period is nearest to

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77
Averages, Ratio and ProportionEASY

If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?

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78
Time, Speed and DistanceEASY

A motorbike leaves point A at 1 pm and moves towards point B at a uniform speed. A car leaves point B at 2 pm and moves towards point A at a uniform speed which is double that of the motorbike. They meet at 3:40 pm at a point which is 168 km away from A. What is the distance, in km, between A and B7

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79
Time and WorkEASY

Amal can complete a job in 10 days and Bimal can complete it in 8 days. Amal, Bimal and Kamal together complete the job in 4 days and are paid a total amount of Rs 1000 as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

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80
Mixtures and SolutionsMEDIUM

Consider three mixtures — the first having water and liquid A in the ratio 1:2, the second having water and liquid B in the ratio 1:3, and the third having water and liquid C in the ratio 1:4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4: 3: 2. Then the resulting mixture has

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81
GeometryMEDIUM

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

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82
GeometryMEDIUM

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

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83
GeometryMEDIUM

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y =3x+c,then c is

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84
GeometryMEDIUMTITA

ABCD is a quadrilateral inscribed in a circle with centre O such that O lies inside the quadrilateral. If ∠COD=120\angle COD = 120∠COD=120 degrees and ∠BAC=30\angle BAC = 30∠BAC=30 degrees, then the value of ∠BCD\angle BCD∠BCD (in degrees) is

85
GeometryMEDIUMTITA

If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is

86
GeometryHARDTITA

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB,BC,and CA is 4(2−1)4(\sqrt{2}-1)4(2​−1) cm,then the area, in sq cm, of the triangle ABC is

87
Number SystemsMEDIUM

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

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88
Logarithms, Surds and IndicesMEDIUM

If x is a real number such that log⁡35=log⁡5(2+x)\log_{3}5= \log_{5}(2 + x)log3​5=log5​(2+x), then which of the following is true?

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89
Functions, Graphs and StatisticsEASY

Let f(x)=x2f(x) = x^{2}f(x)=x2 and g(x)=2xg(x) = 2^{x}g(x)=2x, for all real x. Then the value of f[f(g(x)) + g(f(x))] at x = 1 is

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90
InequalitiesMEDIUM

The minimum possible value of the sum of the squares of the roots of the equation x2+(a+3)x−(a+5)=0x^2+(a+3)x-(a+5)=0x2+(a+3)x−(a+5)=0 is

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91
Logarithms, Surds and IndicesMEDIUM

If 9x−12−22x−2=4x−32x−39^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}9x−21​−22x−2=4x−32x−3, then xxx is

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92
Logarithms, Surds and IndicesMEDIUMTITA

If log(2a×3b×5c)log(2^{a}\times3^{b}\times5^{c} )log(2a×3b×5c)is the arithmetic mean of log(22×33×5)log ( 2^{2}\times3^{3}\times5)log(22×33×5), log(26×3×57)log(2^{6}\times3\times5^{7} )log(26×3×57), and log(2×32×54)log(2 \times3^{2}\times5^{4} )log(2×32×54), then a equals

93
Progressions and SeriesMEDIUMTITA

Let a1,a2,a3,a4,a5a_{1},a_{2},a_{3},a_{4},a_{5}a1​,a2​,a3​,a4​,a5​ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a32a_{3}2a3​
If the sum of the numbers in the new sequence is 450, then a5a_{5}a5​ is

94
Linear EquationsHARDTITA

How many different pairs(a,b) of positive integers are there such that a≥ba\geq ba≥b and 1a+1b=19\frac{1}{a}+\frac{1}{b}=\frac{1}{9}a1​+b1​=91​?

95
Probability, CombinatoricsMEDIUMTITA

In how many ways can 8 identical pens be distributed among Amal, Bimal, and Kamal so that Amal gets at least 1 pen, Bimal gets at least 2 pens, and Kamal gets at least 3 pens?

96
Probability, CombinatoricsHARDTITA

How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?

97
Functions, Graphs and StatisticsMEDIUMTITA

If f(ab) = f(a)f(b) for all positive integers a and b, 

then the largest possible value of f(1) is

98
Functions, Graphs and StatisticsMEDIUM

Let f(x)=2x−5f(x) =2x-5f(x)=2x−5 and g(x)=7−2xg(x) =7-2xg(x)=7−2x. Then |f(x)+ g(x)| = |f(x)|+ |g(x)| if and only if

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99
Progressions and SeriesMEDIUM

An infinite geometric progression a1,a2,...a_1,a_2,...a1​,a2​,... has the property that an=3(an+1+an+2+...)a_n= 3(a_{n+1}+ a_{n+2} + ...)an​=3(an+1​+an+2​+...) for every n ≥\geq≥ 1. If the sum a1+a2+a3...+=32a_1+a_2+a_3...+=32a1​+a2​+a3​...+=32, then a5a_5a5​ is

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100
Progressions and SeriesMEDIUM

If a1=12×5,a2=15×8,a3=18×11,...,a_{1}=\frac{1}{2\times5},a_{2}=\frac{1}{5\times8},a_{3}=\frac{1}{8\times11},...,a1​=2×51​,a2​=5×81​,a3​=8×111​,..., then a1+a2+a3+...+a100a_{1}+a_{2}+a_{3}+...+a_{100}a1​+a2​+a3​+...+a100​ is

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