How to Prepare for Quantitative Aptitude for CAT (2014)

MODEL TEST PAPER

Section I: Quantitative Aptitude and Data Interpretation

Directions for Questions 12 and 13: A, B, and C are three persons on a circular track in random order. They start moving simultaneously with constant speeds such that after some time t, A, B, C are at the initial positions of B, C and A respectively (none of them having completed a full revolution during the time).

Questions (15 and 16): A group of students are asked to take at least one subject from Physics, Chemistry, and Mathematics for their courses.

Directions for Questions 21 to 23: Answer the questions on the basis of data given in the table:

The table below shows the sales and expenditure of three companies—KESARI foods, KASTURI foods and KABULI foods for the financial year 2004-2005. These companies are located in the different parts of the world. Expenditure break-ups are in percentage. Closely analyse the data and answer the questions.

* Sales to be read as ` million/month

* Sales break ups are in percentages (%)

Directions for Questions 24 to 27: Performance study of various brands of soap is given below with their cost/ 100 gm.

Benefit/Rupee spent for a soap is measured by a variable known as ‘R’ where

R₁ = S₁/C, R₂ = S₂/C, R₃ = S₃ /C and so on.

Directions for Questions 28 to 30: Given below is table indicating the individual scores of ten players of two different basketball teams in single match between them. Each had 5 players and all the scoring shots carried either two or three points. The team scoring the maximum points won. Players scored for their own teams only.

The difference between the lowest and the highest individual scores in both the teams is the same.

The highest individual scores from the teams had the same number of scoring shots.

Arun, Dhruv, Fardeen and Geetam had an even number of scoring shots comprising both 2 and 3 –pointers.

Birender, Eleswarappu, and Ishwar had an odd number of scoring shots comprising both 2 and 3 –pointers.

Chiranjeev was another player in his team to score 8 points in 4 shots.

Section Ii: Verbal Ability and Logical Reasoning

Passage I

In this passage from a novel, the narrator has been reading letters of his grandmother. Susan Ward was a young woman—a writer and a mother—whose husband Oliver was working as a mining engineer in Leadville, in the West. Here, the narrator imagines Susan Ward as she spends the winter with her family in Milton, New York, before rejoining her husband in the spring.

From the parental burrow, Leadville seemed so far away that it was only half-real. Unwrapping her apple-cheeked son after a sleigh ride down the lane, she had difficulty in believing that she had ever lived anywhere but here in Milton.

She felt how the placid industry of her days matched the placid industry of all the days that had passed over that farm through six generations. Present and past were less continuous than synonymous. She did not have to come at her grandparents through a time machine. Her own life and that of the grandfather she was writing about showed her similar figures in an identical landscape. At the milldam where she had learned to skate she pulled her little boy on his sled, and they watched a weasel snow-white for winter flirt his black-tripped tail in and out of the mill’s timbers. She might have been watching with her grandfather’s eyes.

Watching a wintry sky die out beyond black elms, she could not make her mind restore the sight of the western mountains at sunset from her cabin door, or the cabin itself, or Oliver, or their friends. Who were those glittering people intent on raiding the continent for money or for scientific knowledge? What illusion was it that she bridged between this world and that? She paused sometimes; cleaning the room she had always called Grandma’s Room, and thought with astonishment of the memory of Oliver’s great revolver lying on the dresser when he, already a thoroughing Westerner, had come to the house to court her.

The town of Milton was dim and gentle, molded by gentle lives, the current of change as slow through it, as the seep of water through a bog. More than once she thought how wrong those women in San Francisco had been, convinced that their old homes did not welcome them on their return. Last year when Oliver’s professional future was uncertain, she would have agreed. Now, with the future assured in the form of Oliver’s appointment as manager of the Adelaide mine in Leadville, the comfortable past asserted itself unchanged. Need for her husband, like worry over him, was turned low. Absorbed in her child and in the writing of her book, she was sunk in her affection for home. Even the signs of mutability that sometimes jolted her—the whiteness of her mother’s hair, the worn patience of her sister’s face, the morose silences of her brothers-in-law, now so long and black that the women worried about him in low voices—could not more than briefly interrupt the deep security and peace.

I wonder if ever again Americans can have that experience of returning to a home place so intimately known, profoundly felt, deeply loved, and absolutely submitted to. It is not quite true that you can’t go home again. But it gets less likely. We have had too many divorces, we have consumed too much transpiration, we have lived too shallowly in too many places. I doubt that any one of my son’s generation could comprehend the home feelings of someone like Susan Ward. Despite her unwillingness to live separately from her husband, she could probably have stayed on indefinitely in Milton, visited only occasionally by an asteroid husband. Or she would have picked up the old home and remade it into a new place. What she resisted was being a woman with no real home.

When frontier historians theorize about the uprooted, the lawless, the purseless, and the socially cut-off who emigrated to the West, they are not talking about people like my grandmother, so much that was cherished and loved, women like her had to give up; and the more they gave it up, the more they carried it helplessly with them. It was a process like ionization: what was subtracted from one pole was added to the other. For that sort of pioneer, the west was not a new country being created, but an old one being reproduced; in that sense our pioneer women were always more realistic than our pioneer men. The moderns, carrying little baggage of the cultural kind, not even living in traditional air, but breathing in to their space helmets, a scientific mixture of synthetic gases (and polluted at that) are the true pioneers. Their circuitry seems to include no domestic sentiment; they have had their empathy removed. Their computers have no ghostly feedback of home, Sweet Home. How marvelously free they are! How unutterably deprived!

Passage II

When one company acquires another, the larger firm usually takes over the smaller one. There are exceptions to the rule, however, such as the Good—Value Mart merger.

Once the leading chain of supermarkets in New England, Good Food Stores has been steadily declining for twenty years. Their sales fell from 25 per cent to 5 per cent of the market. During the same period (1958-1978), earning plunged from over 8 million to a loss of 23 million. With such a track record, Good Food stores hardly seemed a likely candidate for acquisition.

But the Midwest-based Value Mart chain acquired Good Food earlier this year with high hopes of turning around the New England chain. Value Mart is a privately owned chain of supermarkets, with approximately sixty stores throughout the Midwest. The average sales for last year ran a little over 6 million per store. On the other hand, Good Food is a publicly held company that averaged sales of 4 million in each of its 230 stores. In the last five years, Value Mart’s earnings reached nearly 15 million, while Good Food lost 40 million during that same period.

The chairman of Value Mart, Harold Brown, is an old hand at putting ailing supermarkets back on their feet. In 1963, Mr. Brown helped turn around an old Cincinnati chain; he changed it from an unprofitable, out of date store to a market leader with a profit of 7 million in just six years. After leaving the Cincinnati chain, Brown, along with thirty other investors, bought Value Mart and turned it around, so that in the past year it has surpassed even the Cincinnati chain in sales. Brown’s two success stories now account for 60 percent of the supermarket business in the Cincinnati area.

Although Brown’s track record has been good (and was, In fact, the reason Value Mart was able to obtain the necessary funds to acquire Good Food), there has been some speculation on whether Value Mart has undertaken more than it can handle. A powerful New England trade member wonders whether Value Mart has the know-how and strength to take on the leading established New England chains.

Good Food’s problems started in the late 1950’s and early 1960’s, when they failed to follow their competitors move to the suburbs and large shopping centers. This put Good Food behind in market share.

Good Food then made another bad move in 1962 in an attempt to regain some of its lost market share. They acquired a wavering division of supermarkets in the New York area and tried to establish themselves there, while maintaining a policy of low investment and high prices back home in New England. The strategy did not work, and consequently Good Food had to pull to out of New York. In addition, Good Food has lost customers in New England.

Good Food’s woes were increased by mismanagement. Complacent task forces were formed to “study” problems instead of dealing with them immediately. Coupled with this was a group of directors who were, for the most part, not industry experts but bankers and lawyers.

The choices facing Good Food in 1976 were as follows: sell, if possible; liquidate; or push onwards. The decision was made to seek a merger partner, and Value Mart was contacted through Good Food’s investment counselor. Given Good Food’s unpromising situation, it seems surprising that Value Mart was interested. Mr. Brown, however, fresh out of a Cincinnati price war, realized that his home market was saturated and that acquisition or territorial expansion was the necessary means for growth.

Value Mart took charge of the situation and began to reorganise even before the merger was completed. Their top executives took over key positions in the Good Food organisation, a move that included ousting Good Food’s president. In an attempt to drastically cut down on administrative expenses, over two hundred jobs at the management level were abolished. (it is expected that this alone will result in savings of over 3 million).

Another change was placing control of grocery merchandising and buying in the hands of those at the corporate level, rather than dividing this function amongst Good Food’s store managers and executives. This facilitated the introduction of Value Mart’s tried-and-true policy of “deal buying,” or taking advantage of cut-rate prices to buy huge quantities of canned or packaged goods. Because “buying” in such quantity necessitates ample inventory space, construction was begun the day after the merger, to increase Good Food’s warehousing facilities to the tune of 7 million. The new warehouse will be the largest supermarket warehouse in the United States, and it is expected to save in cost and avoid out-of-stock problems.

The Value Mart strategy for turning around the New England chain also involves deemphasizing nonfood items and hence attracting customers by placing emphasis on the quality of its produce (fruits and vegetables) and meats. Problems at the store level are being corrected by extending work hours at individual stores, cleaning up dirty premises(Good Food had reduced personnel in its stores in an attempt to cut labor costs, resulting in dirty stores and low morale among the employees), and teaching store managers how to repackage and maintain their fresh produce.

Visits to each Good Food store by a Value Mart senior vice-president of operations resulted in control and, equally as important, a demonstrated and direct interest by top management in individual store operations.

This top-level involvement in daily store routine is a far cry from the old Good Food “hands off” approach. The Midwestern senior vice-president not only visits each store to make suggestions, but also comes back unannounced to check on the implementations of changes.

Mr. Brown’s immediate objective is to increase business from present customers. He estimates an increase in volume of over 100 million if sales per customer can be improved by only 10 percent. Once sales are up and stores are operating smoothly, Brown plans to renovate about sixty-five of Good Food’s largest stores, a move that should bring in an additional 6- 7 million in weekly sales.

Finally, the older and smaller Good Food stores will be given a facelift with the increased revenue from the redone larger stores. Value Mart intends to feed its profits back into the entire operation to keep it going and constantly moving ahead.

Directions for Questions 44 to 46: The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.

Directions for Questions 47 to 50: Fill in the blanks with the appropriate words from the options given below.

For Questions 51 to 55 read the following instructions: Sunday morning, local pediatrician Dr. Raju Sarma had appointments with five infants scheduled at 9:00, 9:30, 10:00, 10:30, and 11:00. Each of the five, including the Oke baby, is a different number--1, 2, 3, 4, or 5--of months old. The following notes are available.

Directions for Questions 56 to 58: Read the information given below and answer the questions that follow.

Four men - Amar, Bijay, Chetan and Derek and four women - Preeti, Queen, Raveena and Surabhi are sitting for a formal get together, in such a way that they face the centre and form a circle. No two women and no two men are next to each other, Amar is to the immediate left of Raveena, who is opposite to Queen. Preeti and Queen have only Chetan dancing between them. Preeti is sitting opposite to Surabhi, who is sitting to the immediate right of Bijay.

Directions for Questions 59 and 60: Six persons-Akshay, Bobby, Celina, Dimple, Esha, and Faisal took up a job with XYZ Consultants in a week from Monday to Saturday. Each of them joined for different posts on different days. The posts were of-Clerk, Officer, Technician, Manager, Supervisor and Sales Executive though not in the same order.

Faisal joined as a Manager on the first day. Bobby joined as a Supervisor but neither on Wednesday nor Friday. Dimple joined as a Technician on Thursday. The officer joined the firm on Wednesday. Esha joined as a clerk on Tuesday. Akshay joined as a Sales Executive.

Solutions

Section I

1.Let us look at the two equations. Let (7 apples + 9 oranges + 5 guavas) cost ` x … (1). Hence, (11 apples + 18 oranges + 10 guavas) will cost ` 1.75x … (2). Had, in the second case, Rajan decided to buy 14 apples instead of 11, the quantity of each one of them would have doubled over the first case and hence it would have cost me ` 2x. So (14 apples + 18 oranges + 10 guavas ) = ` 2x … (3)

Now subtracting the second equation from the third, we get 3 apples cost ` 0.25x. Since 3 apples cost Re 0.25x, 7 of them will cost Re 0.583x. This is the amount that I spent on apples. Hence, fraction of the total amount paid = 0.583 = 58.3%.

Hence, Option (c) is correct.

2.Let |x – 2|= y

y² + y – 2 = 0

y = -2,1

|x – 2|= 1

x – 2 = 1, x – 2 = -1

x = 3, 1

sum of roots=4

Hence, Option(a) is correct.

3.Squaring the given equation

x + 1 + x – 1 – 2(x² – 1)^0.5 = 4x – 1

4(x² – 1) = 4x² + 1 – 4x

x = 5/4

but this value of x does not satisfy the given equation

Hence, Option (a) is correct.

4.case 1: ⁴C₃ ⁴C₃ = 16

case 2: ( ⁴C₂ ³C₁ )(³C₁⁴C₂) = 324

case 3: ( ⁴C₁³C₂ )(³C₂⁴C₁) = 144

case4: ³C₃ ³C₃ = 1

total = 485

Hence, Option (d) is correct.

5.Since no box remains empty possible balls can be distributed in manner(2, 2, 1) or (3, 1, 1)

i.e. (⁵C₂ ³C₂ ¹C₁ + ⁵C₃ ²C₁ ¹C₁)3! = 300

Hence, Option (c) is correct.

6.solution nth term = n/(1 + n² + n⁴) = n/((n² + 1)²-n²) = n/(n² – n + 1)(n² + n + 1)

½(1/(n² – n + 1)–1/(n² + n + 1))

sum =1/2

Hence, Option (b) is correct.

You can also solve this question using values.

7.The ratio of the speeds of Ishant and Ganguly is 2 : 1. Hence they should meet at only

one point on the circumference i.e. the starting point (As the difference in the ratio in reduced form is 1). For the two of them to meet for the first time, Ishant should have completed one complete round over Ganguly. Since the two of them meet for the first time after 3.5 mins, Ishant should have completed 2 rounds (i.e. 2000 m) and Ganguly should have completed 1 round. (i.e. 1000 m) in this time. Thus, Ishant would complete the race (i.e. 4000 m) in 7 min. Hence, Option (d) is correct.

8.Lets say one boy can do the x part of the work in 1 day.. On the first day only 1 boy works, he can do xth part of the work. On the second day 2 more join him...together the boys can do x(1 + 2) of the work on second day. On third day 3 more boys join the group...they can do x(1 + 2 + 3) part o the work on 3rd day....and so on...Hence we have the sum x(1) + x(1 + 2) + x(1 + 2 + 3).....so on till 25 terms = 1 (as the work is completed in 25 days) now this is nothing but the summation x * sigma[n(n + 1)/2] from n = 1 to n = 25 this can be spit into x/2*(sigma (n^2) + sigma(n)) n = 1 to n = 25 applying formula for sigma(n ^ 2) = n(n + 1)(2n + 1)/6 and sigma(n) = n(n+ 1)/2 and substituting n = 25, we get x*2925 = 1 or x = 1/2925. Hence one boy can do the work in 2925 days. One man can do it in half the no. of days, ie 1462.5 = 1463 days. and so 10 men can do it in 146.3 = 147 days.

Hence, Option (d) is correct.

9.The possibilities are:

1,2,10

1,3,9

1,4,8

1,5,7

2,3,8

2,4,7

2,5,6

3,4,6

When Twinkle is not able to respond after seeing the left most card, we can assume that 3, 4, 6 was not the correct order. Akshay knows this when he sees his card, and hence he must not have seen any of 10,9 or 6. This leaves us with the possible combinations 1, 4, 8;

1, 5, 7; 2, 3, 8 and 2, 4, 7. If Raveena had seen a 3 or 5 she would have known all the cards. Since she does not answer, she must have seen a 4 on the middle card.

Hence, Option (c) is correct.

10.The sum of the positives is 25 and the negatives is 17. The best way to distribute the +8 is 5 and 3 by taking 13, 2, –5 and –7 in the first bracket and the remaining values 4, 6, –2 and –3 in the second bracket. The required answer would be 34.

Hence, Option (a) is correct.

11.The values at which this would occur would be X = 24% and Y = 29%.

Hence, Option (b) is correct

12.This question is based on the concept that the net distance travelled by all three of them (added up) together is going to be either 1 full round (For the circular order ABC) or 2 full rounds (For the circular order ACB). It can be seen that with the given times for completing a round, if t = 120, then the net distance covered by them is equal to 1 complete round. For t = 240 seconds it becomes two complete rounds.

Hence, Option (d) is correct.

13.Using the logic that the net distance traveled by all three of them (added up) together is going to be either 1 full round (For the circular order ABC) or 2 full rounds (For the circular order ACB). Since, all three of them are at their respective starting points after an hour, the times required by each of them must be a factor of 60 minutes. (& Can only be 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 or 60 minutes). With these values, we can see that for t equal to 10,12 or 15 minutes it is possible to have either 1 complete round or 2 complete rounds as the total distance traveled by all three of them. Only 18 minutes gives no possibility of creating a total of 1 complete round or 2 complete rounds. Option (d) is correct.

14.Plot the graph of the three lines and realize the maximum point for f(x) would be at the intersection of x + 2 and -2x + 4. This occurs at x = 2/3, and f(x) is 8/3 at that point. Hence, Option (d) is correct.

15.Solve using options. If you put 9 in the middle (all three) you get 36 for only Physics & Physics+ 1 more subject. Similarly, 35 for only Chemistry & Chemistry+ one more subject, 39 for Mathematics & Mathematics + 1 more subject.

The sum of these numbers should be equal to [number of students taking only 1 subject + 2 times number of students taking exactly two subjects] = 50 + 30 + 30 = 110.

Since, 36 + 35 + 39 is also 110, this is the correct answer. The other options won’t work here.

Hence, Option (a) is correct.

16.If you were to plot a venn diagram for this question you would realize that we do not know the number of students having only Physics and Chemistry, Only Chemistry and Mathematics and also only Physics and Mathematics. Also, we do not know the value of the total number of students. Hence, we cannot determine the answer to this question. Hence, Option (d) is correct.

17.The required sum would be given by: (1/99 + 2/99 +….+ 98/99) – (11/99 + 22/99 +…+ 88/99)– (9/99 + 18/99 + … 90/99) = 40. Option (b) is correct.

18.We have to find the value of n for which 3ⁿ > 900 Æ n > 7

Hence, Option (c) is correct.

19.g(x)>1 for all x

f(g(x)) =1

Option (c) is correct.

20.When we expand 30!...we get 1 × 2 × 3 ... 30. 2²⁶ × 3¹⁴ × 5⁷ × 7⁴ × 11² × 13² × 17¹ × 19¹ × 23¹ × 29¹

From this list it is clear that the constraint for the maximum value of n would be either due to the 2’s, the 3’s, the 5’s or the 29’s.

301! has 150 + 75 + 37 + 18 + 9 + 4 + 2 + 1 = 296 twos and hence has [296/26]=11 instances of 2²⁶.

301! has 100 + 33 + 11 + 3 + 1 = 148 threes and hence has [148/14]=10 instances of 3¹⁴.

301! has 60 + 12 + 2 = 74 fives and hence has [74/7] = 10 instances of 5⁷.

301! has 10 instances of 29¹.

Hence, the correct answer would be 10. Hence, Option (d) is correct.

21.It can be seen that Option (b) is correct, as the expenditure of Kesari Foods on these 4 categories are 4.575 while the combined expenditure of Kasturi and Kabuli is lower than that. Hence, Option (b) is correct.

22.If there is a 1% reduction in interest, there would be an increment of 0.0075 million in the operating profit. Hence, Option (c) is correct.

23.0.12 × 6900000/9517.24 = 87. Hence, Option (d) is correct.

24.Soap Effectiveness Index for B₁ is (199/100)/100 = 0.0199

Soap Effectiveness Index for B2 is (152/50)/100 = 0.0304

Soap Effectiveness Index for B3 is (212/50)/100 = =0.0424

Soap Effectiveness Index for B4 is (232/25)/100 = =0.0928

Soap Effectiveness Index for B5 is (139/100)/100 = =0.0139

Hence, B₁, B₂, B₃, B₄ is the correct order.

Option (a) is correct.

25.Quality wise the value of R₁, R₂, R₃, R₄ and R₅ are all maximum only for B4. Hence, the correct option is None of these. Option (d) is correct.

26.B3 is better than B₄ in S₁ and S₂ only. For all other values, B₄ has a higher value (in spite of the scheme which has the effect of B₄’s cost coming down to 40.) Option (c) is correct.

27.Only Brand B₃ satisfies the first condition (of having the highest value in at least 3 of the first four categories- however, the brand does not satisfy the other criteria. Hence, Option (d) is correct.

28.The only way to divide the teams would be given by the following table:

Further, Hasan and Jeetu having the same number of scoring shots means three possibilities for them:

Based on the above tables we can conclude that the difference between the number of 3 pointers would always be 6.

Hence, Option (c) is correct.

29.The only way to divide the teams would be given by the following table:

Further, Hasan and Jeetu having the same number of scoring shots means three possibilities for them:

Based on the above tables we can conclude that the difference between the number of 2 pointers and 3 pointers for the teams could be either 0, 10 or 20. Only option (d) gives a possible value of this difference.

30.The only way to divide the teams would be given by the following table:

From the above table, it is clear that Fardeen has the highest ratio of 2.66.

Option (d) is correct.

Section II

31.Option (b);The phrase is used in order to suggest the peaceful atmosphere.

32.Option (b); Third paragraph, second line clearly suggests that the writer’s life resembled his grandparents’

33.Option (c); She was imitating her grandfather.

34.Option (b); In the whole fifth paragraph, the reference is being given to the peace in milton.

35.Option (d); As per the paragraph 5^th, the Ward was free to enjoy her life.

36.Option (c);[clearly mentioned in the passage]

37.Option (c) This is an indirect question and the answer lies in the 8^th and 9^th paragraph.

38.Option (c) Given in sixth paragraph

39.Option (c) This is also gives in the seventh paragraph

40.Option (a) This is given in the tenth paragraph

41.Option (b)This is given in the eleventh paragraph

42. The correct answer is option (b). [This is clearly an irrelevant option]

43.The correct answer is (b).[this is the summary which covers the main idea.]

44. In the above paragraph, the starting sentence is already defined. The sentence sequence 1DA is using a double contrast- A kind of flip flop argument. Statement D opposes(contrasts) the idea of 1, while statement A again contrasts the opposition of D. In this question, recognizing this structure is sufficient to get to the correct answer. Option (d) is correct.

45.In the above question, the key sentence sequence is the BA sequence, which is in the form of an idea transformation since, B introduces the concept of the component parts, while A refers to these components in a different context altogether. Hence, the correct answer is option (b).

46.The sentence sequence AB is in the form of an idea elaboration, while the sentence sequence DC is in the form of generic to specific. Hence, the correct answer is (a).

47.Option (c) [assented in the sense of agreed]

48.Option (b) [given permission, thus authorised is the answer]

49.Option (d) [ in the sense of - to forgive]

50.Option (a) [ in the sense of disagree/not allow]

51.Option (d) is correct.

52.Option (b) is correct.

53.Option (c) is correct.

54.Option (c) is correct.

55.Option (a) is correct.

Solutions for 56 to 58:

The two possible distributions of the eight in clockwise fashion are:

Possibility 1: APCQDSBR

Possibility 2: ASBQCPDR

Based on these arrangements the answers are:

56.This case is referring to possibility 2. Derek would be opposite Bijay ( gap of 3 people between any 2 opposite persons on the table). Option (d) is correct.

57.Possibility 2 is reflected in Option (b). Hence, Option (b) is correct.

58.Preeti and Surabhi are always opposite each other as are Queen and Raveena (in both cases). Hence, Option (d) is correct.

Solutions for 59 to 60:

Six persons A, B, C, D, E & F on six days, Monday to Saturday, six posts –Clerk (C), Officer (O), Technician (T), Manager (M), Supervisor (S) and Sales Executive (SE).

The second paragraph gives the clues directly to fit in the following table:

We also know that the officer joined on Wednesday. It can only be Celina (C). Thus, the table will look like:

Thus, the answers are:

59.Celina. Option (b) is correct.

60.Bobby. Option (c) is correct.