Cl Mock Cat 10 Key 2008

Mock CAT – 10

Answers and Explanations 1

2

2

3

3

1

4

5

5

2

6

3

7

4

8

4

9

5

10

4

11

2

12

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13

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14

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1

17

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18

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19

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20

5

21

3

22

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23

2

24

1

25

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26

5

27

3

28

4

29

1

30

4

31

3

32

2

33

5

34

4

35

2

36

3

37

1

38

4

39

5

40

2

41

1

42

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43

3

44

5

45

5

46

1

47

3

48

5

49

2

50

4

51

4

52

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53

4

54

5

55

2

56

3

57

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58

2

59

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60

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61

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62

4

63

3

64

1

65

2

66

5

67

3

68

2

69

3

70

4

71 81 91 101

1 4 4 3

72 82 92 102

2 1 1 4

73 83 93 103

1 1 5 5

74 84 94 104

1 3 4 3

75 85 95 105

5 2 1 2

76 86 96

1 3 2

77 87 97

5 1 2

78 88 98

2 4 2

79 89 99

3 3 5

80 90 100

3 2 3

MY PERFORMANCE Total Time Taken Total Correct Incorrect Net Questions (Min) Attempts Attempts Attempts Score Logical Reasoning based Data Interpretation Language Comprehension and English Usage Quantitative Ability TOTAL

Section Section Section Section Section Section

A B A B A B

20 15 20 15 20 15 105

150

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MCT-0014/08 010

1

For question 1 to 5: Let the total number of Linen shirts manufactured by all the given companies = X. Therefore, the number of Linen shirts manufactured by the companies

5. 2

Referring to the solution given above it can be concluded that only statement II is correct as shown in the table above.

6. 3

Options 1, 2, 4 and 5 are exaggerated conclusions. Only option 3 can be inferred from the paragraph. The fact that Washington post has taken the bold decision in response to the blogger-mentality indicates option 3.

7. 4

If option 4 is true, then traffic cannot be a determinant of whether one is socialising or not.

8. 4

Option 1 cannot be inferred from the paragraph. If it was easy to understand babies then there would be no need for research on this area. Option 3 goes beyond the scope of the passage as the passage focuses on infant behaviour. The word ‘impossible’ is extreme in the context. Option 5 cannot be inferred as no such comparison of behaviour has been indicated in the passage. Option 4 is a reasonable inference from the paragraph as it talks of babies using self-understanding to understand others.

9. 5

A, B and C are too definitive and general. They go beyond the scope of the paragraph. Regarding A, Rousseau has nowhere hinted that inequality is good. Or that it has hampered human evolution(B). We can at best infer from the paragraph that modern political institutions have created inequality or are unequal. C is a far-fetched conclusion.

10. 4

Anna continues serving Normal Indian food in the first three days though customers are disgruntled. The next 3 days consist of special food which is costlier. This shows that Anna is assuming that 3 days of special food would be enough to retain customers. Hence option 4 is being assumed by Anna.

11. 2

It is given that if either Salsa or Techno is chosen, then Odissi is not chosen. So if Odissi is chosen we can be sure that both Salsa and Techno are not chosen by Raman.

12. 4

Option 4 directly follows from the given question.

13. 2

The inference is definitely true as seen from the question where Parrots becomes a subset of frogs.

14. 4

Option 4 is the correct interpretation of the question statement.

15. 3

Since only club members are allowed inside the club premises, option 3 is false.

X X X 3X respectively. P, Q, R and S is , , and 4 4 5 10 Therefore, the total number of shirts manufactured by the companies P, Q, R and S is

5X 5X 4X 6X respectively. , , and 6 4 3 5

1. 2

Therefore the total number of shirts manufactured by the company Q is the second largest.

2. 3

Assume that the total number of Linen shirts manufactured by all the companies is 100. Therefore, the total number of Linen shirts manufactured by the companies P, Q, R and S is 25, 25, 20 and 30 respectively. The following table lists down the number of shirts of each type of cloth manufactured by each of the companies, when the total number of Linen shirts manufactured is 100.

Company

Silk

Cotton

Polyester

Total

P

15

20

Linen Khadi 25

10

13.33

83.33

Q

37.5

25

25

18.75

18.75

125

R

40

28

20

16

29.33

133.33

S

22.8

19.2

30

24

24

120

Therefore, for the number of shirts of each type of cloth to be an integer we need to convert all the decimal values in the table to the nearest integer. Minimum possible number of shirts manufactured by all the companies = (83.33 + 125 + 133.33 + 120) × 60 = 27700. 3. 1

Given that the difference between the profit generated by both the companies is Rs.15000. From the explanation given above, the number of shirts manufactured by the companies Q and S is

5X 6X and 4 5

respectively. Difference in the profit generated by the two companies Q and S will be

5X 6X X 15000 − = = = 1500. 4 5 20 10

⇒ X = 3 × 104

Difference between the number of Poleyster shirts manufactured by the companies P and R is

(

)

4 × 3 × 104  16 5X   22 4X  4X = 960  100 × 6  –  100 × 3  = 25 = 25     4. 5

2

Let the profit per Khadi shirt and per Cotton shirt be 3y and 4y respectively. Assume that the company R manufactures 400 shirts. So, total profit generated by selling Khadi shirts will be 48 × 3y = 144y and the total profit generated by selling Cotton shirts will be 84 × 4y = 336y. Required ratio is 7:3.

010

Therefore, Y + 2x + 7x = 720 and Y cannot be more than 6 + 6 = 12. So, the value of ‘x’ can be 80 or 79. Required difference 500 – 2x – (688 – 7x) = 5x – 188 If ‘x’ is equal to 80, then the required difference is 212 and if ‘x’ is equal to 79, then the required difference is 207.

For questions 16 to 20: It is clear that C + F + H + B + S + V = 18 Also, from the bar – graph, the value of C, F, B, H and V is 3, 2, 5, 2 and 4 respectively. Therefore, S = 18 – (3 + 2 + 5 + 2 + 4) = 2. Since, the number of siblings who chose Basketball is 5 and there are exactly three sports that have not been chosen by Aslam as well as Ahmad (Additional information II), therefore, Aslam as well as Ahmad chose Basketball. Also, form additional information II, Aslam and Azhar chose Cricket and Swimming. Since, the number of siblings who chose Volleyball is 4, therefore except for Ahmad and Azhar, every other sibling chose Volleyball. Since, Armaan did not choose Basketball and there is one sport that has not been chosen by Armaan but is chosen by Atif, therefore that sport is Basketball. Also, the three sports chosen by Armaan are Football, Hockey and Volleyball.

Azhar

Atif

Aslam

Aaqib

Armaan

Ahmad

Cricket

Yes

No

Yes

No

No

Yes

Football

No

No

Yes

No

Hockey

No

No

Yes

No

Basketball

Yes

Yes

Yes

Yes

No

Yes

Swimming

No

No

Yes

No

No

Yes

Volleyball

Yes

Yes

No

Yes

Yes

No

16. 1

The value of 6 – S = 6 – 2 = 4.

17. 4

From additional information (III): Ahmad chose Cricket and Swimming. In additional information (II) it is given that there are exactly two sports that have been chosen by Azhar as well as Aslam. Since, the number of siblings who chose Swimming is 2; therefore Azhar definitely chose Cricket and Basketball.

18. 3

Except for Atif and Aaqib, for every other sibling the sports chosen by them can be uniquely determined. Hence, the required answer is 4.

19. 2

Aslam did not play Volleyball.

20. 5

It cannot be uniquely determined.

For questions 23 and 24: Given that all the bottles containing one or the other of the three acids namely Sulphuric, Nitirc and Nitrous are in one or the other of the three categories S, M and L. Total number of bottles containing one or the other of three acids namely Sulphuric, Nitric and Nitrous acid is 384 + 367 + 402 = 1153 Total number of bottles of acids in the three categories S, M and L = 360 + 600 + 240 = 1200. Difference = 1200 – 1153 = 47. 23. 2

Out of the options given only option (2) can be a possible ratio of a: b: c.

24. 1

Maximum possible value of ‘a’ could be 47. So, in order to minimize the number of bottles of Benzoic acid in Lab 2 that do not belong to any of the three categories S, M and L we need to maximize the number of bottles of Benzoic acid that belong to one or the other of three categories S, M and L. So, required answer is 123 – 47 = 76.

25. 4

Average number of bottles per variety of the mentioned acids is 400. Therefore, number of bottles of Sulphuric, Nitric and Salicylic acid is less than the average number of bottles per variety of acid.

For questions 26 to 30: The total number of participants in the surveys conducted in each of the three market segments is 1000. The exact number of participants selecting the four options, across the three market segments is given in the following table.

Market Segments

For questions 21 to 25: For questions 21 and 22: Given that In Lab 2 as well as Lab 3, the number of bottles of acids in the category XL as a percentage of the total number of bottles of acids in the respective laboratories is not more than 1%. 21. 3

A maximum of 6 bottles each in Lab 2 and Lab 3 can be in the category XL. Also, a maximum of 688 bottles in Lab 4 can be in the category XL. So, in Lab 1, the number of bottles of acid in the category XL cannot be less than 720 – 6 – 6 – 688 = 20 Required percentage =

22. 4

010

20 × 100 = 4% 500

Let the number of the number of bottles of acids in Lab 1 and Lab 4 that are in the category XL be ‘2x’ and ‘7x’ respectively. Therefore, the number of bottles of acids in Lab 1 and Lab 4 that are not in the category XL will be ‘500 – 2x’ and ‘688 – 7x’ respectively. Also, let the number of bottles of acids in Lab 2 and Lab 3 that are in category XL be ‘Y’.

P

Q

Villages

95

390

135 380 1000

Towns

210

220

220 350 1000

Metros

180

405

230 185 1000

Total

R

S

Total

485 1015 585 915 3000

The two observations made by the brand manager, hold true only for the following four cases.

Possible P Q Cases Case I Cream Rejected All

R

S

Chilly

Mint

Cream

Mint

Case II

Chilly

Rejected All

Case III

Mint

Chilly

Rejected All Cream

Case IV

Mint

Cream

Rejected All

26. 5

Chilly

If the statement given in the problem is true, then the selection of option P, in the survey form, must indicate that the participant had liked the Mint flavour, the least. Accordingly, either Case III or Case IV could be true and the two flavours-(Chilly & Cream) must be indicated by the two options-(Q & S) but their exact order cannot be concluded. Further, selection of option R, in the survey form, indicated that the participant had rejected all the three flavours. Hence none of the options (1) or (2) or (3) or (4) can definitely be concluded but option (5) can definitely be concluded.

3

27. 3

28. 4

29. 1

If the statement given in the problem is true, then option P given in the survey form must indicate Cream flavour. Accordingly, only Case I is valid. Statement given in option (3) is definitely false as the minimum number belonged to the market segment, Towns. From the problem statement. We can conclude that option P in the survey form, indicates Mint flavour. Accordingly, options Q and S could indicate Chilly and Cream flavours. Option R indicated rejection of all the three flavours. Note that, in any of the given market segments, the number of participants who selected neither option P nor Q is the sum of the number of participants who selected either option R or options S. Each of the five answer options can be verified. Option (4) is correct.

L9

L8

L2

L13

6 levers

10 levers

6 levers

8 levers

I

Conclusion P indicated selection of Cream flavour.

III

S indicated selection of Chilly flavour.

IV

Either Q or R indicated selection of Cream Flavour. P indicated selection of Mint flavour.

V

Statements I, III, IV and V can simultaneously be true. Hence option (1) is the correct answer. Only Chilly and Cream flavours can be simultaneously selected for large scale productions. Hence (4) is correct.

L1

L7

L8

L4

L11

L4

Day 2

L3

L15

L14 L12

L8

L12

Day 3

L2

L7

L15

L9

L10

L7

Day 4

L15

L13

L10

L3

L6

Day 5

L2

L15

L9

L10

L5

Day 6

L13

L6

L1

L8

L10

Day 7

L14

L11

L8

L2

L13 L8

Day 8

L5

L6

L10 L14 L11

L3 L15

L1

8 levers

L7

6 levers

6 levers

L8

10 levers L14 6 levers

L3 10 levers

L9

6 levers

L4

L10 10 levers

8 levers

L3

L4

L7

L12

8 levers

6 levers

10 levers

31. 3

On five days, i.e. Day 1, Day 2, Day 3, Day 4 and Day 6 it can be uniquely determined which lock has been unlocked by Devendra.

32. 2

For the aggregate levers to be minimum and also out of the locks unlocked by him, the number of locks having six levers has to be less than the number of locks having eight levers. Hence, the only possible case is

6 levers

Day 7

Day 8

8

8

6

Day 5 Day 7 Day 8 Case 1

8

6

10

24

Case 2

8

8

10

26

Case 3

6

8

10

24

Not Possible Case 4

6

10

10

26

Case 5

8

10

6

24

Case 4 is not possible because out of the locks unlocked by him, the number of locks of 6 levers is less than the number of locks of 8 levers. 33. 5

Out of the given locks, it cannot be confirmed which one was unlocked by Devendra.

34. 4

If L9 is not unlocked, then L15 is definitely unlocked by Devendra on Day 5 and also L8 is unlocked by Devendra on Day 7. This confirms that it is Case 5 The lock that has 6 levers from the choices available on Day 8 is either L6 or L14. So, one out of these two locks is definitely unlocked by Devendra. Option (4) is the correct choice.

35. 2

If out of out of the locks unlocked by him, the number of locks of 10 levers is less than the number of locks of 8 levers, then the only feasible case is Case 2. So, the lock unlocked on Day 7 is L13.

36. 3

D necessarily follows A as it talks about taking it forward, B discusses the problem which was pertaining to the carriage, E elaborates the plan of action and C concludes the chain of thought.

37. 1

E stems out from the opening generalized statement about Vedic hymns, EC form a mandatory pair taking a cue from the phrase “on the other hand”, D talks about the praises being showered on various deities, B is the logical conclusion.

L13

L13 8 levers L15 8 levers

L12 10 levers

Also, out of L15 and L9, one lock has been definitely unlocked by Devendra. Out of L8, L2 and L13, one lock has been definitely unlocked by Devendra Out of L5, L6, L10, L14 and L11, one lock has been definitely opened by Devendra.

4

Day 5

For questions 33 to 35: Given that after Day 8 Devendra found that aggregate levers of all the locks that he has unlocked is more than 64 but not more than 68. Therefore, the aggregate levers of the locks unlocked on Day 5, Day 7 and Day 8 has to be greater than 22 but not more than 26. The following cases are possible

L5 10 levers L11 10 levers L6

L 11 10 levers

10 levers

Out of the locks unlocked by him, the number of locks of 6 levers is less than the number of locks of 8 levers.

L2

L14 6 levers

L9 L1

L2

L10 10 levers

L1

For questions 31 to 35: As per the information given, the following can be concluded, where the possible list of locks unlocked by Devendra on each of the eight days is given in “grey”

Day 1

L6 6 levers

8 levers

R indicated rejection of all the flavours.

II

L5 10 levers

The levers of the locks definitely unlocked by Devendra are as follows.

From each of the five given statements, we can make the following conclusions:

Statement

30. 4

L 15 8 levers

010

38. 4

D necessarily follows A as it is in continuation of the exposition of Takashi Murakami the artist, E takes it forward forming a pair with B as it defines the ‘divide’ and C is the concluding statement on Takashi.

39. 5

D essentially follows A as it explains how managers manage by ‘walking about’, C takes it forward, E & D further explain the scenario of the 1950s.

40. 2

C is incorrect, has the error of incorrect parallelism, and should be ‘collecting’ instead of collect. E is incorrect as the correct phrase is ‘appealing to’ and not ‘for’.

41. 1

B is incorrect, use the article ‘a’ before leading to define it, similarly use the indefinite article ‘a’ before lazy habit.

42. 3

B is incorrect, use the singular ‘relative’ to define motion, relatives renders the meaning incorrect, C is incorrect, use ‘produce’ as the sentence is in the present. In D, it should be ‘is’ instead of ‘are’.

43. 3

A is incorrect, use an article before ‘main theme’, use the preposition ‘in’ before America in B, C is incorrect, used the past tense ‘cohered’ as the sentence is in the past tense.

52. 3

The first paragraph of the passage talks about the matter of technology of climate change being not so simple as it is prone to zealotry and taboos.

53. 4

The passage mentions the three Achilles heels of the cells making option 4 the correct answer.

54. 5

All, except option 5, have been mentioned as reasons for the debacle of the fuel cells.

55. 2

The passage discusses the taboos governing geo-engineering and the fear expressed in the lines “Scientists and policymakers have been reluctant even to discuss the subjectmuch less research it, because they worry that it could cause more problems than it solves and that it will give politicians an excuse to avoid curbing carbon emissions” supports the option. Hence option 2 is best.

56. 3

Option 3 can be easily inferred from para 1.

57. 5

Refer to para 3 where the author feels that the invisibility stems from varied prejudices.

58. 2

The passage mentions that Nabokov escaped the 20th century’s greatest tyrannies which were the Bolshevik upheavals and the Nazi persecution.

59. 3

The paragraph on Vawdrey emphasizes the fact that the writer’s work is steeped in greatness and people get to know of only the outer layer, the real personality of the writers comes through only in their work.

44. 5

Option 5 is the correct answer as it takes both the subject matter and the last line of the paragraph forward.

45. 5

Option 5 is correct; take a cue from the last line of the paragraph, the word ‘end’ has a negative connotation, making it the logical continuation of the passage.

46. 1

The passage is celebrating the success of Paru Jaykrishna, logically option 1 takes this thought further as it comments directly on this success, the other options follow this.

60. 2

In the olden days, ether was used to anesthetize patients.

61. 4

The phrase “muttering retreats” makes option 4 correct.

The term “Stage moms” refers to parents who live vicariously or moms who manage their children’s business, since the passage ends with a mention of something ‘comical’, option 3 is the most amusing.

62. 4

The passage stresses on the fact that “there will be time” for everything.

63. 3

The lines “And indeed… I presume?” spell out the circle of concern which is limited to the immediate and the temporal world, nowhere do the lines depict any issues with the larger picture in life. The author is in a ‘status quo’ and deciding what to do.

64. 1

The passage talks about “hole is liberalism’s silence about the place and significance of groups” making option 1 correct.

65. 2

The passage expresses the views that “Liberalism established the principle of religious toleration-the idea that religious goals could not be pursued in the public sphere in a way that restricted the religious freedom of other sects” making option 2 correct.

66. 5

The Reformation identified “true religiosity as an individual’s subjective state”, making option 5 correct.

67. 3

The passage talks about “One’s social status was now achieved rather than ascribed; it was the product of one’s talents, work and effort rather than an accident of birth”, the elimination of traditional barriers resulted in an emphasis on the fulfillment of the self rather than anything else.

68. 2

BBAAA: The sentence is in the past tense so option ‘B’ is correct, heel means the part of the foot and heals - to cure. Assented means to agree and ascent an upward movement, Plum is a fruit and plumb means to examine closely or deeply. Choral means of a choir and coral is the hard, variously colored, calcareous skeleton secreted by certain marine polyps as in, something made of coral.

47. 3

48. 5

49. 2

Option 5 is incorrect as a game cannot be ‘see through’, one can use it in the sense of a strategy in a sentence like “I saw through their game”, which means to be able to ascertain the strategy. In option 1 it means the score at a particular stage in a game, in 2 it is a particular manner or style of playing a game, in 3 it is any object of pursuit, attack, abuse, etc. and in 4 it is a business or profession. Option 2 is incorrect as it seems that the accounts were fighting with each other. ‘On conflict’ is an incorrect usage. The correct usage should be “The two accounts of what had happened were conflicting”, in option 1 it means disagreement, in 3 it means a state of opposition between persons or ideas or interests; in 4 it means opposition between two simultaneous but incompatible feelings and in 5 it describes a state of being.

50. 4

Option 4 is incorrect, no such thing as pure genetics exists, and the correct usage is ‘pure lineage’. In option 1 the word means a homogeneous or uniform composition, in 2 it means free of dirt, in 3 it means sinless and in 5 it means unadulterated.

51. 4

Option 4 is incorrect as ‘her study’ implies the physical premises, correct usage is only ‘study’ which implies being lost in a reverie. In option 1 it means the subject of concern, in 2 it implies research or a detailed examination and analysis of a subject, in 3 it means a written account and in 5 means as a guide for a finished production.

010

5

69. 3

70. 4

71. 1

ABBAA: Scull means a pair of oars and skull the head as the center of knowledge and understanding, Levee is an embankment designed to prevent the flooding of a river and Levy-an imposing or collecting of a tax. ‘Who’ is used for people, here the subject is offer so ‘that’ should be used, and the definite article should be used before union. Profit is to gain an advantage or benefit, prophet is a person who practices divination. BBABA: Baron means a person with great power, barren means lacking, bereft. Coal is a piece of glowing, charred, or burned wood or other combustible substance. Kohl is powder used to darken eyelids, glowed means to burn brightly and glowered means to show anger. FRIEZE - any decorative band at the top or beneath the cornice of an interior wall, a piece of furniture, etc., freeze means change from the liquid to the solid state. Synch means harmony or harmonious relationship, Sink is to fall or descend into or below the surface or to the bottom.

74. 1

While selling he sells 0.9 meter of cloth at the price of (100 – 10% of 100) = Rs.90. So, he will sell 110 cm of cloth at the price of Rs.110.  (110 – 95 )  Percentage profit =   × 100 = 15.8%. 95  

75. 5

(

If we observe the equation carefully we can come to the conclusion that the value of ‘x’ has to be 1. The given equation will hold true for any integral value of ‘y’ and x = 1. Hence, option (5) is the correct choice.

76. 1

Total surface area of one fourth portion of the solid sphere having radius ‘r’ units = curved surface area + plane surface area =

Let the marked price of 1 meter of cloth be Rs.100. If he buys 1 meter of cloth, then he gets 1.1 meter of cloth at the cost of (100 – 5% of 100) = Rs.95.

The length of the line segment BG will be minimum possible when the point E coincides with the point B and the point F coincides with the point C. In this case, point G is the point of intersection of the diagonals of the square.

)

1 1  4πr 2 + 2  πr 2  = 2πr 2 square units. 4 2 

A

(B ,E )

Sum of the areas of one-fourth portion of each of the two solid spheres having radii 4 units and 6 units is 2π42 + 2π62.

G

Total surface area of the solid given in the question will be

72. 2

1 units 2 Note that the length of the line segment BG will be maximum when the point E coincides with the point A and the point F coincides with the point B.

The length of line segment BG =

Let the total number of large boxes that have been left empty in the game = ‘x’. Therefore, the total number of medium boxes used by Richa is 5 × (9 – x) = 45 – 5x.

In this case the length of the line segment BG will be = 1 unit. For any position of the point E between the points A and B, the length of the line segment BG will be less than 1 unit but more

Let the total number of medium boxes that have been left empty in the game = ‘y’.

than

Therefore, the total number of small boxes used by Richa is 5 × (45 – 5x – y) = 225 – 25x – 5y. It is also known that total number of boxes that have been left empty = 41. Therefore, x + y + 225 – 25x – 5y = 41. 24x + 4y = 184. 6x + y = 46.

(C ,F )

D

1  2π42 + 2π62 − 2  π42  = 88π square units. 2  Hence, option (1) is the correct choice.

1 units. 2

Hence, option (1) is the correct choice. 77. 5

When the value of x = 0, the value of f(x) will be 1. Also, the minimum possible value of f(x) will be 1. Therefore, the graph of f(x) is as is shown in the figure given below.

Total number of boxes used by Richa in the game is 9 + 45 – 5x + 225 – 25x – 5y = 279 – 5 (6x + y) = 279 – 5 × 46 = 49. Hence, option (2) is the correct choice. 73. 1

N = 46 + 68 = 212 + 28 × 38

(

⇒ N= 2 × 2 + 3 8

4

8

)=2

8

(0,1 )

(1, 1 )

× 6577

Now, 6577 is a prime number, therefore the number of factors of the number N = 18. Hence, option (5) is the correct choice.

6

010

For questions 78 and 79: Let A, B, C, D and E denote the weight of Amir, Bhutal, Chetali, Dhani and Esha respectively.

f(z)

∴

f(z 2 )

Given that C = 2 + E, B = 8 + A and D = 78. Hence,

Also, the total weight of the couples = 2 × (79 + 82) = 322 kg and that of all the five persons = 5 × 80 = 400 kg.

)

f(z) f(z2 )

is a linear function.

Hence, option (1) is the correct choice.

Therefore, the weight of the unmarried person = 400 – 322 = 78 kg which is that of Dhani. Now, 8 + A + C = B + 2 + E ⇒ 6 + A + C = B + E ⇒ (B + E) – (A + C) = 6

(

 1  2 = × z −1 = z +1  z − 1

83. 1

Also, the difference between the total weights of couples is 2 × (82 – 79) = 6.

a

A

B

b

d

As the weight of no two persons is the same, therefore (Bhutal, Esha) and (Amir and Chetali) are the two married couples.

c

D

78. 2

C

Area of the rectangle ABCD = a × b.

1 1 (2a × 2b ) = (a + c ) × (b + d) 4 4 Therefore, option (1) is the correct choice.

79. 3

⇒ a×b =

A

80. 3

84. 3

If the lines y = x and y = – x are concurrent, then the point of intersection of these two mentioned lines is the origin. Hence, both the lines y = ax + c and y = – ax – c should pass through the origin, which is only possible for c = 0. Hence, option (3) is the correct choice.

6 0°

P

85. 2 3 0°

The value of ‘z’ at x = 1 is 3.

circle passing through three vertices A, B and C of the ∆ABC ⇒ PC = PA = PB = 10 cm

Since, the value of ‘z’ is not equal to 0, therefore the product of ‘y’ and ‘z’ will be minimum at x = 1.

Let my current age be ‘m’

Therefore, the maximum possible value of the expression

Let the current age of Richa and Namita be ‘x’ and ‘y’ respectively.

1

2p 3 For the minimum possible integral difference, ‘p’ has to be 3. Therefore, x – y = 2 Hence, option (4) is the correct choice. ⇒ x−y=

=

1

( yz ) (5 × 3 )

As per the information given in the question m = 3x + 2 ...(i) After ‘p’ years: m + p = 3(y + p) + 2 ...(ii) Solving equation (i) and (ii), we get that 3x – 3y = 2p

we need to find

y = 4x + 41 – x will have its minimum value at x = 0 and x = 1.

Observing, we can easily say P is the circumcenter of the

81. 4

1

( yz )

the minimum possible value of the product of y and z.

C

B

To find the maximum possible value of

=

1 15

Hence, option (2) is the correct choice. 86. 3

Using statement A: XXYY = 11(X0Y). Now, here X0Y has to be a multiple of 11 and obviously 11 (X0Y) is a perfect square. The value of X0Y has to be 704. No other value of X0Y is possible. Hence, the value of Y is 4.

82. 1

1 1 1 Given that f(z) = + 2 + 3 + ..... + ∞, | z | > 1 z z z

1 ⇒ f(z) = z −1

( )

Similarly, f z2 =

010

1 z2 − 1

Hence, statement A alone is sufficient to answer the question. Using statement B: The number of natural numbers from 1 and 3000000 that are divisible by 2 but not by 3 can be easily calculated and is a unique value. Hence, the value of Y can also be uniquely determined. Hence, statement B alone is sufficient to answer the question. Hence, option (3) is the correct choice.

7

87. 1

Sum of all the terms in an Arithmetic progression

n × (a1 + an) = 2 where n is the total number of terms a1 is the first term in the series. ‘an’ is the last term in the series. Mean =

(a1 + an )

2 It implies, sum of an A.P = n × mean

Using statement A: We have the total number of terms of all the A.P.’s. Hence, the sum of all the A.P.’s can be found. Hence, statement A alone is sufficient to answer the question. Using statement B: If the total number of terms in all the four mentioned series are in a A.P. and two out of the four are 2 and 4, then the remaining two terms can be 1, 3 or 6, 8.

As per the information given in the question

Also,

Also, x +

∆MNC =

Hence, we cannot uniquely determine the sum of all the four A.P.’s.

91. 4

Hence, statement B alone is not sufficient to answer the question.

92. 1

(

)

1 1 1 × ( 4 − y ) × x = × ( 4x − 1) = 7 3 − 4 m2 2 2 2

Since, a two-digit number has exactly four factors, therefore the number has to be a product of two prime numbers or a perfect cube. Case I: When one of the numbers in the product is 2. The other number in the product can be 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. There are 13 such possible products. Case II: When one of the numbers in the product is 3. The other number in the product can be 5, 7, 11, 13, 17, 19, 23, 29 and 31. There are 9 such possible products.

Here, we will go through all the 4! combinations of the words starting with the alphabet C and all the 4! combinations of the words starting with the alphabet I. Hence, the first alphabet of the 60th word is O. Likewise, for the remaining four alphabets CIWT, we will go through all the combinations starting with C, and the 60th word will be the last combination starting with the alphabet I, that is IWTC. So, the 60th word written is OIWTC.

Case III: When one of the numbers in the product is 5. The other number in the product can be 7, 11, 13, 17 and 19. There are 5 such possible products.

Lets assume that x litres of acid having concentration 20%, y litres of acid having concentration 30% and (10 – x – y) litres of acid having concentration 50% are mixed by Sunil to get a final concentration of 40%.

Case IV: When one of the numbers in the product is 7. The other number in the product can be 11 and 13. There are 2 such possible products.

 x × 20 + y × 30 + (10 − x – y ) × 50  ⇒   = 40 10  

Case V: When the two-digit number is a perfect cube. There is only one such number, i.e. 27

⇒ 3x + 2y = 10 The only possible solutions are (x = 2, y = 2) or (x = 0, y = 5) ⇒ Minimum amount spent = 2 × 20 + 2 × 30 + 6 × 40 = Rs.340.

For questions 91 and 92:

Therefore, in total there are 30 such two-digit numbers that have exactly 4 factors. 94. 4

The three-digit number EEE can be written as E × 3 × 37. So, when one of the two-digit numbers is 37, then the other two-digit number can be 12, 18, 24.

A

Also, when one of the two-digit numbers is 74, then the other two-digit number can be 12. (In all the other cases the condition that A, B, C, D and E are distinct is not satisfied)

3 –x 5 M x y

4 –y

N 4

8

1 = 4. x

x ≠ 2 + 3 as the value of x has to be less than 3.

Therefore, f(6) = 1 + 1 – 4 – 4 + 9 + 9 = 2(1 + 9 – 4) = 12. Therefore the minimum value of the function is 12.

B

16 − 2 = 14 meter

Therefore, x = 2 − 3

The given function is also symmetric about x = 6. So, the vertex must be at x = 6.

3

( x + y )2 − 2xy =

⇒ x =2± 3

Therefore, the graph of f(x) is an upward-pointing parabola, and the minimum value of the function is attained at its vertex.

90. 2

1 2

xy 1 = ⇒ xy = 1 12 − xy 11

MN = x 2 + y 2 =

93. 5

89. 3

=

⇒x+y=4

f(x) is a quadratic function and the coefficient of x2 is 1 + 1 – 1 – 1 + 1 + 1 = 2 > 0.

88. 4

x+y

(3 − x ) + ( 4 − y ) + 5

C

Therefore, the possible values of AB can be 37, 74, 12, 18, 24. Required sum = 37 + 74 + 12 + 18 + 24 = 165.

010

For question 95 and 96: M ario (40 )

There are 16 points having integral coordinates on the X-axis and 10 points with integral coordinates on the Y-axis other than the origin.

N in te nd o (90 )

In the first quadrant, for y = 1, 2, 3, 4 and 5 we get 7, 5, 4, 2 and 1 points respectively, having integral coordinates inside the region enclosed by the graph in the first quadrant.

a n

m x b

Therefore, there are 1 + 2 + 4 + 5 + 7 = 19 points having integral coordinates in each of the four quadrants other than the points on the Y-axis and X-axis.

c

The total number of points having integral coordinates inside the region enclosed by the graph = 16 + 10 + 1 + 4 × 19 = 103. Hence, option (2) is the correct choice.

f N FS (14 5)

98. 2

m + n + f + a + b + c + x = 150 ...(i) m + a + b + x = 40 ...(ii) a + c + n + x = 90 ...(iii) b + c + f + x =145 ...(iv) Adding equation (ii), (iii) and (iv) we get, 2a + 2b + 2c + 3x + m + n + f = 275 ...(v) Subtracting equation (i) from (v), we get a + b + c + 2x = 125 ...(vi) 95. 1

The following cases are possible to make ab a perfect square. Case I: ab will be a perfect square when ‘b’ is an even number and ‘a’ any number from 1 to 6. (1, 2) (1, 4) (1, 6) (2, 2) (2, 4) (2, 6) . . (6, 2) (6, 4) (6, 6) = 18 cases

125 persons played atleast two games, which implies that a + b + c + x = 125, but from equation (vi) a + b + c + 2x = 125, hence x = 0. m + n + f = 25.

Case II: a = 1 and b = 1, 3 or 5 (1, 1) (1, 3) (1, 5) = 3 cases

So, to minimize ‘f’ we need to maximize m + n, and the maximum value that (m + n) can take is 5, so the minimum number of persons that played only NFS is 20. 96. 2

Case III: a = 4 and b = 1, 3 or 5 (4, 1) (4, 3) (4, 5) = 3 cases ⇒ Total of 24 cases.

In order to minimize the amount we need to minimize the number of persons playing all the three games and maximize the number of persons playing exactly one of the games. M ario (40 )

Required probability =

N in te nd o (90 )

99. 5

5 0

0 0

24 2 = 36 3

The only possible perfect squares which can be obtained are 1, 4, 9, 16, 25 and 36. These perfect squares can be obtained in the following ways: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (1, 4) and (4, 1)

85

35

When two dice are tossed simultaneously there are 6 × 6 = 36 possible outcomes.

⇒ Therefore, total of 8 cases.

25

Hence, required probability =

8 2 = 36 9

N FS (14 5)

Therefore, minimum possible amount that the persons paid for playing the games is 25 × 2 + 125 × 3 = Rs.425. 97. 2

The graph of 2|x| + 3|y| = 18 is given below.

A 5 1813 = 113.3125 = 113 = B 16 16 Let A = 1813K (Where K is a natural number) B = 16K When (A2 – 4) is divided by B:

100. 3 As per the question

( A − 2 )( A + 2 ) = (1813K − 2)(1813K + 2 )

Y

B

(0 ,6)

(– 9,– 0 )

= (9 ,0)

(0 ,–6 )

010

16K

X

(5K + 2 )(5K − 2 ) 16K

25K 2 − 4 16K Remainder will be 0 when K = 2. ⇒ B = 16K = 16 × 2 = 32. =

9

101. 3 Sum of 8 can be obtained by adding either 1, 2 and 5 or 1, 3 and 4, so ball no. that were pocketed in first three strokes can either be either 9, 8 and 5 or 9, 7 and 6. Sum of 22 can be obtained by adding either adding 5, 8 and 9 or 6, 7 and 9, so ball that were pocketed in last three strokes can either be either 5, 2 and 1 or 4, 3 and 2.

CASE I

CASE II

CASE III

103. 5 It is given that a1 + a2 + a3 + a4 = 210 Also, 210 = 5 × 7 × 2 × 3 Few possible ways ‘210’ can be split into four parts are I. a1 + a2 + a3 + a4 = 21 × 2 + 21 × 2 + 21 × 2 + 21 × 4 LCM (a1, a2, a3 ,a4 = LCM (42, 42, 42, 84) = 84 II. a1 + a2 + a3 + a4 = 35 × 1 + 35 × 1 + 35 × 2 + 35 × 2 LCM (35, 35, 70, 70) = 70

First three stroke

9, 7 and 6 9, 7 and 6 9, 8 and 5

4th, 5th and 6th stroke

3, 4 and 8 1, 5 and 8 1, 6 and 7

III. a1 + a2 + a3 + a4 = 60 × 1 + 60 × 1 + 60 × 1 + 30 × 1 LCM (60, 60, 60, 30) = 60

Last three stroke

5, 2 and 1 4, 3 and 2 4, 3 and 2

The minimum possible LCM will be achieved in (III).

Sum of 19 can be obtained by 9 + 8 + 2 from CASE II Sum of 12 can be obtained by 7 + 3 + 2 from CASE I Sum of 8 can be obtained by 5 +1 + 2 from CASE III but sum of 23 is not possible 102. 4 Let the length of the other two sides of the triangle be ‘a’ and ‘b’ respectively, ⇒ a2 + b2 = 2402 = 57600 Also, a + b + 240 must be a perfect square. Perimeter of a right angled triangle is maximized when the two sides other than its hypotenuse are equal in length. Therefore, the maximum perimeter of the right angled triangle will be 120

( 2 ) + 120 ( 2 ) + 240 = 579(approx).

Also, the perimeter of the triangle should be greater than twice of the length of the hypotenuse of the triangle. Therefore, the perimeter of the triangle should be greater than 480 and less than 579. Possible squares in the above range are 484, 529 and 576. But, as per the information given in the question, the perimeter can only be equal to 576.

Hence, option (5) is the correct choice. 104. 3 Weight of 1 unit of B = 1 × 5 + 4 × 3 + 1 × 8 = 25 kgs. Weight of 1 unit of C = 2 × 5 + 6 × 3 + 1 × 8 = 36 kgs Therefore, weight of 1 unit of A = weight of 4 units of B + weight of 5 units of C = 4 × 25 + 5 × 36 = 280 kgs. Therefore, 1400 kgs of A will have

1400 = 5 units of A. 280

Therefore, the number of units of B and C required to make 1400 units of A is 4 × 5 and 5 × 5 respectively. Therefore, the number of units of Y required to make 20 units of B and 25 units of C is 20 × 4 and 25 × 6. Weight of Y required = (20 × 4 + 25 × 6) × 3 = 690 kgs. 105. 2 If we choose the 10 points on the X-axis having coordinates (0,1), (0, 2), ...., (0, 10), then the coordinates of the midpoints obtained on joining every possible pair of two points is 0.5, 1.5, 2, 2.5, ....., 9 and 9.5. Therefore, the number of points that are marked with red colour is 9 + 8 = 17.

The values of ‘a’ and ‘b’ will be 192 and 144 units not necessarily in that particular order. Hence, option (4) is the correct choice.

10

010