CL Mock CAT 10 Key 2008

010 1
MCT-0014/08
Discuss this test online at PREPZONE
http://www.careerlauncher.co.in/prepzone
Check detailed analysis of this test at
http://www.careerlauncher.com/sis
Mock CAT – 10
Answers and Explanations
Total
Questions
Time Taken
(Min)
Total
Attempts
Correct
Attempts
Incorrect
Attempts
Net
Score
Section A 20
Section B 15
Section A 20
Section B 15
Section A 20
Section B 15
TOTAL 105 150
Quantitative Ability
Language Comprehension
and English Usage
MY PERFORMANCE
Logical Reasoning based
Data Interpretation
1 2 2 3 3 1 4 5 5 2 6 3 7 4 8 4 9 5 10 4
11 2 12 4 13 2 14 4 15 3 16 1 17 4 18 3 19 2 20 5
21 3 22 4 23 2 24 1 25 4 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 3 43 3 44 5 45 5 46 1 47 3 48 5 49 2 50 4
51 4 52 3 53 4 54 5 55 2 56 3 57 5 58 2 59 3 60 2
61 4 62 4 63 3 64 1 65 2 66 5 67 3 68 2 69 3 70 4
71 1 72 2 73 1 74 1 75 5 76 1 77 5 78 2 79 3 80 3
81 4 82 1 83 1 84 3 85 2 86 3 87 1 88 4 89 3 90 2
91 4 92 1 93 5 94 4 95 1 96 2 97 2 98 2 99 5 100 3
101 3 102 4 103 5 104 3 105 2
2 010
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
P, Q, R and S is
X X X 3X
, , and
4 4 5 10
respectively.
Therefore, the total number of shirts manufactured by the companies
P, Q, R and S is
5X 5X 4X 6X
, , and
6 4 3 5
respectively.
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 Linen Khadi Polyester Total
P 15 20 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
⇒ · ×
4
X 3 10
Difference between the number of Poleyster shirts
manufactured by the companies P and R is
( )
× ×
| ` | `
× × · · ·

. , . ,
4
4 3 10
16 5X 22 4X 4X
– 960
100 6 100 3 25 25
4. 5 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.
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.
010 3
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 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
· × ·
20
100 4%
500
22. 4 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’.
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 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 P Q R S Total
Villages 95 390 135 380 1000
Towns 210 220 220 350 1000
Metros 180 405 230 185 1000
Total 485 1015 585 915 3000
The two observations made by the brand manager, hold true only for
the following four cases.
Possible
Cases
P Q R S
Case I Cream Rejected All Chilly Mint
Case II Chilly Rejected All Cream Mint
Case III Mint Chilly Rejected All Cream
Case IV Mint Cream Rejected All Chilly
26. 5 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.
4 010
27. 3 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.
28. 4 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.
29. 1 From each of the five given statements, we can make the
following conclusions:
Statement Conclusion
I R indicated rejection of all the flavours.
II P indicated selection of Cream flavour.
III S indicated selection of Chilly flavour.
IV Either Q or R indicated selection of Cream
Flavour.
V P indicated selection of Mint flavour.
Statements I, III, IV and V can simultaneously be true. Hence
option (1) is the correct answer.
30. 4 Only Chilly and Cream flavours can be simultaneously selected
for large scale productions. Hence (4) is correct.
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 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 L3
Day 5 L2 L15 L9 L10 L5 L15 L9
Day 6 L13 L6 L1 L8 L10 L1
Day 7 L14 L11 L8 L2 L13 L8 L2 L13
Day 8 L5 L6 L10 L14 L11
Out of the locks unlocked by him, the number of locks of 6 levers is
less than the number of locks of 8 levers.
L1 8 levers L7 6 levers L13 8 levers
L2 6 levers L8 10 levers L14 6 levers
L3 10 levers L9 6 levers L15 8 levers
L4 8 levers L10 10 levers
L5 10 levers L11 10 levers
L6 6 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.
L 15 L9 L8 L2 L13
8 levers 6 levers 10 levers 6 levers 8 levers
L5 L6 L10 L14 L 11
10 levers 6 levers 10 levers 6 levers 10 levers
The levers of the locks definitely unlocked by Devendra are as follows.
L1 L3 L4 L7 L12
8 levers 10 levers 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
Day 5 Day 7 Day 8
8 8 6
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
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.
010 5
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.
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.
47. 3 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.
48. 5 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.
49. 2 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.
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 subject-
much 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
20
th
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.
60. 2 In the olden days, ether was used to anesthetize patients.
61. 4 The phrase “muttering retreats” makes option 4 correct.
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.
6 010
69. 3 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.
70. 4 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.
71. 1 Total surface area of one fourth portion of the solid sphere
having radius ‘r’ units = curved surface area + plane surface
area
( )
2 2 2
1 1
4 r 2 r 2 r square units.
4 2
| `
· π + π · π

. ,
Sum of the areas of one-fourth portion of each of the two
solid spheres having radii 4 units and 6 units is
2 2
2 4 2 6 . π + π
Total surface area of the solid given in the question will be
2 2 2
1
2 4 2 6 2 4 88 square units.
2
| `
π + π − π · π

. ,
Hence, option (1) is the correct choice.
72. 2 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.
Let the total number of medium boxes that have been left
empty in the game = ‘y’.
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.
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
· + · + ×
6 8 12 8 8
N 4 6 2 2 3
( )
⇒ · × + · ×
8 4 8 8
N 2 2 3 2 6577
Now, 6577 is a prime number, therefore the number of
factors of the number N = 18.
74. 1 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.
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 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.
A
D
G
(B,E)
(C,F)
The length of line segment BG
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.
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
than
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.
( 1, 1 ) ( 0, 1)
Hence, option (5) is the correct choice.
010 7
For questions 78 and 79:
Let A, B, C, D and E denote the weight of Amir, Bhutal, Chetali, Dhani
and Esha respectively.
Given that C = 2 + E, B = 8 + A and D = 78.
Also, the total weight of the couples = 2 × (79 + 82) = 322 kg and that
of all the five persons = 5 × 80 = 400 kg.
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
Also, the difference between the total weights of couples is
2 × (82 – 79) = 6.
As the weight of no two persons is the same, therefore
(Bhutal, Esha) and (Amir and Chetali) are the two married couples.
78. 2
79. 3
80. 3
A
B
C
60°
30°
P
Observing, we can easily say P is the circumcenter of the
circle passing through three vertices A, B and C of the ABC ∆
⇒ PC = PA = PB = 10 cm
81. 4 Let my current age be ‘m’
Let the current age of Richa and Namita be ‘x’ and ‘y’
respectively.
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
⇒ − ·
2p
x y
3
For the minimum possible integral difference, ‘p’ has to be 3.
Therefore, x – y = 2
Hence, option (4) is the correct choice.
82. 1 Given that
2 3
1 1 1
f(z) ..... , | z | 1
z
z z
· + + + + ∞ >
1
f(z)
z 1
⇒ ·
−
Similarly,
( )
2
2
1
f z
z 1
·
−
( )
2
2
f(z) 1
z 1 z 1
z 1
f(z )
| `
∴ · × − · +

−
. ,
Hence,
2
f(z)
f(z )
is a linear function.
Hence, option (1) is the correct choice.
83. 1
A
a
B
b
C
c
D
d
Area of the rectangle ABCD = a × b.
( ) ( ) ( )
1 1
a b 2a 2b a c b d
4 4
⇒ × · × · + × +
Therefore, option (1) is the correct choice.
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.
85. 2 To find the maximum possible value of
( )
1
yz
we need to find
the minimum possible value of the product of y and z.
y = 4
x
+ 4
1 – x
will have its minimum value at x = 0 and
x = 1.
The value of ‘z’ at x = 1 is 3.
Since, the value of ‘z’ is not equal to 0, therefore the product
of ‘y’ and ‘z’ will be minimum at x = 1.
Therefore, the maximum possible value of the expression
( ) ( )
· ·
×
1 1 1
yz 5 3 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.
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.
8 010
87. 1 Sum of all the terms in an Arithmetic progression
=
n
2
× (a
1
+ a
n
)
where n is the total number of terms
a
1
is the first term in the series.
‘a
n
’ is the last term in the series.
Mean =
( ) +
1 n
a a
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.
Hence, we cannot uniquely determine the sum of all the four
A.P.’s.
Hence, statement B alone is not sufficient to answer the
question.
88. 4 f(x) is a quadratic function and the coefficient of x
2
is
1 + 1 – 1 – 1 + 1 + 1 = 2 > 0.
Therefore, the graph of f(x) is an upward-pointing parabola,
and the minimum value of the function is attained at its vertex.
The given function is also symmetric about x = 6.
So, the vertex must be at x = 6.
Therefore, f(6) = 1 + 1 – 4 – 4 + 9 + 9 = 2(1 + 9 – 4) = 12.
Therefore the minimum value of the function is 12.
89. 3 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 60
th
word is O.
Likewise, for the remaining four alphabets CIWT, we will go
through all the combinations starting with C, and the 60
th
word will be the last combination starting with the alphabet I,
that is IWTC. So, the 60
th
word written is OIWTC.
90. 2 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%.

( ) x 20 y 30 10 x – y 50
40
10
| ` × + × + − ×
⇒ ·


. ,
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:
3–x
3
M
5
A
B y N 4–y
x
C
4
As per the information given in the question
( ) ( )
x y 1
3 x 4 y 5 2
+
·
− + − +
⇒ x + y = 4
Also,
xy 1
xy 1
12 xy 11
· ⇒ ·
−
( )
2 2 2
MN x y x y 2xy 16 2 14 meter · + · + − · − ·
Also,
1
x 4.
x
+ ·
x 2 3 ⇒ · t
x 2 3 ≠ + as the value of x has to be less than 3.
Therefore, x 2 3 · −
( ) ( ) ( )
2
1 1 1
MNC 4 y x 4x 1 7 3 4 m
2 2 2
∆ · × − × · × − · −
91. 4
92. 1
93. 5 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.
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.
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.
Case V:
When the two-digit number is a perfect cube.
There is only one such number, i.e. 27
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.
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)
Therefore, the possible values of AB can be 37, 74, 12, 18,
24.
Required sum = 37 + 74 + 12 + 18 + 24 = 165.
010 9
For question 95 and 96:
Mario (40) Nintendo (90)
NFS (145)
m
a
n
x
c
b
f
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. 1 125 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.
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 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.
Mario (40) Nintendo (90)
NFS (145)
0
5
0
0
85
35
25
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.
(0,6)
(9,0)
X
Y
(0,–6)
(–9,–0)
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.
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.
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.
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.
98. 2 When two dice are tossed simultaneously there are 6 × 6 = 36
possible outcomes.
The following cases are possible to make a
b
a perfect square.
Case I:
a
b
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
Case II:
a = 1 and b = 1, 3 or 5
(1, 1) (1, 3) (1, 5) = 3 cases
Case III:
a = 4 and b = 1, 3 or 5
(4, 1) (4, 3) (4, 5) = 3 cases
⇒ Total of 24 cases.
Required probability
24 2
36 3
· ·
99. 5 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)
⇒ Therefore, total of 8 cases.
Hence, required probability
8 2
36 9
· ·
100. 3 As per the question
· · ·
A 5 1813
113.3125 113
B 16 16
Let A = 1813K (Where K is a natural number)
B = 16K
When (A
2
– 4) is divided by B:
( )( ) ( )( ) A 2 A 2 1813K 2 1813K 2
B 16K
− + − +
·

( )( ) 5K 2 5K 2
16K
+ −
·

2
25K 4
16K
−
·
Remainder will be 0 when K = 2.
⇒ B = 16K = 16 × 2 = 32.
10 010
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
First three stroke 9, 7 and 6 9, 7 and 6 9, 8 and 5
4
th
, 5
th
and 6
th
stroke 3, 4 and 8 1, 5 and 8 1, 6 and 7
Last three stroke 5, 2 and 1 4, 3 and 2 4, 3 and 2
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,
⇒ a
2
+ b
2
= 240
2
= 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.
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.
103. 5 It is given that a
1
+ a
2
+ a
3
+ a
4
= 210
Also, 210 = 5 × 7 × 2 × 3
Few possible ways ‘210’ can be split into four parts are
I. a
1
+ a
2
+ a
3
+ a
4
= 21 × 2 + 21 × 2 + 21 × 2 + 21 × 4
LCM (a
1
, a
2
, a
3
,a
4
= LCM (42, 42, 42, 84) = 84
II. a
1
+ a
2
+ a
3
+ a
4
= 35 × 1 + 35 × 1 + 35 × 2 + 35 × 2
LCM (35, 35, 70, 70) = 70
III. a
1
+ a
2
+ a
3
+ a
4
= 60 × 1 + 60 × 1 + 60 × 1 + 30 × 1
LCM (60, 60, 60, 30) = 60
The minimum possible LCM will be achieved in (III).
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
280
· units of A.
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.