CAT Past Year Question Paper Solution - 1995 | Additional Study Material for CAT PDF Download

 Page 1


Page 1 CAT 1995 Actual Paper

	






1 a 2 b 3 a 4 b 5 c 6 c 7 d 8 c 9 b 10 d
11 c 12 d 13 c 14 d 15 c 16 c 17 d 18 b 19 b 20 a
21 d 22 b 23 c 24 b 25 a 26 b 27 a 28 d 29 b 30 d
31 d 32 d 33 b 34 c 35 d 36 d 37 a 38 b 39 d 40 b
41 d 42 b 43 c 44 b 45 a 46 d 47 a 48 a 49 d 50 c
51 b 52 b 53 a 54 c 55 d 56 a 57 b 58 c 59 d 60 a
61 c 62 d 63 b 64 * 65 b 66 c 67 a 68 a 69 a 70 b
71 a 72 a 73 c 74 d 75 d 76 c 77 d 78 a 79 b 80 b
81 b 82 a 83 b 84 d 85 d 86 c 87 d 88 a 89 d 90 b
91 d 92 a 93 d 94 a 95 c 96 b 97 a 98 c 99 c 100 c
101 d 102 b 103 d 104 a 105 b 106 a 107 c 108 a 109 c 110 c
111 b 112 b 113 a 114 b 115 a 116 b 117 d 118 d 119 a 120 c
121 c 122 c 123 b 124 a 125 a 126 c 127 c 128 d 129 d 130 a
131 b 132 b 133 a 134 b 135 c 136 a 137 c 138 d 139 a 140 d
141 b 142 c 143 c 144 a 145 b 146 d 147 b 148 a 149 c 150 b
151 d 152 a 153 d 154 a 155 a 156 b 157 b 158 d 159 a 160 b
161 a 162 b 163 d 164 d 165 c 166 b 167 d 168 c 169 d 170 a
171 c 172 a 173 b 174 d 175 c 176 b 177 d 178 a 179 a 180 c
181 a 182 b 183 c 184 d 185 b
Page 2


Page 1 CAT 1995 Actual Paper

	






1 a 2 b 3 a 4 b 5 c 6 c 7 d 8 c 9 b 10 d
11 c 12 d 13 c 14 d 15 c 16 c 17 d 18 b 19 b 20 a
21 d 22 b 23 c 24 b 25 a 26 b 27 a 28 d 29 b 30 d
31 d 32 d 33 b 34 c 35 d 36 d 37 a 38 b 39 d 40 b
41 d 42 b 43 c 44 b 45 a 46 d 47 a 48 a 49 d 50 c
51 b 52 b 53 a 54 c 55 d 56 a 57 b 58 c 59 d 60 a
61 c 62 d 63 b 64 * 65 b 66 c 67 a 68 a 69 a 70 b
71 a 72 a 73 c 74 d 75 d 76 c 77 d 78 a 79 b 80 b
81 b 82 a 83 b 84 d 85 d 86 c 87 d 88 a 89 d 90 b
91 d 92 a 93 d 94 a 95 c 96 b 97 a 98 c 99 c 100 c
101 d 102 b 103 d 104 a 105 b 106 a 107 c 108 a 109 c 110 c
111 b 112 b 113 a 114 b 115 a 116 b 117 d 118 d 119 a 120 c
121 c 122 c 123 b 124 a 125 a 126 c 127 c 128 d 129 d 130 a
131 b 132 b 133 a 134 b 135 c 136 a 137 c 138 d 139 a 140 d
141 b 142 c 143 c 144 a 145 b 146 d 147 b 148 a 149 c 150 b
151 d 152 a 153 d 154 a 155 a 156 b 157 b 158 d 159 a 160 b
161 a 162 b 163 d 164 d 165 c 166 b 167 d 168 c 169 d 170 a
171 c 172 a 173 b 174 d 175 c 176 b 177 d 178 a 179 a 180 c
181 a 182 b 183 c 184 d 185 b
Page 2
CAT 1995 Actual Paper
1. a All others are synonyms meaning 'to tear or cut'.
2. b All others are synonyms of control.
3. a All others mean 'to start'; cease means to stop.
4. b All others mean 'on the edge'.
5. c All others refer to something said in praise.
6. c All others refer to a feeling of hatred.
7. d All others are adjectives meaning 'skillful'.
8. c All others are adjectives for persons who do not speak
much.
9. b All others are synonyms.
10. d All others refer to persons who are madly enthusiastic
about something.
11. c 'The student's' should be replaced with 'his'.
12. d We are talking about 'every man or woman', therefore
the pronoun used should be singular 'his/her', instead of
'their'.
13. c The pronoun should remain consistent throughout the
sentence, hence 'you' should be replaced with 'one'.
14. d 'Assure' is an intransitive verb and should be followed
by an object. The correct usage here would be 'be sure
of'.
15. c The man being referred here is the object to the verb,
hence 'who' should be replaced with 'whom'.
16. c Both are pairs of antonyms.
17. d 'Alleviate' is an extended form of 'ease' and 'interrogate'
is an extended form of 'question'.
18. b Both are pairs of synonyms. All four words mean 'secret’.
19. b Audience watch a drama and spectators watch a game.
20. a Just as a building can have many stories, a book can
have many chapters.
21. d All others are pairs of synonyms.
22. b In all other pairs, the first word is a part of the second
word.
23. c In all other pairs, the first word is an adjective referring
to the second word.
24. b In all other pairs, the first word is an adjective derived
from the second pair.
25. a In all other pairs, the first word refers to a fear of the
second word.
26. b D tells us that the passage is about continuation of
previous night's discussion. B states what the discussion
was about. C adds a point to it by using 'also'. A answers
the question raised in C about the reason of conflicts.
27. a B states that the document tells us about history, A states
which part of history does it relate to, D elaborates further
on the first generation poets by referring to Wordsworth
and Coleridge.
28. d C introduces the poet's large plans, A shows how they
were replaced by new plans, D states how even these
plans remained unfulfilled and B tells us what was the
ultimate outcome of the plans.
29. b B states our attitude towards value of time as we
advance in life; C refers to the same by using the phrase
'we become miser in this sense'; and D shows how we
become misers. A presents the concluding statement.
30. d C relates knowledge to ignorance; B relates our thinking
to our knowledge and states that our knowledge is
always limited, a fact which leads to D that states that as
knowledge is limited, our thinking is also limited. A
concludes the passage.
31. d C states India's position on exchange rate; A states why
India's position is not surprising; B continues with the
idea; D gives examples of exceptions to B.
32. d D talks about the 'power' introduced in 1. A states that if
'it is an anchor in difficulties, it should be remembered in
good times too'. C states the work done by some
organizations and B adds to it.
33. b B states what happens in the absence of punishment; A
talks about the effect of such a situation; C adds to it by
using 'also' and D states what can be done instead.
34. c C continues with the fact that the vessel was moving
away; A states that he looked around; D states that it
was of no use; B explains why there was no use of
looking  around.
35. d A continues with the idea introduced in 1. C states that
the leader should be personally seen; D states what
else should be insisted upon. B talks of allocating work
to members in clear terms, and this should precede 6,
which states how this has to be done.
36. d A states that true friends are very rare; C states that as
they are rare, they should be respected; B states some
factors which should not be considered while making
friends; and D states that in business realities, all the
acquaintances are motivated by self interest and thus
cannot be treated as genuine friends.
37. a 1 states what managers should guard against; D states
how one can do so; C continues by using 'also'. A states
that external appearances can be deceptive; B
elaborates on the fact and leads to 6.
38. b A states how demands for resources are made; C states
what is done to offset adverse effects of cuts imposed
by seniors; B states the importance of availability of
adequate resources; and D re-emphasizes the point
made in B.
39. d B continues with the idea introduced in 1. A relates the
idea to managers in an organization, who have to take
ruthless decisions; D states how these decisions can
be made easier to accept. C talks about delegation of
power, an idea that is continued in 6.
Page 3


Page 1 CAT 1995 Actual Paper

	






1 a 2 b 3 a 4 b 5 c 6 c 7 d 8 c 9 b 10 d
11 c 12 d 13 c 14 d 15 c 16 c 17 d 18 b 19 b 20 a
21 d 22 b 23 c 24 b 25 a 26 b 27 a 28 d 29 b 30 d
31 d 32 d 33 b 34 c 35 d 36 d 37 a 38 b 39 d 40 b
41 d 42 b 43 c 44 b 45 a 46 d 47 a 48 a 49 d 50 c
51 b 52 b 53 a 54 c 55 d 56 a 57 b 58 c 59 d 60 a
61 c 62 d 63 b 64 * 65 b 66 c 67 a 68 a 69 a 70 b
71 a 72 a 73 c 74 d 75 d 76 c 77 d 78 a 79 b 80 b
81 b 82 a 83 b 84 d 85 d 86 c 87 d 88 a 89 d 90 b
91 d 92 a 93 d 94 a 95 c 96 b 97 a 98 c 99 c 100 c
101 d 102 b 103 d 104 a 105 b 106 a 107 c 108 a 109 c 110 c
111 b 112 b 113 a 114 b 115 a 116 b 117 d 118 d 119 a 120 c
121 c 122 c 123 b 124 a 125 a 126 c 127 c 128 d 129 d 130 a
131 b 132 b 133 a 134 b 135 c 136 a 137 c 138 d 139 a 140 d
141 b 142 c 143 c 144 a 145 b 146 d 147 b 148 a 149 c 150 b
151 d 152 a 153 d 154 a 155 a 156 b 157 b 158 d 159 a 160 b
161 a 162 b 163 d 164 d 165 c 166 b 167 d 168 c 169 d 170 a
171 c 172 a 173 b 174 d 175 c 176 b 177 d 178 a 179 a 180 c
181 a 182 b 183 c 184 d 185 b
Page 2
CAT 1995 Actual Paper
1. a All others are synonyms meaning 'to tear or cut'.
2. b All others are synonyms of control.
3. a All others mean 'to start'; cease means to stop.
4. b All others mean 'on the edge'.
5. c All others refer to something said in praise.
6. c All others refer to a feeling of hatred.
7. d All others are adjectives meaning 'skillful'.
8. c All others are adjectives for persons who do not speak
much.
9. b All others are synonyms.
10. d All others refer to persons who are madly enthusiastic
about something.
11. c 'The student's' should be replaced with 'his'.
12. d We are talking about 'every man or woman', therefore
the pronoun used should be singular 'his/her', instead of
'their'.
13. c The pronoun should remain consistent throughout the
sentence, hence 'you' should be replaced with 'one'.
14. d 'Assure' is an intransitive verb and should be followed
by an object. The correct usage here would be 'be sure
of'.
15. c The man being referred here is the object to the verb,
hence 'who' should be replaced with 'whom'.
16. c Both are pairs of antonyms.
17. d 'Alleviate' is an extended form of 'ease' and 'interrogate'
is an extended form of 'question'.
18. b Both are pairs of synonyms. All four words mean 'secret’.
19. b Audience watch a drama and spectators watch a game.
20. a Just as a building can have many stories, a book can
have many chapters.
21. d All others are pairs of synonyms.
22. b In all other pairs, the first word is a part of the second
word.
23. c In all other pairs, the first word is an adjective referring
to the second word.
24. b In all other pairs, the first word is an adjective derived
from the second pair.
25. a In all other pairs, the first word refers to a fear of the
second word.
26. b D tells us that the passage is about continuation of
previous night's discussion. B states what the discussion
was about. C adds a point to it by using 'also'. A answers
the question raised in C about the reason of conflicts.
27. a B states that the document tells us about history, A states
which part of history does it relate to, D elaborates further
on the first generation poets by referring to Wordsworth
and Coleridge.
28. d C introduces the poet's large plans, A shows how they
were replaced by new plans, D states how even these
plans remained unfulfilled and B tells us what was the
ultimate outcome of the plans.
29. b B states our attitude towards value of time as we
advance in life; C refers to the same by using the phrase
'we become miser in this sense'; and D shows how we
become misers. A presents the concluding statement.
30. d C relates knowledge to ignorance; B relates our thinking
to our knowledge and states that our knowledge is
always limited, a fact which leads to D that states that as
knowledge is limited, our thinking is also limited. A
concludes the passage.
31. d C states India's position on exchange rate; A states why
India's position is not surprising; B continues with the
idea; D gives examples of exceptions to B.
32. d D talks about the 'power' introduced in 1. A states that if
'it is an anchor in difficulties, it should be remembered in
good times too'. C states the work done by some
organizations and B adds to it.
33. b B states what happens in the absence of punishment; A
talks about the effect of such a situation; C adds to it by
using 'also' and D states what can be done instead.
34. c C continues with the fact that the vessel was moving
away; A states that he looked around; D states that it
was of no use; B explains why there was no use of
looking  around.
35. d A continues with the idea introduced in 1. C states that
the leader should be personally seen; D states what
else should be insisted upon. B talks of allocating work
to members in clear terms, and this should precede 6,
which states how this has to be done.
36. d A states that true friends are very rare; C states that as
they are rare, they should be respected; B states some
factors which should not be considered while making
friends; and D states that in business realities, all the
acquaintances are motivated by self interest and thus
cannot be treated as genuine friends.
37. a 1 states what managers should guard against; D states
how one can do so; C continues by using 'also'. A states
that external appearances can be deceptive; B
elaborates on the fact and leads to 6.
38. b A states how demands for resources are made; C states
what is done to offset adverse effects of cuts imposed
by seniors; B states the importance of availability of
adequate resources; and D re-emphasizes the point
made in B.
39. d B continues with the idea introduced in 1. A relates the
idea to managers in an organization, who have to take
ruthless decisions; D states how these decisions can
be made easier to accept. C talks about delegation of
power, an idea that is continued in 6.
Page 3 CAT 1995 Actual Paper
40. b C states how the first two categories mentioned in 1
should be dealt with, D talks about the last category; A
continues by referring to 'the persons in this category'. B
states how the wicked must be dealt with and leads to 6.
41. d Some dubbles are not bubbles but all dubbles are rubbles,
so it follows that some of the rubbles are not bubbles.
42. b If all men are sad and all bad things are men, it follows
that some sad things are bad.
43. c All T oms are bright, but no bright T om is a Dick. Therefore,
no Dick is a Tom.
44. b If all witches are devils and all devils are nasty, it implies
that all witches are also nasty.
45. a No tingo is a bingo but all jingoes are bingoes. Hence, no
jingo is a tingo.
46. d One cannot devote one's whole life to understanding
another culture, if to appreciate other cultures first one
has to spend time understanding one's own culture and
people.
47. a Fresh experience enriches the writers soul, thus
renewing him, in turn leading to the writer being fertile.
48. a An idea that brings in a tremendous disparity would not
be able to work for general convenience and advantage,
as stated in the argument.
49. d
50. c The passage states that even those whom we intimately
know, can surprise us at times with some unknown
facet of their personality.
51. b Since base of each triangle will be counted once,
Sum of perimeters of the triangles = Perimeter of the
square + 2 × (Sum of its diagonals).
But each of the other two sides of the triangles is common
to two triangles, so it will be counted twice.
Area of the square = 4, therefore length of its side = 2
and perimeter = 8.
Also its diagonal = 2v2.
So the required perimeter = (8 + 2 × 4v2) = 8(1 + v2).
52. b 5
6
 – 1 = (5
3
)
2
 – 1 = (125)
2
 – (1)
2
 = (125 + 1) (125 – 1)
= 124 × 126 = 31 × 4 × 126.
So among the given answer choices, it is divisible by 31.
53. a After 2 years, the price of the flat will be (1)(1.10)
2
= Rs.1.21 lakh.
Correspondingly the price of the land will be
(1.1)(1.05)
2
 = Rs.1.21275 lakh.
Hence, the price of the plot = Rs.(1.21275 – 1.21) lakh
= Rs.275 more than that of the flat.
Hence, if they exchange, Ram will have to pay this
amount to Prem .
For questions 54 to 57:
Please note that the best way to solve this question is by working
backwards.
E.g. after the 4th round, each one of them had Rs.32. Since it is
Vibha who lost in this round, all the remaining three must have
doubled their share.
In other words, they would have had Rs.16 each after the 3rd
round.
Since the increase is of Rs.16 in each one’s share, i.e., Rs.48
overall which comes from Vibha's share, her share before the
4th round was (32 + 48) = Rs.80, after the 3rd round.
Working backwards in this manner, we can get the following
table.
h c a e f o e r a h S
a n r a v uSa r aTa mUa h b i V
a h b i V . 4 2323232 3
a m U . 3 61616 1
) 8 4 + 2 3 (
0 8 =
a r a T . 2 88
+ 0 4 + 6 1 (
2 7 = ) 8 + 8
0 4
a n r a v u S . 1 4
6 3 + 4 + 8 (
8 6 = ) 0 2 +
630 2
l a i t i n I
8 1 + 4 3 + 4 (
6 6 = ) 0 1 +
43810 1
54. c Suvarna started with Rs.66.
55. d It was Vibha who started with the lowest amount, viz.
Rs.10.
56. a It was Suvarna who started with the highest amount,
viz. Rs.66.
57. b At the end of the second round, Uma had Rs.72.
58. c     Hint: The best way to solve this question is to multiply
the alternatives by 72 and find which one gives you
the middle three digits as 96.7.
To save time, you can multiply 72 by integer values
only.
E.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.
It is to be noted that when the decimal part of the
answer will be multiplied by 72, the actual answer will
increase.
Let us now roughly multiply the decimal values of the
options also by 72. E.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2
and 72 × 0.5 = 36.
So option (a) will yield (216 + 14) = 230
(approximately), (b) will yield (360 + 7) = 367
(approximately), (c) will yield (360 + 36) = 396
(approximately) and (d) will yield (504 + 14) = 528
(approximately).
Of these, only option (c) satisfies our requirement of
2nd and 3rd digits being 96.
Page 4


Page 1 CAT 1995 Actual Paper

	






1 a 2 b 3 a 4 b 5 c 6 c 7 d 8 c 9 b 10 d
11 c 12 d 13 c 14 d 15 c 16 c 17 d 18 b 19 b 20 a
21 d 22 b 23 c 24 b 25 a 26 b 27 a 28 d 29 b 30 d
31 d 32 d 33 b 34 c 35 d 36 d 37 a 38 b 39 d 40 b
41 d 42 b 43 c 44 b 45 a 46 d 47 a 48 a 49 d 50 c
51 b 52 b 53 a 54 c 55 d 56 a 57 b 58 c 59 d 60 a
61 c 62 d 63 b 64 * 65 b 66 c 67 a 68 a 69 a 70 b
71 a 72 a 73 c 74 d 75 d 76 c 77 d 78 a 79 b 80 b
81 b 82 a 83 b 84 d 85 d 86 c 87 d 88 a 89 d 90 b
91 d 92 a 93 d 94 a 95 c 96 b 97 a 98 c 99 c 100 c
101 d 102 b 103 d 104 a 105 b 106 a 107 c 108 a 109 c 110 c
111 b 112 b 113 a 114 b 115 a 116 b 117 d 118 d 119 a 120 c
121 c 122 c 123 b 124 a 125 a 126 c 127 c 128 d 129 d 130 a
131 b 132 b 133 a 134 b 135 c 136 a 137 c 138 d 139 a 140 d
141 b 142 c 143 c 144 a 145 b 146 d 147 b 148 a 149 c 150 b
151 d 152 a 153 d 154 a 155 a 156 b 157 b 158 d 159 a 160 b
161 a 162 b 163 d 164 d 165 c 166 b 167 d 168 c 169 d 170 a
171 c 172 a 173 b 174 d 175 c 176 b 177 d 178 a 179 a 180 c
181 a 182 b 183 c 184 d 185 b
Page 2
CAT 1995 Actual Paper
1. a All others are synonyms meaning 'to tear or cut'.
2. b All others are synonyms of control.
3. a All others mean 'to start'; cease means to stop.
4. b All others mean 'on the edge'.
5. c All others refer to something said in praise.
6. c All others refer to a feeling of hatred.
7. d All others are adjectives meaning 'skillful'.
8. c All others are adjectives for persons who do not speak
much.
9. b All others are synonyms.
10. d All others refer to persons who are madly enthusiastic
about something.
11. c 'The student's' should be replaced with 'his'.
12. d We are talking about 'every man or woman', therefore
the pronoun used should be singular 'his/her', instead of
'their'.
13. c The pronoun should remain consistent throughout the
sentence, hence 'you' should be replaced with 'one'.
14. d 'Assure' is an intransitive verb and should be followed
by an object. The correct usage here would be 'be sure
of'.
15. c The man being referred here is the object to the verb,
hence 'who' should be replaced with 'whom'.
16. c Both are pairs of antonyms.
17. d 'Alleviate' is an extended form of 'ease' and 'interrogate'
is an extended form of 'question'.
18. b Both are pairs of synonyms. All four words mean 'secret’.
19. b Audience watch a drama and spectators watch a game.
20. a Just as a building can have many stories, a book can
have many chapters.
21. d All others are pairs of synonyms.
22. b In all other pairs, the first word is a part of the second
word.
23. c In all other pairs, the first word is an adjective referring
to the second word.
24. b In all other pairs, the first word is an adjective derived
from the second pair.
25. a In all other pairs, the first word refers to a fear of the
second word.
26. b D tells us that the passage is about continuation of
previous night's discussion. B states what the discussion
was about. C adds a point to it by using 'also'. A answers
the question raised in C about the reason of conflicts.
27. a B states that the document tells us about history, A states
which part of history does it relate to, D elaborates further
on the first generation poets by referring to Wordsworth
and Coleridge.
28. d C introduces the poet's large plans, A shows how they
were replaced by new plans, D states how even these
plans remained unfulfilled and B tells us what was the
ultimate outcome of the plans.
29. b B states our attitude towards value of time as we
advance in life; C refers to the same by using the phrase
'we become miser in this sense'; and D shows how we
become misers. A presents the concluding statement.
30. d C relates knowledge to ignorance; B relates our thinking
to our knowledge and states that our knowledge is
always limited, a fact which leads to D that states that as
knowledge is limited, our thinking is also limited. A
concludes the passage.
31. d C states India's position on exchange rate; A states why
India's position is not surprising; B continues with the
idea; D gives examples of exceptions to B.
32. d D talks about the 'power' introduced in 1. A states that if
'it is an anchor in difficulties, it should be remembered in
good times too'. C states the work done by some
organizations and B adds to it.
33. b B states what happens in the absence of punishment; A
talks about the effect of such a situation; C adds to it by
using 'also' and D states what can be done instead.
34. c C continues with the fact that the vessel was moving
away; A states that he looked around; D states that it
was of no use; B explains why there was no use of
looking  around.
35. d A continues with the idea introduced in 1. C states that
the leader should be personally seen; D states what
else should be insisted upon. B talks of allocating work
to members in clear terms, and this should precede 6,
which states how this has to be done.
36. d A states that true friends are very rare; C states that as
they are rare, they should be respected; B states some
factors which should not be considered while making
friends; and D states that in business realities, all the
acquaintances are motivated by self interest and thus
cannot be treated as genuine friends.
37. a 1 states what managers should guard against; D states
how one can do so; C continues by using 'also'. A states
that external appearances can be deceptive; B
elaborates on the fact and leads to 6.
38. b A states how demands for resources are made; C states
what is done to offset adverse effects of cuts imposed
by seniors; B states the importance of availability of
adequate resources; and D re-emphasizes the point
made in B.
39. d B continues with the idea introduced in 1. A relates the
idea to managers in an organization, who have to take
ruthless decisions; D states how these decisions can
be made easier to accept. C talks about delegation of
power, an idea that is continued in 6.
Page 3 CAT 1995 Actual Paper
40. b C states how the first two categories mentioned in 1
should be dealt with, D talks about the last category; A
continues by referring to 'the persons in this category'. B
states how the wicked must be dealt with and leads to 6.
41. d Some dubbles are not bubbles but all dubbles are rubbles,
so it follows that some of the rubbles are not bubbles.
42. b If all men are sad and all bad things are men, it follows
that some sad things are bad.
43. c All T oms are bright, but no bright T om is a Dick. Therefore,
no Dick is a Tom.
44. b If all witches are devils and all devils are nasty, it implies
that all witches are also nasty.
45. a No tingo is a bingo but all jingoes are bingoes. Hence, no
jingo is a tingo.
46. d One cannot devote one's whole life to understanding
another culture, if to appreciate other cultures first one
has to spend time understanding one's own culture and
people.
47. a Fresh experience enriches the writers soul, thus
renewing him, in turn leading to the writer being fertile.
48. a An idea that brings in a tremendous disparity would not
be able to work for general convenience and advantage,
as stated in the argument.
49. d
50. c The passage states that even those whom we intimately
know, can surprise us at times with some unknown
facet of their personality.
51. b Since base of each triangle will be counted once,
Sum of perimeters of the triangles = Perimeter of the
square + 2 × (Sum of its diagonals).
But each of the other two sides of the triangles is common
to two triangles, so it will be counted twice.
Area of the square = 4, therefore length of its side = 2
and perimeter = 8.
Also its diagonal = 2v2.
So the required perimeter = (8 + 2 × 4v2) = 8(1 + v2).
52. b 5
6
 – 1 = (5
3
)
2
 – 1 = (125)
2
 – (1)
2
 = (125 + 1) (125 – 1)
= 124 × 126 = 31 × 4 × 126.
So among the given answer choices, it is divisible by 31.
53. a After 2 years, the price of the flat will be (1)(1.10)
2
= Rs.1.21 lakh.
Correspondingly the price of the land will be
(1.1)(1.05)
2
 = Rs.1.21275 lakh.
Hence, the price of the plot = Rs.(1.21275 – 1.21) lakh
= Rs.275 more than that of the flat.
Hence, if they exchange, Ram will have to pay this
amount to Prem .
For questions 54 to 57:
Please note that the best way to solve this question is by working
backwards.
E.g. after the 4th round, each one of them had Rs.32. Since it is
Vibha who lost in this round, all the remaining three must have
doubled their share.
In other words, they would have had Rs.16 each after the 3rd
round.
Since the increase is of Rs.16 in each one’s share, i.e., Rs.48
overall which comes from Vibha's share, her share before the
4th round was (32 + 48) = Rs.80, after the 3rd round.
Working backwards in this manner, we can get the following
table.
h c a e f o e r a h S
a n r a v uSa r aTa mUa h b i V
a h b i V . 4 2323232 3
a m U . 3 61616 1
) 8 4 + 2 3 (
0 8 =
a r a T . 2 88
+ 0 4 + 6 1 (
2 7 = ) 8 + 8
0 4
a n r a v u S . 1 4
6 3 + 4 + 8 (
8 6 = ) 0 2 +
630 2
l a i t i n I
8 1 + 4 3 + 4 (
6 6 = ) 0 1 +
43810 1
54. c Suvarna started with Rs.66.
55. d It was Vibha who started with the lowest amount, viz.
Rs.10.
56. a It was Suvarna who started with the highest amount,
viz. Rs.66.
57. b At the end of the second round, Uma had Rs.72.
58. c     Hint: The best way to solve this question is to multiply
the alternatives by 72 and find which one gives you
the middle three digits as 96.7.
To save time, you can multiply 72 by integer values
only.
E.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.
It is to be noted that when the decimal part of the
answer will be multiplied by 72, the actual answer will
increase.
Let us now roughly multiply the decimal values of the
options also by 72. E.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2
and 72 × 0.5 = 36.
So option (a) will yield (216 + 14) = 230
(approximately), (b) will yield (360 + 7) = 367
(approximately), (c) will yield (360 + 36) = 396
(approximately) and (d) will yield (504 + 14) = 528
(approximately).
Of these, only option (c) satisfies our requirement of
2nd and 3rd digits being 96.
Page 4
CAT 1995 Actual Paper
59. d Let us assume that the person has Rs.100.
With this, he can buy 50 oranges or 40 mangoes.
In other words, the price of an orange is Rs.2 and that of
a mango is Rs.2.50.
If he decides to keep 10% of his money for taxi fare, he
would be left with Rs.90.
Now if he buys 20 mangoes, he would spend Rs.50 and
will be left with Rs.40.
Thus, he can buy 20 oranges.
60. a The given expression is of the form
33
22
[x y ]
[x – xy y ]
+
+
.
We know, 



 + = (x + y)( x
2
 – xy + y
2
).
Thus, required value = (x + y) = (55 + 45) = 100.
61. c The largest angle in a right-angled triangle is 90º, which
corresponds to the highest part of the ratio.
Let us evaluate each option.
In (a), the remaining two angles would be 30º and 60º,
which is possible.
 In (b), the remaining two angles would be 45º each,
which is again possible.
 In (c), the remaining two angles would be 15º and 45º,
which is not possible as the sum of the angles is not
180º.
62. d Since n(n + 1) are two consecutive integers, one of
them will be even and thus their the product will always
be even.
Also, sum of the squares of first ‘n’ natural numbers is
given by 
6
) 1 n 2 ( ) 1 n ( n + +
.
Hence, our product will always be divisible by this.
Also you will find that the product is always divisible by
3 (you can use any value of n to verify this).
However, we can find that option (d) is not necessarily
true. E.g. If n = 118, (2n + 1) = 237 or if n = 236, then (n +
1) = 237 or if n itself is 237, etc.
63. b The best way to solve this question is by the method of
simulation. Choose any prime number greater than 6 and
verify the result.
When 7 is divided by 6, it gives a remainder 1. So our
answer could be (a) or (b). When 11 is divided by 6, it
gives a remainder 5. Hence, our answer is (b).
64. * There cannot be four or more blue balls.
Case 1:
If there are three blue balls, then they can be only in
box 1, 3 and 5.
Case 2:
If there are two blue balls, then total number of cases
= 
5
C
2
 = 10
But in 4 cases the blue ball will be in adjacent boxes.
These cases are when blue balls in boxes 1 and 2 or
2 and 3 or 3 and 4 or 4 and 5.
Therefore, total number of cases when there are two
blue balls = 10 – 4 = 6
Case 3:
If there are one blue ball, then total number of cases =
5
C
1
= 5
Case 4:
If there are no blue ball, then total number of cases =
5
C
5
= 1
Hence, total number of cases = 1 + 6 + 5 + 1 = 13.
* The correct answer is not available in the
given options.
65. b
A
B
C
D
E
30
In ? ABC, ?ACB = 180 – 90 – 30 = 60°.
? ?DCE = 30°, since ?CDE = 90°.
 In  ? CED, ?CED = 180 – 90 – 30 = 60°.
66. c Using alligation, the ratio of the amounts invested at both
the rates = 2 : 1.
 Since he has invested Rs.3,000 at 5%, he should further
invest Rs.1,500 at 8% to earn a total interest of 6% per
annum.
Initial rate of
investment 
Ratio of am ounts
invested
Resultant rate
of investm ent 
5% 8%
2          : 1
6%
Alternative method:
Let the amount invested at 8% be Rs.x.
Then,
105 108
3000 x
100 100
×+×
100
106
) x 3000 ( + =
? 0.02x = 30 ? x = 1,500
? He should further invest Rs.1,500 at 5% to earn a total
interest of 6% per annum.
67. a Let there be 100 voters in all.
Initially, 40 of these promised to vote for P, while 60 of
them promised  to vote for Q.
On the last day, (15% of 40) = 6 voters went back of
their promise and voted for Q.
Also, 25% of 60 = 15 voters shifted their interest from Q
to P .
So finally, P end up getting (40 – 6 + 15) = 49 votes and
Q end up getting (60 – 15 + 6) = 51 votes.
Hence, margin of victory for Q = (51 – 49) = 2, which is
true. Hence, there were 100 voters in all.
68. a In the given figure, the area of the circle = pr
2
.
To find out the area of the circle, we need to find out the
length of the side of the square.
 We know, OR = OT + TR = OT + OS = 2r.
In right-angled triangle ORS, OR = 2r and OS = r.
So SR
2
 = OR
2
 – OS
2
.
But SR
2
 = Area of the square = 4r
2
 – r
2
 = 3r
2
.
Hence, the required ratio = 
3
p
.
Page 5


Page 1 CAT 1995 Actual Paper

	






1 a 2 b 3 a 4 b 5 c 6 c 7 d 8 c 9 b 10 d
11 c 12 d 13 c 14 d 15 c 16 c 17 d 18 b 19 b 20 a
21 d 22 b 23 c 24 b 25 a 26 b 27 a 28 d 29 b 30 d
31 d 32 d 33 b 34 c 35 d 36 d 37 a 38 b 39 d 40 b
41 d 42 b 43 c 44 b 45 a 46 d 47 a 48 a 49 d 50 c
51 b 52 b 53 a 54 c 55 d 56 a 57 b 58 c 59 d 60 a
61 c 62 d 63 b 64 * 65 b 66 c 67 a 68 a 69 a 70 b
71 a 72 a 73 c 74 d 75 d 76 c 77 d 78 a 79 b 80 b
81 b 82 a 83 b 84 d 85 d 86 c 87 d 88 a 89 d 90 b
91 d 92 a 93 d 94 a 95 c 96 b 97 a 98 c 99 c 100 c
101 d 102 b 103 d 104 a 105 b 106 a 107 c 108 a 109 c 110 c
111 b 112 b 113 a 114 b 115 a 116 b 117 d 118 d 119 a 120 c
121 c 122 c 123 b 124 a 125 a 126 c 127 c 128 d 129 d 130 a
131 b 132 b 133 a 134 b 135 c 136 a 137 c 138 d 139 a 140 d
141 b 142 c 143 c 144 a 145 b 146 d 147 b 148 a 149 c 150 b
151 d 152 a 153 d 154 a 155 a 156 b 157 b 158 d 159 a 160 b
161 a 162 b 163 d 164 d 165 c 166 b 167 d 168 c 169 d 170 a
171 c 172 a 173 b 174 d 175 c 176 b 177 d 178 a 179 a 180 c
181 a 182 b 183 c 184 d 185 b
Page 2
CAT 1995 Actual Paper
1. a All others are synonyms meaning 'to tear or cut'.
2. b All others are synonyms of control.
3. a All others mean 'to start'; cease means to stop.
4. b All others mean 'on the edge'.
5. c All others refer to something said in praise.
6. c All others refer to a feeling of hatred.
7. d All others are adjectives meaning 'skillful'.
8. c All others are adjectives for persons who do not speak
much.
9. b All others are synonyms.
10. d All others refer to persons who are madly enthusiastic
about something.
11. c 'The student's' should be replaced with 'his'.
12. d We are talking about 'every man or woman', therefore
the pronoun used should be singular 'his/her', instead of
'their'.
13. c The pronoun should remain consistent throughout the
sentence, hence 'you' should be replaced with 'one'.
14. d 'Assure' is an intransitive verb and should be followed
by an object. The correct usage here would be 'be sure
of'.
15. c The man being referred here is the object to the verb,
hence 'who' should be replaced with 'whom'.
16. c Both are pairs of antonyms.
17. d 'Alleviate' is an extended form of 'ease' and 'interrogate'
is an extended form of 'question'.
18. b Both are pairs of synonyms. All four words mean 'secret’.
19. b Audience watch a drama and spectators watch a game.
20. a Just as a building can have many stories, a book can
have many chapters.
21. d All others are pairs of synonyms.
22. b In all other pairs, the first word is a part of the second
word.
23. c In all other pairs, the first word is an adjective referring
to the second word.
24. b In all other pairs, the first word is an adjective derived
from the second pair.
25. a In all other pairs, the first word refers to a fear of the
second word.
26. b D tells us that the passage is about continuation of
previous night's discussion. B states what the discussion
was about. C adds a point to it by using 'also'. A answers
the question raised in C about the reason of conflicts.
27. a B states that the document tells us about history, A states
which part of history does it relate to, D elaborates further
on the first generation poets by referring to Wordsworth
and Coleridge.
28. d C introduces the poet's large plans, A shows how they
were replaced by new plans, D states how even these
plans remained unfulfilled and B tells us what was the
ultimate outcome of the plans.
29. b B states our attitude towards value of time as we
advance in life; C refers to the same by using the phrase
'we become miser in this sense'; and D shows how we
become misers. A presents the concluding statement.
30. d C relates knowledge to ignorance; B relates our thinking
to our knowledge and states that our knowledge is
always limited, a fact which leads to D that states that as
knowledge is limited, our thinking is also limited. A
concludes the passage.
31. d C states India's position on exchange rate; A states why
India's position is not surprising; B continues with the
idea; D gives examples of exceptions to B.
32. d D talks about the 'power' introduced in 1. A states that if
'it is an anchor in difficulties, it should be remembered in
good times too'. C states the work done by some
organizations and B adds to it.
33. b B states what happens in the absence of punishment; A
talks about the effect of such a situation; C adds to it by
using 'also' and D states what can be done instead.
34. c C continues with the fact that the vessel was moving
away; A states that he looked around; D states that it
was of no use; B explains why there was no use of
looking  around.
35. d A continues with the idea introduced in 1. C states that
the leader should be personally seen; D states what
else should be insisted upon. B talks of allocating work
to members in clear terms, and this should precede 6,
which states how this has to be done.
36. d A states that true friends are very rare; C states that as
they are rare, they should be respected; B states some
factors which should not be considered while making
friends; and D states that in business realities, all the
acquaintances are motivated by self interest and thus
cannot be treated as genuine friends.
37. a 1 states what managers should guard against; D states
how one can do so; C continues by using 'also'. A states
that external appearances can be deceptive; B
elaborates on the fact and leads to 6.
38. b A states how demands for resources are made; C states
what is done to offset adverse effects of cuts imposed
by seniors; B states the importance of availability of
adequate resources; and D re-emphasizes the point
made in B.
39. d B continues with the idea introduced in 1. A relates the
idea to managers in an organization, who have to take
ruthless decisions; D states how these decisions can
be made easier to accept. C talks about delegation of
power, an idea that is continued in 6.
Page 3 CAT 1995 Actual Paper
40. b C states how the first two categories mentioned in 1
should be dealt with, D talks about the last category; A
continues by referring to 'the persons in this category'. B
states how the wicked must be dealt with and leads to 6.
41. d Some dubbles are not bubbles but all dubbles are rubbles,
so it follows that some of the rubbles are not bubbles.
42. b If all men are sad and all bad things are men, it follows
that some sad things are bad.
43. c All T oms are bright, but no bright T om is a Dick. Therefore,
no Dick is a Tom.
44. b If all witches are devils and all devils are nasty, it implies
that all witches are also nasty.
45. a No tingo is a bingo but all jingoes are bingoes. Hence, no
jingo is a tingo.
46. d One cannot devote one's whole life to understanding
another culture, if to appreciate other cultures first one
has to spend time understanding one's own culture and
people.
47. a Fresh experience enriches the writers soul, thus
renewing him, in turn leading to the writer being fertile.
48. a An idea that brings in a tremendous disparity would not
be able to work for general convenience and advantage,
as stated in the argument.
49. d
50. c The passage states that even those whom we intimately
know, can surprise us at times with some unknown
facet of their personality.
51. b Since base of each triangle will be counted once,
Sum of perimeters of the triangles = Perimeter of the
square + 2 × (Sum of its diagonals).
But each of the other two sides of the triangles is common
to two triangles, so it will be counted twice.
Area of the square = 4, therefore length of its side = 2
and perimeter = 8.
Also its diagonal = 2v2.
So the required perimeter = (8 + 2 × 4v2) = 8(1 + v2).
52. b 5
6
 – 1 = (5
3
)
2
 – 1 = (125)
2
 – (1)
2
 = (125 + 1) (125 – 1)
= 124 × 126 = 31 × 4 × 126.
So among the given answer choices, it is divisible by 31.
53. a After 2 years, the price of the flat will be (1)(1.10)
2
= Rs.1.21 lakh.
Correspondingly the price of the land will be
(1.1)(1.05)
2
 = Rs.1.21275 lakh.
Hence, the price of the plot = Rs.(1.21275 – 1.21) lakh
= Rs.275 more than that of the flat.
Hence, if they exchange, Ram will have to pay this
amount to Prem .
For questions 54 to 57:
Please note that the best way to solve this question is by working
backwards.
E.g. after the 4th round, each one of them had Rs.32. Since it is
Vibha who lost in this round, all the remaining three must have
doubled their share.
In other words, they would have had Rs.16 each after the 3rd
round.
Since the increase is of Rs.16 in each one’s share, i.e., Rs.48
overall which comes from Vibha's share, her share before the
4th round was (32 + 48) = Rs.80, after the 3rd round.
Working backwards in this manner, we can get the following
table.
h c a e f o e r a h S
a n r a v uSa r aTa mUa h b i V
a h b i V . 4 2323232 3
a m U . 3 61616 1
) 8 4 + 2 3 (
0 8 =
a r a T . 2 88
+ 0 4 + 6 1 (
2 7 = ) 8 + 8
0 4
a n r a v u S . 1 4
6 3 + 4 + 8 (
8 6 = ) 0 2 +
630 2
l a i t i n I
8 1 + 4 3 + 4 (
6 6 = ) 0 1 +
43810 1
54. c Suvarna started with Rs.66.
55. d It was Vibha who started with the lowest amount, viz.
Rs.10.
56. a It was Suvarna who started with the highest amount,
viz. Rs.66.
57. b At the end of the second round, Uma had Rs.72.
58. c     Hint: The best way to solve this question is to multiply
the alternatives by 72 and find which one gives you
the middle three digits as 96.7.
To save time, you can multiply 72 by integer values
only.
E.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.
It is to be noted that when the decimal part of the
answer will be multiplied by 72, the actual answer will
increase.
Let us now roughly multiply the decimal values of the
options also by 72. E.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2
and 72 × 0.5 = 36.
So option (a) will yield (216 + 14) = 230
(approximately), (b) will yield (360 + 7) = 367
(approximately), (c) will yield (360 + 36) = 396
(approximately) and (d) will yield (504 + 14) = 528
(approximately).
Of these, only option (c) satisfies our requirement of
2nd and 3rd digits being 96.
Page 4
CAT 1995 Actual Paper
59. d Let us assume that the person has Rs.100.
With this, he can buy 50 oranges or 40 mangoes.
In other words, the price of an orange is Rs.2 and that of
a mango is Rs.2.50.
If he decides to keep 10% of his money for taxi fare, he
would be left with Rs.90.
Now if he buys 20 mangoes, he would spend Rs.50 and
will be left with Rs.40.
Thus, he can buy 20 oranges.
60. a The given expression is of the form
33
22
[x y ]
[x – xy y ]
+
+
.
We know, 



 + = (x + y)( x
2
 – xy + y
2
).
Thus, required value = (x + y) = (55 + 45) = 100.
61. c The largest angle in a right-angled triangle is 90º, which
corresponds to the highest part of the ratio.
Let us evaluate each option.
In (a), the remaining two angles would be 30º and 60º,
which is possible.
 In (b), the remaining two angles would be 45º each,
which is again possible.
 In (c), the remaining two angles would be 15º and 45º,
which is not possible as the sum of the angles is not
180º.
62. d Since n(n + 1) are two consecutive integers, one of
them will be even and thus their the product will always
be even.
Also, sum of the squares of first ‘n’ natural numbers is
given by 
6
) 1 n 2 ( ) 1 n ( n + +
.
Hence, our product will always be divisible by this.
Also you will find that the product is always divisible by
3 (you can use any value of n to verify this).
However, we can find that option (d) is not necessarily
true. E.g. If n = 118, (2n + 1) = 237 or if n = 236, then (n +
1) = 237 or if n itself is 237, etc.
63. b The best way to solve this question is by the method of
simulation. Choose any prime number greater than 6 and
verify the result.
When 7 is divided by 6, it gives a remainder 1. So our
answer could be (a) or (b). When 11 is divided by 6, it
gives a remainder 5. Hence, our answer is (b).
64. * There cannot be four or more blue balls.
Case 1:
If there are three blue balls, then they can be only in
box 1, 3 and 5.
Case 2:
If there are two blue balls, then total number of cases
= 
5
C
2
 = 10
But in 4 cases the blue ball will be in adjacent boxes.
These cases are when blue balls in boxes 1 and 2 or
2 and 3 or 3 and 4 or 4 and 5.
Therefore, total number of cases when there are two
blue balls = 10 – 4 = 6
Case 3:
If there are one blue ball, then total number of cases =
5
C
1
= 5
Case 4:
If there are no blue ball, then total number of cases =
5
C
5
= 1
Hence, total number of cases = 1 + 6 + 5 + 1 = 13.
* The correct answer is not available in the
given options.
65. b
A
B
C
D
E
30
In ? ABC, ?ACB = 180 – 90 – 30 = 60°.
? ?DCE = 30°, since ?CDE = 90°.
 In  ? CED, ?CED = 180 – 90 – 30 = 60°.
66. c Using alligation, the ratio of the amounts invested at both
the rates = 2 : 1.
 Since he has invested Rs.3,000 at 5%, he should further
invest Rs.1,500 at 8% to earn a total interest of 6% per
annum.
Initial rate of
investment 
Ratio of am ounts
invested
Resultant rate
of investm ent 
5% 8%
2          : 1
6%
Alternative method:
Let the amount invested at 8% be Rs.x.
Then,
105 108
3000 x
100 100
×+×
100
106
) x 3000 ( + =
? 0.02x = 30 ? x = 1,500
? He should further invest Rs.1,500 at 5% to earn a total
interest of 6% per annum.
67. a Let there be 100 voters in all.
Initially, 40 of these promised to vote for P, while 60 of
them promised  to vote for Q.
On the last day, (15% of 40) = 6 voters went back of
their promise and voted for Q.
Also, 25% of 60 = 15 voters shifted their interest from Q
to P .
So finally, P end up getting (40 – 6 + 15) = 49 votes and
Q end up getting (60 – 15 + 6) = 51 votes.
Hence, margin of victory for Q = (51 – 49) = 2, which is
true. Hence, there were 100 voters in all.
68. a In the given figure, the area of the circle = pr
2
.
To find out the area of the circle, we need to find out the
length of the side of the square.
 We know, OR = OT + TR = OT + OS = 2r.
In right-angled triangle ORS, OR = 2r and OS = r.
So SR
2
 = OR
2
 – OS
2
.
But SR
2
 = Area of the square = 4r
2
 – r
2
 = 3r
2
.
Hence, the required ratio = 
3
p
.
Page 5 CAT 1995 Actual Paper
69. a In the same time as A runs 200 m in the race, S runs 180
m and N runs 160 m.
In other words, in the same time as S runs 180 m, N runs
160 m.
So in the same time as S runs 100 m, N will run
?
?
?
?
?
?
?
?
×
180
160
100
 = 88.89 m.
Hence, in a 100 m race, S will beat N by (100 – 88.89) =
11.11 m.
70. b If the numbers are (x – 2), x and (x + 2), then
3(x – 2) – 2 = 2(x + 2).
? x + 2 = 14.
71. a If x men were there on day one, there would be (x – 110)
men on the 12th day.
Hence, on an average, there were (x – 55) men.
The job takes
2
3
 times the normal time.
Hence, the average number of people = 
3
2
.
? x – 55 = 
x
3
2
Hence, x = 165
72. a Total number of four-digit numbers that can be
formed = 4!.
If the number is divisible by 25, then the last two
digits are 25.
So the first two digits can be arranged in 2! ways.
Hence, required probability = 
12
1
! 4
! 2
=
.
73. c Let the first typist takes X hours and the second takes
Y hours to do the whole job.
When the first was busy typing for 3 hr, the second
was busy only for 2 hr.
Both of them did 
11
20
 of the whole work.
?
20
11
Y
2
X
3
= +
.
When the assignment was completed, it was revealed
that each typist had done half the work.
?
The first one spent 
2
X
 hr, and the second, 
2
Y
 hr.
And since the first had begun one hour before the
second, we have 1
2
Y
2
X
= -
? X = 10 hr, Y = 8 hr.
74. d Since I live X floors above the ground floor and it takes
me 30 s per floor to walk down and 2 s per floor to ride
the lift, it takes 30X s to walk down and 2X s to ride   the
lift after waiting 420 s.
? 30X = 2X + 420 ? X = 15.
Alternative method:
X > 14 as time taken to walk has to be greater than
7 min.
75. d Since 5-12-13 forms a Pythagorean triplet, the triangle
under consideration is a right-angled triangle with height
12 and base 5.
So area of the triangle = ?
?
?
?
?
?
?
?
2
1
(12)(5) = 30 sq. units.
If area of the rectangle with width 10 units is 30 sq.
units, its length = 3 units.
Hence, its perimeter = 2(10 + 3) = 26 units.
76. c Since AD = BC  (Opposite sides of a rectangle are equal.)
AB + AC = 5BC and AC – BC = 8  or AC = BC + 8
?
AB = 4(BC – 2)
By Pythagoras’ Theorem, AB
2
 + BC
2
 = AC
2
Expressing AB and AC in terms of BC we get, BC = 5.
 ? AB = 12 and AC = 13
So area of the rectangle = 5 × 12 = 60.
77. d If the roots are a and a
2
, the product of roots = a
3
 = –8.
? a = –2.
Hence, sum of the roots = k = –(a + a
2
) = –(–2 + 4) = – 2.
78. a
A
B
D
C
If we draw the imaginary lines AC and BD, we find that
?CAD and ?CBD are subtended by the same chord DC.
?
?CAD = ?CBD = 30°.
Thus, ?DBA = (70 – 30) = 40°.
Also, ?DBA and ?ACD are subtended by the same chord
DA.
Hence, ?ACD = DBA = ?40°.
79. b
A
B
E
C
D
3
9
The figure can be drawn as shown above.
Height of the wall = AD = AC = (AB + 3) or AB = (AC – 3).
In right-angled triangle ABC, AB
2
 + BC
2
 = AC
2
.
Thus, (AC – 3)
2
 + 81 = AC
2
.
?
 AC = 15 m.
Hence, height of the wall = 15 m.
Hint: Please note that the same multiple of all the triplets
should also be triplets. E.g. if 3-4-5 is a triplet, then 3(3-
4-5) should also be triplet or 9-12-15 is also a triplet.
Note that the base of the triangle is 9, so other two sides
should be 12 and 15.