CAT Past Year Question Paper Solution - 1991 | Additional Study Material for CAT PDF Download

 Page 1


Page 1 CAT 1991 Actual Paper

	





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


Page 1 CAT 1991 Actual Paper

	






1 a 21 c 41 b 61 b 81 a 101 d 121 c 141 c 161 c
2 a 22 c 42 d 62 c 82 a 102 d 122 b 142 c 162 d
3 b 23 c 43 d 63 a 83 c 103 a 123 b 143 c 163 a
4 b 24 c 44 a 64 c 84 b 104 d 124 a 144 d 164 b
5 b 25 b 45 b 65 b 85 a 105 c 125 c 145 c 165 a
6 a 26 b 46 d 66 c 86 a 106 c 126 d 146 c 166 d
7 d 27 c 47 d 67 a 87 c 107 a 127 a 147 d 167 a
8 b 28 a 48 d 68 b 88 b 108 a 128 b 148 d 168 a
9 c 29 d 49 a 69 a 89 b 109 d 129 d 149 b 169 d
10 d 30 d 50 c 70 c 90 d 110 c 130 c 150 b 170 b
11 a 31 d 51 c 71 b 91 b 111 c 131 a 151 b 171 a
12 c 32 a 52 b 72 c 92 b 112 b 132 c 152 b 172 d
13 c 33 c 53 a 73 d 93 a 113 d 133 b 153 d 173 c
14 c 34 d 54 a 74 d 94 c 114 b 134 b 154 b 174 a
15 d 35 b 55 b 75 d 95 d 115 d 135 d 155 c 175 a
16 b 36 c 56 a 76 b 96 c 116 d 136 c 156 b 176 d
17 c 37 a 57 c 77 a 97 d 117 d 137 b 157 d 177 d
18 d 38 c 58 d 78 b 98 a 118 b 138 c 158 d 178 b
19 c 39 c 59 d 79 d 99 a 119 a 139 b 159 a 179 d
20 a 40 a 60 c 80 b 100 c 120 a 140 a 160 d 180 b
Page 2
CAT 1991 Actual Paper
1. a The subject here is ‘the best part’, which is singular
and should therefore be followed by a singular verb.
2. a When using ‘as well as’ to introduce a complex subject,
the phrase should be set off by commas, and the verb
agrees with the main subject, which in this case is
‘the professor’.
3. b As the first part of the sentence provides the reason
for his being unwilling to testify, ‘because’ should be
used to introduce it. Moreover a comma should always
be used to separate two distinct phrases in a
sentence.
4. b The pronoun should remain consistent throughout the
sentence.
5. b When ‘either’ and ‘neither’ are followed by ‘or’ and
‘nor’ respectively, the verb depends on the noun
following ‘or’ and ‘nor’.
6. a The sentence has three different clauses, which
should be separated by semi colons.
7. d When ‘neither’ is followed by ‘nor’, the verb depends
on the noun following ‘nor’. In this case it is singular,
hence the verb should also be singular.
8. b Before a gerund a noun should appear in the
possessive form.
9. c The sentence does not need any commas.
10. d The sentence needs no commas.
11. a We should use ‘who’ for subjects who do the action.
In the given sentence ‘who’ is the subject of the verb
‘were’.
12. c The correct usage would be, ‘a network to facilitate
contacts’.
13. c The correct phrase would be, ‘to the perceived
problems’.
14. c ‘The Indian Government’s choice’ is a singular noun
and should have a singular verb ‘stems’.
15. d The correct quantifier to be used here is ‘most’.
16. b Here we should use the verb in past participle, i.e.
‘you would have’ as we are talking about an unreal
past condition.
17. c ‘Requires’ should be replaced with ‘assumes’.
18. d The noun ‘choice’ is singular and should be followed
by a singular verb ‘invites’.
19. c We already have a subject ‘who’ for the verb ‘decided’,
so ‘he then’ is wrongly used here.
20. a ‘Of’ should be replaced with ‘off’.
21. c Here minorities are being treated as a specific group
and should therefore be preceded by ‘the’.
22. c ‘Aspiring’ cannot be used as an adjective for students
here, as those who are studying management are
already students.
23. c D. introduces the ‘institutional truth of the financial
world’, B. elaborates the idea, A continues with B. and
C. presents the conclusion.
24. c B. introduces the subject of the passage, C. elaborates
on the idea, and use of ‘then’ in A. shows that it should
follow D.
25. b A. introduces the age of pragmatism as the topic of
the passage, C. explains what has changed in the
new age, B. explains the characteristic of the old
world and D. comments on the position today.
26. b D. shows that the passage is about cognitive age, B.
explains what it implies, A. talks about a research
related to the subject and C. explains the implications
of the research.
27. c The sentence C. introduces ‘her eyes’, and should be
the first sentence. A. elaborates on the eyes, so A
should follow C. No other option has CA as the
mandatory pair. So, answer is (c).
28. a B. shows that the topic is ‘intelligence’, D. uses ‘these’
to refer to the different abilities associated with
intelligence, as presented in B. A. explains what
intelligence actually is and C. talks about the true test
of intelligence.
29. d The passage is about difference in pronunciation of
words in different situations. A. explains what the
difference is. Use of ‘further’ and ‘yet’ in D. and B.
respectively show the order in which they should
occur.
30. d Broad and powerful thinking is needed to solve the
problems.
31. d The funds are being ‘raised’ for the purpose of having
money to spend on the search of alternative sources
of energy.
32. a If you look before you leap you will be forewarned
and thus can be forearmed.
33. c As the king, the fate of the economy and the subjects
would be in the ruler’s hands.
34. d We should be prepared to ‘break’ something to
‘reconstruct’ it.
Page 3


Page 1 CAT 1991 Actual Paper

	






1 a 21 c 41 b 61 b 81 a 101 d 121 c 141 c 161 c
2 a 22 c 42 d 62 c 82 a 102 d 122 b 142 c 162 d
3 b 23 c 43 d 63 a 83 c 103 a 123 b 143 c 163 a
4 b 24 c 44 a 64 c 84 b 104 d 124 a 144 d 164 b
5 b 25 b 45 b 65 b 85 a 105 c 125 c 145 c 165 a
6 a 26 b 46 d 66 c 86 a 106 c 126 d 146 c 166 d
7 d 27 c 47 d 67 a 87 c 107 a 127 a 147 d 167 a
8 b 28 a 48 d 68 b 88 b 108 a 128 b 148 d 168 a
9 c 29 d 49 a 69 a 89 b 109 d 129 d 149 b 169 d
10 d 30 d 50 c 70 c 90 d 110 c 130 c 150 b 170 b
11 a 31 d 51 c 71 b 91 b 111 c 131 a 151 b 171 a
12 c 32 a 52 b 72 c 92 b 112 b 132 c 152 b 172 d
13 c 33 c 53 a 73 d 93 a 113 d 133 b 153 d 173 c
14 c 34 d 54 a 74 d 94 c 114 b 134 b 154 b 174 a
15 d 35 b 55 b 75 d 95 d 115 d 135 d 155 c 175 a
16 b 36 c 56 a 76 b 96 c 116 d 136 c 156 b 176 d
17 c 37 a 57 c 77 a 97 d 117 d 137 b 157 d 177 d
18 d 38 c 58 d 78 b 98 a 118 b 138 c 158 d 178 b
19 c 39 c 59 d 79 d 99 a 119 a 139 b 159 a 179 d
20 a 40 a 60 c 80 b 100 c 120 a 140 a 160 d 180 b
Page 2
CAT 1991 Actual Paper
1. a The subject here is ‘the best part’, which is singular
and should therefore be followed by a singular verb.
2. a When using ‘as well as’ to introduce a complex subject,
the phrase should be set off by commas, and the verb
agrees with the main subject, which in this case is
‘the professor’.
3. b As the first part of the sentence provides the reason
for his being unwilling to testify, ‘because’ should be
used to introduce it. Moreover a comma should always
be used to separate two distinct phrases in a
sentence.
4. b The pronoun should remain consistent throughout the
sentence.
5. b When ‘either’ and ‘neither’ are followed by ‘or’ and
‘nor’ respectively, the verb depends on the noun
following ‘or’ and ‘nor’.
6. a The sentence has three different clauses, which
should be separated by semi colons.
7. d When ‘neither’ is followed by ‘nor’, the verb depends
on the noun following ‘nor’. In this case it is singular,
hence the verb should also be singular.
8. b Before a gerund a noun should appear in the
possessive form.
9. c The sentence does not need any commas.
10. d The sentence needs no commas.
11. a We should use ‘who’ for subjects who do the action.
In the given sentence ‘who’ is the subject of the verb
‘were’.
12. c The correct usage would be, ‘a network to facilitate
contacts’.
13. c The correct phrase would be, ‘to the perceived
problems’.
14. c ‘The Indian Government’s choice’ is a singular noun
and should have a singular verb ‘stems’.
15. d The correct quantifier to be used here is ‘most’.
16. b Here we should use the verb in past participle, i.e.
‘you would have’ as we are talking about an unreal
past condition.
17. c ‘Requires’ should be replaced with ‘assumes’.
18. d The noun ‘choice’ is singular and should be followed
by a singular verb ‘invites’.
19. c We already have a subject ‘who’ for the verb ‘decided’,
so ‘he then’ is wrongly used here.
20. a ‘Of’ should be replaced with ‘off’.
21. c Here minorities are being treated as a specific group
and should therefore be preceded by ‘the’.
22. c ‘Aspiring’ cannot be used as an adjective for students
here, as those who are studying management are
already students.
23. c D. introduces the ‘institutional truth of the financial
world’, B. elaborates the idea, A continues with B. and
C. presents the conclusion.
24. c B. introduces the subject of the passage, C. elaborates
on the idea, and use of ‘then’ in A. shows that it should
follow D.
25. b A. introduces the age of pragmatism as the topic of
the passage, C. explains what has changed in the
new age, B. explains the characteristic of the old
world and D. comments on the position today.
26. b D. shows that the passage is about cognitive age, B.
explains what it implies, A. talks about a research
related to the subject and C. explains the implications
of the research.
27. c The sentence C. introduces ‘her eyes’, and should be
the first sentence. A. elaborates on the eyes, so A
should follow C. No other option has CA as the
mandatory pair. So, answer is (c).
28. a B. shows that the topic is ‘intelligence’, D. uses ‘these’
to refer to the different abilities associated with
intelligence, as presented in B. A. explains what
intelligence actually is and C. talks about the true test
of intelligence.
29. d The passage is about difference in pronunciation of
words in different situations. A. explains what the
difference is. Use of ‘further’ and ‘yet’ in D. and B.
respectively show the order in which they should
occur.
30. d Broad and powerful thinking is needed to solve the
problems.
31. d The funds are being ‘raised’ for the purpose of having
money to spend on the search of alternative sources
of energy.
32. a If you look before you leap you will be forewarned
and thus can be forearmed.
33. c As the king, the fate of the economy and the subjects
would be in the ruler’s hands.
34. d We should be prepared to ‘break’ something to
‘reconstruct’ it.
Page 3 CAT 1991 Actual Paper
35. b If the future is upon us before we realize it, it will
shape us rather than the other way round.
36. c
Attendants
Qualified
Nurses
37. a If Mary and John are wife and husband and the last
waltz was danced by husbands and wives, it follows
that John danced last with Mary.
38. c Air
Plants
Roses
39. c Laxman is a man and no man is an island, so Laxman
cannot be an island.
40. a If college students are intelligent and Ram is a college
student, it follows that Ram is intelligent.
41. b If all cigarettes are hazardous to health and cham-
cham is a brand of cigarette, then cham-cham would
also be hazardous to health.
42. d If all good bridge players play good chess, then Goran
being a good bridge player should also play good
chess.
43. d
Cold blooded
Reptiles
44. a
Chlorophyll
Leaves
45. b If bald people are intelligent and Raman is bald, it follows
that Raman is intelligent.
46. d
Gentlemen
Barbarians
Rude
47. d Desks are made of metals. So if an object is a desk it
should be made of metal.
48. d Mathew and Paul are siblings and siblings are known
to quarrel often. Therefore it follows that Mathew and
Paul quarrel often.
49. a Art is a symptom of culture and music is a form of art,
therefore music also shows culture.
50. c If primary colours give different hues, and red is a
primary colour, it implies that red also gives different
hues.
51. c The statement I only gives the comparison of the selling
prices. You must realise that this information is not
enough to answer the question as the profit also
depends on cost. So we also need to analyze the
statement II. And since there is no other constraint on
production, we can solely compare the profitability of
two products on the basis of labour. According to it, if
10 units of labour is available, it can produce 5 units of
Q and 2 units of R. So, from 10 units of labour, I can
earn (5 x 1) = 5 units of sales revenue from Q and (2
x 4) = 8 units of sales revenue from R. So by taking
both statements together we can determine which
would be more profitable.
52. b In order to solve the question, we need to know two
things : (a) the original speed of the train or the new
speed of the train and (b) at what distance from A or
after how much time after leaving A the train
brokedown. The statement II provides both of these
data viz. original speed = 20 kmph and distance from A
= 40 kms. and hence only this is required to answer
the question.
For e.g: If the distance between A & B is considered to
be x, then time taken had it not broken down is
x/20 hours. The new time taken is [2 + (x – 40)/5]
hours and we know that this time is 40 min. more than
the original time. The equation becomes : x/20 + 40/60
= [2 + (x – 40)/5], which can be easily solved to get
value of x.
53. a From statement I, 
2
xx 50 +>
and x
2
 + x < 100
             x(x 1) 50 ?+>
            Only prime number 7 satisfies the above equation.
So the question can be answered from statement 1
alone.
Page 4


Page 1 CAT 1991 Actual Paper

	






1 a 21 c 41 b 61 b 81 a 101 d 121 c 141 c 161 c
2 a 22 c 42 d 62 c 82 a 102 d 122 b 142 c 162 d
3 b 23 c 43 d 63 a 83 c 103 a 123 b 143 c 163 a
4 b 24 c 44 a 64 c 84 b 104 d 124 a 144 d 164 b
5 b 25 b 45 b 65 b 85 a 105 c 125 c 145 c 165 a
6 a 26 b 46 d 66 c 86 a 106 c 126 d 146 c 166 d
7 d 27 c 47 d 67 a 87 c 107 a 127 a 147 d 167 a
8 b 28 a 48 d 68 b 88 b 108 a 128 b 148 d 168 a
9 c 29 d 49 a 69 a 89 b 109 d 129 d 149 b 169 d
10 d 30 d 50 c 70 c 90 d 110 c 130 c 150 b 170 b
11 a 31 d 51 c 71 b 91 b 111 c 131 a 151 b 171 a
12 c 32 a 52 b 72 c 92 b 112 b 132 c 152 b 172 d
13 c 33 c 53 a 73 d 93 a 113 d 133 b 153 d 173 c
14 c 34 d 54 a 74 d 94 c 114 b 134 b 154 b 174 a
15 d 35 b 55 b 75 d 95 d 115 d 135 d 155 c 175 a
16 b 36 c 56 a 76 b 96 c 116 d 136 c 156 b 176 d
17 c 37 a 57 c 77 a 97 d 117 d 137 b 157 d 177 d
18 d 38 c 58 d 78 b 98 a 118 b 138 c 158 d 178 b
19 c 39 c 59 d 79 d 99 a 119 a 139 b 159 a 179 d
20 a 40 a 60 c 80 b 100 c 120 a 140 a 160 d 180 b
Page 2
CAT 1991 Actual Paper
1. a The subject here is ‘the best part’, which is singular
and should therefore be followed by a singular verb.
2. a When using ‘as well as’ to introduce a complex subject,
the phrase should be set off by commas, and the verb
agrees with the main subject, which in this case is
‘the professor’.
3. b As the first part of the sentence provides the reason
for his being unwilling to testify, ‘because’ should be
used to introduce it. Moreover a comma should always
be used to separate two distinct phrases in a
sentence.
4. b The pronoun should remain consistent throughout the
sentence.
5. b When ‘either’ and ‘neither’ are followed by ‘or’ and
‘nor’ respectively, the verb depends on the noun
following ‘or’ and ‘nor’.
6. a The sentence has three different clauses, which
should be separated by semi colons.
7. d When ‘neither’ is followed by ‘nor’, the verb depends
on the noun following ‘nor’. In this case it is singular,
hence the verb should also be singular.
8. b Before a gerund a noun should appear in the
possessive form.
9. c The sentence does not need any commas.
10. d The sentence needs no commas.
11. a We should use ‘who’ for subjects who do the action.
In the given sentence ‘who’ is the subject of the verb
‘were’.
12. c The correct usage would be, ‘a network to facilitate
contacts’.
13. c The correct phrase would be, ‘to the perceived
problems’.
14. c ‘The Indian Government’s choice’ is a singular noun
and should have a singular verb ‘stems’.
15. d The correct quantifier to be used here is ‘most’.
16. b Here we should use the verb in past participle, i.e.
‘you would have’ as we are talking about an unreal
past condition.
17. c ‘Requires’ should be replaced with ‘assumes’.
18. d The noun ‘choice’ is singular and should be followed
by a singular verb ‘invites’.
19. c We already have a subject ‘who’ for the verb ‘decided’,
so ‘he then’ is wrongly used here.
20. a ‘Of’ should be replaced with ‘off’.
21. c Here minorities are being treated as a specific group
and should therefore be preceded by ‘the’.
22. c ‘Aspiring’ cannot be used as an adjective for students
here, as those who are studying management are
already students.
23. c D. introduces the ‘institutional truth of the financial
world’, B. elaborates the idea, A continues with B. and
C. presents the conclusion.
24. c B. introduces the subject of the passage, C. elaborates
on the idea, and use of ‘then’ in A. shows that it should
follow D.
25. b A. introduces the age of pragmatism as the topic of
the passage, C. explains what has changed in the
new age, B. explains the characteristic of the old
world and D. comments on the position today.
26. b D. shows that the passage is about cognitive age, B.
explains what it implies, A. talks about a research
related to the subject and C. explains the implications
of the research.
27. c The sentence C. introduces ‘her eyes’, and should be
the first sentence. A. elaborates on the eyes, so A
should follow C. No other option has CA as the
mandatory pair. So, answer is (c).
28. a B. shows that the topic is ‘intelligence’, D. uses ‘these’
to refer to the different abilities associated with
intelligence, as presented in B. A. explains what
intelligence actually is and C. talks about the true test
of intelligence.
29. d The passage is about difference in pronunciation of
words in different situations. A. explains what the
difference is. Use of ‘further’ and ‘yet’ in D. and B.
respectively show the order in which they should
occur.
30. d Broad and powerful thinking is needed to solve the
problems.
31. d The funds are being ‘raised’ for the purpose of having
money to spend on the search of alternative sources
of energy.
32. a If you look before you leap you will be forewarned
and thus can be forearmed.
33. c As the king, the fate of the economy and the subjects
would be in the ruler’s hands.
34. d We should be prepared to ‘break’ something to
‘reconstruct’ it.
Page 3 CAT 1991 Actual Paper
35. b If the future is upon us before we realize it, it will
shape us rather than the other way round.
36. c
Attendants
Qualified
Nurses
37. a If Mary and John are wife and husband and the last
waltz was danced by husbands and wives, it follows
that John danced last with Mary.
38. c Air
Plants
Roses
39. c Laxman is a man and no man is an island, so Laxman
cannot be an island.
40. a If college students are intelligent and Ram is a college
student, it follows that Ram is intelligent.
41. b If all cigarettes are hazardous to health and cham-
cham is a brand of cigarette, then cham-cham would
also be hazardous to health.
42. d If all good bridge players play good chess, then Goran
being a good bridge player should also play good
chess.
43. d
Cold blooded
Reptiles
44. a
Chlorophyll
Leaves
45. b If bald people are intelligent and Raman is bald, it follows
that Raman is intelligent.
46. d
Gentlemen
Barbarians
Rude
47. d Desks are made of metals. So if an object is a desk it
should be made of metal.
48. d Mathew and Paul are siblings and siblings are known
to quarrel often. Therefore it follows that Mathew and
Paul quarrel often.
49. a Art is a symptom of culture and music is a form of art,
therefore music also shows culture.
50. c If primary colours give different hues, and red is a
primary colour, it implies that red also gives different
hues.
51. c The statement I only gives the comparison of the selling
prices. You must realise that this information is not
enough to answer the question as the profit also
depends on cost. So we also need to analyze the
statement II. And since there is no other constraint on
production, we can solely compare the profitability of
two products on the basis of labour. According to it, if
10 units of labour is available, it can produce 5 units of
Q and 2 units of R. So, from 10 units of labour, I can
earn (5 x 1) = 5 units of sales revenue from Q and (2
x 4) = 8 units of sales revenue from R. So by taking
both statements together we can determine which
would be more profitable.
52. b In order to solve the question, we need to know two
things : (a) the original speed of the train or the new
speed of the train and (b) at what distance from A or
after how much time after leaving A the train
brokedown. The statement II provides both of these
data viz. original speed = 20 kmph and distance from A
= 40 kms. and hence only this is required to answer
the question.
For e.g: If the distance between A & B is considered to
be x, then time taken had it not broken down is
x/20 hours. The new time taken is [2 + (x – 40)/5]
hours and we know that this time is 40 min. more than
the original time. The equation becomes : x/20 + 40/60
= [2 + (x – 40)/5], which can be easily solved to get
value of x.
53. a From statement I, 
2
xx 50 +>
and x
2
 + x < 100
             x(x 1) 50 ?+>
            Only prime number 7 satisfies the above equation.
So the question can be answered from statement 1
alone.
Page 4
CAT 1991 Actual Paper
54.  a Sum of  all the three quotations = 110 × 3 = 330
From statement I, if the lowest quotation is 110 then
the sum of other two quotations = 330 – 100 = Rs. 230.
Now, minimum value of second quotation = Rs. 101
Therefore, maximum value of third quotation = 230 –
101 = Rs. 229.
55. b From the statement I, we have the following Venn
diagram :
IE (100) Hindu (50)
TOI (120)
Using this we cannot find the answer.
From the statement II however we can find the answer,
as we get the following Venn diagram.
IE (100)
TOI (120) 70
56.  a Let present age of  X and Y be x and y respectively.
            We have, x3(y 3) =- ... (i)
From statement I, xy 17 =+ ... (ii)
             From statement II, x9 3y += ... (iii)
From (i) and (ii) x = 37.5 years and y = 12.5 years
But, equations (i) and (iii) are same so we cannot find
values of x and y.
57. c Let length of the smaller square be x.
From statement I,Length of ABCDEQ = 10x = 60
x6 =
From statement II, Area of rectangle OPQR =
2
42x 1512 =
             
2
x36 ?=
x6 ?=
By combining results from statement I and II
            we have, x = 6
Now, area under the ling GHI-JKL can be found out
using x.
58. d Let the radius of the circle be r.
From statement I,  
2
r
7
2r
p
>
p
            r14 ?> ...(i)
From statement II, 2r 32 =
r16 ?= ...(ii)
Combining (i) and (ii) 14 r 16 <=
So r can be 15 or 16.
59. d From both statements I and II:
Arrival time of flight by New York local time will be
2 P .M.
Since we don’t know whether the flight landed on
same date or other we can not find the answer.
60. c    From statement I alone no conclusion can be drawn.
From statement II following sequence of stations is
possible
A C/D E C/D B
But, From 1 Mr. Rahman boards the station at D which
is possible at fourth position only because Mr. Thomas
and Mr. Rahman have no common station.
61. b For each of the given expressions, you may have to
simplify and express x in terms of y and hence verify
for which one does the form & structure remain the
same. In general, any function of the form
()
()
ax + b
y = 
bx – a
 reflects on to itself as we arrange it can
be found that 
()
()
ay + b
x = .
by – a
Hence, the answer is (b).
62. c For no solution, lines must be parallel and not over
lapping
             
28 3
k4 10
-
?= ?
k1 ?=-
63. a Three digit number such that 7 follows 5 could be of
the form  57_ or _57
Since, the number is an even number
Therefore  possible numbers are 570,572,574,576 or
578.
            Hence, 5 such numbers are possible.
64. c Let x be the number of tailors initial appointed.
Let n be the number of shirts that had to be stitched
by each tailor initially.
Let y be the number of tailors who did not come.
x × n = 480.
(x – y)(n + 32) = 480
Only option (c) satisfies the equation.
65. b Let Mushtaq has M cards while Iqbal has got I cards
with him.
Let number of cards exchanged be x.
Case 1:   I + x = 4(M – x) ... (i)
Case 2:  I – x = 3(M + x) ... (ii)
From (i) and (ii)
             I = 31x.
Only possible value for I could be 31.
Page 5


Page 1 CAT 1991 Actual Paper

	






1 a 21 c 41 b 61 b 81 a 101 d 121 c 141 c 161 c
2 a 22 c 42 d 62 c 82 a 102 d 122 b 142 c 162 d
3 b 23 c 43 d 63 a 83 c 103 a 123 b 143 c 163 a
4 b 24 c 44 a 64 c 84 b 104 d 124 a 144 d 164 b
5 b 25 b 45 b 65 b 85 a 105 c 125 c 145 c 165 a
6 a 26 b 46 d 66 c 86 a 106 c 126 d 146 c 166 d
7 d 27 c 47 d 67 a 87 c 107 a 127 a 147 d 167 a
8 b 28 a 48 d 68 b 88 b 108 a 128 b 148 d 168 a
9 c 29 d 49 a 69 a 89 b 109 d 129 d 149 b 169 d
10 d 30 d 50 c 70 c 90 d 110 c 130 c 150 b 170 b
11 a 31 d 51 c 71 b 91 b 111 c 131 a 151 b 171 a
12 c 32 a 52 b 72 c 92 b 112 b 132 c 152 b 172 d
13 c 33 c 53 a 73 d 93 a 113 d 133 b 153 d 173 c
14 c 34 d 54 a 74 d 94 c 114 b 134 b 154 b 174 a
15 d 35 b 55 b 75 d 95 d 115 d 135 d 155 c 175 a
16 b 36 c 56 a 76 b 96 c 116 d 136 c 156 b 176 d
17 c 37 a 57 c 77 a 97 d 117 d 137 b 157 d 177 d
18 d 38 c 58 d 78 b 98 a 118 b 138 c 158 d 178 b
19 c 39 c 59 d 79 d 99 a 119 a 139 b 159 a 179 d
20 a 40 a 60 c 80 b 100 c 120 a 140 a 160 d 180 b
Page 2
CAT 1991 Actual Paper
1. a The subject here is ‘the best part’, which is singular
and should therefore be followed by a singular verb.
2. a When using ‘as well as’ to introduce a complex subject,
the phrase should be set off by commas, and the verb
agrees with the main subject, which in this case is
‘the professor’.
3. b As the first part of the sentence provides the reason
for his being unwilling to testify, ‘because’ should be
used to introduce it. Moreover a comma should always
be used to separate two distinct phrases in a
sentence.
4. b The pronoun should remain consistent throughout the
sentence.
5. b When ‘either’ and ‘neither’ are followed by ‘or’ and
‘nor’ respectively, the verb depends on the noun
following ‘or’ and ‘nor’.
6. a The sentence has three different clauses, which
should be separated by semi colons.
7. d When ‘neither’ is followed by ‘nor’, the verb depends
on the noun following ‘nor’. In this case it is singular,
hence the verb should also be singular.
8. b Before a gerund a noun should appear in the
possessive form.
9. c The sentence does not need any commas.
10. d The sentence needs no commas.
11. a We should use ‘who’ for subjects who do the action.
In the given sentence ‘who’ is the subject of the verb
‘were’.
12. c The correct usage would be, ‘a network to facilitate
contacts’.
13. c The correct phrase would be, ‘to the perceived
problems’.
14. c ‘The Indian Government’s choice’ is a singular noun
and should have a singular verb ‘stems’.
15. d The correct quantifier to be used here is ‘most’.
16. b Here we should use the verb in past participle, i.e.
‘you would have’ as we are talking about an unreal
past condition.
17. c ‘Requires’ should be replaced with ‘assumes’.
18. d The noun ‘choice’ is singular and should be followed
by a singular verb ‘invites’.
19. c We already have a subject ‘who’ for the verb ‘decided’,
so ‘he then’ is wrongly used here.
20. a ‘Of’ should be replaced with ‘off’.
21. c Here minorities are being treated as a specific group
and should therefore be preceded by ‘the’.
22. c ‘Aspiring’ cannot be used as an adjective for students
here, as those who are studying management are
already students.
23. c D. introduces the ‘institutional truth of the financial
world’, B. elaborates the idea, A continues with B. and
C. presents the conclusion.
24. c B. introduces the subject of the passage, C. elaborates
on the idea, and use of ‘then’ in A. shows that it should
follow D.
25. b A. introduces the age of pragmatism as the topic of
the passage, C. explains what has changed in the
new age, B. explains the characteristic of the old
world and D. comments on the position today.
26. b D. shows that the passage is about cognitive age, B.
explains what it implies, A. talks about a research
related to the subject and C. explains the implications
of the research.
27. c The sentence C. introduces ‘her eyes’, and should be
the first sentence. A. elaborates on the eyes, so A
should follow C. No other option has CA as the
mandatory pair. So, answer is (c).
28. a B. shows that the topic is ‘intelligence’, D. uses ‘these’
to refer to the different abilities associated with
intelligence, as presented in B. A. explains what
intelligence actually is and C. talks about the true test
of intelligence.
29. d The passage is about difference in pronunciation of
words in different situations. A. explains what the
difference is. Use of ‘further’ and ‘yet’ in D. and B.
respectively show the order in which they should
occur.
30. d Broad and powerful thinking is needed to solve the
problems.
31. d The funds are being ‘raised’ for the purpose of having
money to spend on the search of alternative sources
of energy.
32. a If you look before you leap you will be forewarned
and thus can be forearmed.
33. c As the king, the fate of the economy and the subjects
would be in the ruler’s hands.
34. d We should be prepared to ‘break’ something to
‘reconstruct’ it.
Page 3 CAT 1991 Actual Paper
35. b If the future is upon us before we realize it, it will
shape us rather than the other way round.
36. c
Attendants
Qualified
Nurses
37. a If Mary and John are wife and husband and the last
waltz was danced by husbands and wives, it follows
that John danced last with Mary.
38. c Air
Plants
Roses
39. c Laxman is a man and no man is an island, so Laxman
cannot be an island.
40. a If college students are intelligent and Ram is a college
student, it follows that Ram is intelligent.
41. b If all cigarettes are hazardous to health and cham-
cham is a brand of cigarette, then cham-cham would
also be hazardous to health.
42. d If all good bridge players play good chess, then Goran
being a good bridge player should also play good
chess.
43. d
Cold blooded
Reptiles
44. a
Chlorophyll
Leaves
45. b If bald people are intelligent and Raman is bald, it follows
that Raman is intelligent.
46. d
Gentlemen
Barbarians
Rude
47. d Desks are made of metals. So if an object is a desk it
should be made of metal.
48. d Mathew and Paul are siblings and siblings are known
to quarrel often. Therefore it follows that Mathew and
Paul quarrel often.
49. a Art is a symptom of culture and music is a form of art,
therefore music also shows culture.
50. c If primary colours give different hues, and red is a
primary colour, it implies that red also gives different
hues.
51. c The statement I only gives the comparison of the selling
prices. You must realise that this information is not
enough to answer the question as the profit also
depends on cost. So we also need to analyze the
statement II. And since there is no other constraint on
production, we can solely compare the profitability of
two products on the basis of labour. According to it, if
10 units of labour is available, it can produce 5 units of
Q and 2 units of R. So, from 10 units of labour, I can
earn (5 x 1) = 5 units of sales revenue from Q and (2
x 4) = 8 units of sales revenue from R. So by taking
both statements together we can determine which
would be more profitable.
52. b In order to solve the question, we need to know two
things : (a) the original speed of the train or the new
speed of the train and (b) at what distance from A or
after how much time after leaving A the train
brokedown. The statement II provides both of these
data viz. original speed = 20 kmph and distance from A
= 40 kms. and hence only this is required to answer
the question.
For e.g: If the distance between A & B is considered to
be x, then time taken had it not broken down is
x/20 hours. The new time taken is [2 + (x – 40)/5]
hours and we know that this time is 40 min. more than
the original time. The equation becomes : x/20 + 40/60
= [2 + (x – 40)/5], which can be easily solved to get
value of x.
53. a From statement I, 
2
xx 50 +>
and x
2
 + x < 100
             x(x 1) 50 ?+>
            Only prime number 7 satisfies the above equation.
So the question can be answered from statement 1
alone.
Page 4
CAT 1991 Actual Paper
54.  a Sum of  all the three quotations = 110 × 3 = 330
From statement I, if the lowest quotation is 110 then
the sum of other two quotations = 330 – 100 = Rs. 230.
Now, minimum value of second quotation = Rs. 101
Therefore, maximum value of third quotation = 230 –
101 = Rs. 229.
55. b From the statement I, we have the following Venn
diagram :
IE (100) Hindu (50)
TOI (120)
Using this we cannot find the answer.
From the statement II however we can find the answer,
as we get the following Venn diagram.
IE (100)
TOI (120) 70
56.  a Let present age of  X and Y be x and y respectively.
            We have, x3(y 3) =- ... (i)
From statement I, xy 17 =+ ... (ii)
             From statement II, x9 3y += ... (iii)
From (i) and (ii) x = 37.5 years and y = 12.5 years
But, equations (i) and (iii) are same so we cannot find
values of x and y.
57. c Let length of the smaller square be x.
From statement I,Length of ABCDEQ = 10x = 60
x6 =
From statement II, Area of rectangle OPQR =
2
42x 1512 =
             
2
x36 ?=
x6 ?=
By combining results from statement I and II
            we have, x = 6
Now, area under the ling GHI-JKL can be found out
using x.
58. d Let the radius of the circle be r.
From statement I,  
2
r
7
2r
p
>
p
            r14 ?> ...(i)
From statement II, 2r 32 =
r16 ?= ...(ii)
Combining (i) and (ii) 14 r 16 <=
So r can be 15 or 16.
59. d From both statements I and II:
Arrival time of flight by New York local time will be
2 P .M.
Since we don’t know whether the flight landed on
same date or other we can not find the answer.
60. c    From statement I alone no conclusion can be drawn.
From statement II following sequence of stations is
possible
A C/D E C/D B
But, From 1 Mr. Rahman boards the station at D which
is possible at fourth position only because Mr. Thomas
and Mr. Rahman have no common station.
61. b For each of the given expressions, you may have to
simplify and express x in terms of y and hence verify
for which one does the form & structure remain the
same. In general, any function of the form
()
()
ax + b
y = 
bx – a
 reflects on to itself as we arrange it can
be found that 
()
()
ay + b
x = .
by – a
Hence, the answer is (b).
62. c For no solution, lines must be parallel and not over
lapping
             
28 3
k4 10
-
?= ?
k1 ?=-
63. a Three digit number such that 7 follows 5 could be of
the form  57_ or _57
Since, the number is an even number
Therefore  possible numbers are 570,572,574,576 or
578.
            Hence, 5 such numbers are possible.
64. c Let x be the number of tailors initial appointed.
Let n be the number of shirts that had to be stitched
by each tailor initially.
Let y be the number of tailors who did not come.
x × n = 480.
(x – y)(n + 32) = 480
Only option (c) satisfies the equation.
65. b Let Mushtaq has M cards while Iqbal has got I cards
with him.
Let number of cards exchanged be x.
Case 1:   I + x = 4(M – x) ... (i)
Case 2:  I – x = 3(M + x) ... (ii)
From (i) and (ii)
             I = 31x.
Only possible value for I could be 31.
Page 5 CAT 1991 Actual Paper
66. c We know that x + y + z = T and x + 2y + 3z = R
T
, where
x = number of members belonging to exactly 1 set
y = number of members belonging to exactly 2 sets
= 9
z = number of members belonging to exactly 3 sets
= 1
T = Total number of members
R
T
 = Repeated total of all the members = (22 + 15 + 14)
= 51
R
T 
= T + y + 2z
Thus we have two equations and two unknowns.
Solving this we get T = 40.
In other words, the number of teachers owing at least
1 out of the three items = 40. Hence the number of
teachers owing none = 50 – 40 = 10.
67. a Let the 3 odd numbers be (x – 2), x and (x + 2). It is
given that 3(x – 2) = 3 + 2(x + 2).
Hence x = 13. So the third integer is (x + 2) = 15.
68. b Total number of ways to reach A to B = 4 × 2 × 2 × 1
= 16.
69. a Let side of square be a.
Area quadrilateral EFDG = ar (DGF) ar (GEF) ?+?             
1a 1 a
aa
22 2 2
=× × + ×
2
1
a.
2
=
     
A
E B
G
O
F
D C
a/2
1
Ar(EFDG) : Ar(S)
2
?=
70. c 2
73
 – 2
72
 – 2
71
 = 2
71
 (2
2
 – 2 – 1) = 2
71
 (4 – 2 – 1) = 2
71
.
71. b The two equations can be simplified into n= 2 and
n= 2. The only value that satisfies both these conditions
is n = 2.
72. c Since the sum of reciprocals is 
5
12
. The two numbers
must have their LCM as 12  and their sum as given will
be 10.
Possible numbers are 4 and 6 only.
73. d As it is apparent from the following diagram, the
diameter of the inscribed circle is equal to the side of
the square, while the diameter of the circumscribed
square is equal to the diagonal of the square. Since
the ratio of any two circles is equal to the ratio of the
squares of their diameters, in this case the required
ratio is equal to (side)
2
 : (diagonal)
2
.
Now, the ratio of the side to the diagonal of a square
= 1: 2, the ratio of their squares will be 1 : 2.
74. d    y = f(x) = 
1x
1x
-
+
? y(1 + x) = 1 – x
? y + xy = 1 – x
? x + xy = 1 – x
? x(1 + y) = 1 – y)
?
1y
xf(y)
1y
-
==
+
For questions 75 and 76:
0
0
0
30 2X
X/2
X
Play Ground Laboratory
Library
It is given that x + 2x + x/2 = 35.
Hence x =10.
75. d Total number of schools that had at least one of the
three = 30 + 10 + 20 + 5 = 65. Hence the number of
schools having none of them = 100 – 65 = 35.
76. b Number of schools having library = 15. And number of
schools having laboratory = 25.
Hence the ratio = 25 : 15 = 5 : 3.
77. a Since in the long run the probability of each number
appearing is the same, we can say in ‘n’ throws one
can get 1, 2, 3, 4, 5 and 6, 
n
6
times each. Hence he
would earn 
(1 + 2 + 3 + 4 + 5 + 6)n 7n
 = Rs. .
62
In order to make a profit of 1 Re. per throw he has to
totally earn a profit of Rs.n. Hence his cost for the n
throws should be 
7n
–n.
2 
 So his cost per throw
should be 
75
 – 1 =  = Rs.2.50.
22
??
??
??