cat 2004 detailed solutions

7/27/2019 CAT 2004 Detailed Solutions

1/18

M-PP-01 B1. 1 www.TestFunda.com

1. Let us denote University 1 as U1, University 2 as U2 andso on.

Consider day 3. 2 students from UK and 1 student from

USA visited the homepage. Also, 2 and 1 student fromU4 and U6 respectively visited the homepage.

U4 is in UK and U6 is in USA. Similarly, consideringday 2, U3 is in Netherlands and U8 is in India.

Canada has 2, 0 and 0 visitors on days 1, 2 and 3 and so

have U2 and U7. One of U2 and U7 is in Canada.UK has 2, 0 and 2 visitors on days 1, 2 and 3 and we

know that U4 is in UK. But as U4 has 0 visitors on day 1,

we can say that either U2 or U7 is in UK. (If we assume

that UK has three of the eight listed universities, U4, U1

and U5, then considering the number of visitors on day

1, we do not find appropriate universities for India and

Netherlands.)

Similarly, considering India and Netherlands, U5 and U1

will be in these countries. Thus, we have the following

table.

University Country

University 1 India/Netherlands

University 2 UK/Canada

University 3 Netherlands

University 4 UK

University 5 Netherlands/India

University 6 USA

University 7 Canada/UK

University 8 India

University 1 can belong to Netherlands or India.Hence, option 3.

2. University 5 can belong to the Netherlands or India.Hence, option 1.

3. Students from University 4 and University 2/7 from UKvisited Prof. Singhs homepage in the three days.

Hence, option 2.

4. From the table, none of the countries can host morethan two of the listed universities.

Hence, option 1.

5. Let us consider the options:1. Malaysia and China: The maximum level of

dissimilarity is 4 for V or N.

2. China and Thailand: The maximum level ofdissimilarity is 4 for V.

3. Thailand and Japan: The maximum level ofdissimilarity is 4 for D.

4. Japan and Malaysia: The maximum level ofdissimilarity is 3 for V or N.

Hence, option 4.

6.China Japan Malaysia Thailand

C 1 2 3 1

P 1 3 1 2

N 2 1 2 0

V 1 0 3 3

D 1 4 3 0

The table gives levels of dissimilarity between India

and the other countries for all traits.

Clearly, Japan is most dissimilar to India (since its level

of dissimilarity is 4).

Hence, option 2.

7.China Japan Malaysia Thailand

C 1 2 3 1

P 1 3 1 2

N 2 1 2 0

V 1 0 3 3

D 1 4 3 0

From the above table, China is least dissimilar to India

(since its level of dissimilarity is only 2).

Hence, option 1.

8. Consider the levels of dissimilarities for the fouroptions.

China and Japan 3 (for 'D')

India and China 2 (for 'N')

Malaysia and Japan 3 (for 'N' or 'V')

Thailand and Japan 4 (for 'D')

Hence, option 4.

9. All these questions can be solved by mere observation.

The shaded portion of the graph is the region where

Income > Expenditure and the unshaded portion is

where Expenditure > Income.

DETAILED SOLUTIONCAT 2004B1


2/18

CAT 2004


By observation we can see that the average

expenditure of the Dubey family is approximately

2000. The average expenditures of the Ahuja family,

the Bose family and the Coomar family are definitely

lesser than this.

Hence, option 4.

10.

By observation, the Coomar family has the lowestaverage income.

Hence, option 3.

11. A member of the Ahuja family has the highest incomeand lowest expenditure. He/she has the highest

amount of savings.

Hence, option 1.

12. Both the members of the Dubey family have Incomesthat is almost equal to their Expenditures.

Their average savings are the lowest.Hence, option 4.

13.

Taras total grade points = 2.4 5 = 12She gets B 4 in Finance. As she gets the same grade in

three courses, she would have got B in 3 subjects and F

in 2. (Getting a D in 4 subjects would also give the

correct GPA. However, this is not possible since it is

stated that Tara received the same grade in exactly

three courses.)

Thus, she would have got either B or F in Operations,

but only B is provided in the options (i.e. Manab's

grade).

Hence, option 4.

14. Preetis total grade points = 3.2 5 = 16Her grade points in Finance, Marketing and Strategy =0 + 2 + 2 = 4

She scores 12 in Statistics and Operations, which ispossible only if she obtains an A in both these subjects.

Hence, option 1.

15. Utkarshs grade in Marketing= Fazals grade in Strategy

= (2.4 5 2 0 4 2) = 4 B

Utkarshs grade in Finance = (3 5 6 3 0 4) = 2 D

Hence, option 3.

16. Gowris grade points in Strategy= (3.8 5 3 3 6 4) = 3 C

Fazals grade points in Strategy

= 4 B (from the previous answer)

Haris grade points in Strategy and Finance

= (2.8 5 4 6 2) = 2, i.e. he got grades F and D in

Strategy and Finance, in some order.

Nishas grade points in Strategy = 6 A

Rahuls grade points in Strategy

= 4.2 5 6 3 6 0 = 6 A

Gowris grade point in Strategy is higher than Haris.

Hence, option 2.

17. The number of mixer-grinders in operation in any yearcan be divided into four categories: Newly purchased,

one year old, two year old and older.

Consider Naya mixer-grinders.

As 30 mixer-grinders were in operation in 1997 and

the brand itself was introduced in that year, all 30 werenewly purchased.

In 1998, 80 were in operation, out of which 30 were

one-year old.

50 were newly purchased.In 1999, 124 were in operation, out of which 50 were

one-year old.

Out of the 30 purchased in 1997, 20% or 6 were

disposed of in 1999.

30 0.8 = 24 out of the 124 were two-year old.Similarly in 2000, 134 were in operation, out of which

50 were one year old, 40 were two years old and 24

were older than two years.

Thus we have the following:

Naya Mixer-Grinders

Old

YearIn

Operation

1

year

2

yearsOlder New

Disposed

of

1997 30 0 0 0 30 0

1998 80 30 0 0 50 0

1999 124 50 24 0 50 6

2000 134 50 40 24 20 10

Consider Purana Mixer-grinders. As 10 of these were

disposed of in 1997,

70 mixer-grinders in operation in 1995 were old. Thebreak-up of these however cannot be found.

Out of the 162 in operation in 1996, 50 were one year

old. The break-up of the rest cannot be found as we do

not have data of years before 1995 and we have not

been given the number of mixer-grinders purchased in

1996.

In 1997, 182 were in operation and 10 were disposed

of. Thus 182 + 10 = 192 mixer-grinders were either

newly purchased or old.

Out of these 192, 162 existed in 1996 too.

192 162 = 30 were newly purchased in 1997.As the number of newly purchased mixer-grinders in

1996 is not known, the number that were disposed of

in 1998 cannot be found. Consequently, the number

that were newly purchased also cannot be found.

Continuing this process for the years 1999 and 2000,

the entire data can be presented as follows:


3/18

CAT 2004


Purana Mixer-Grinders

YearIn

OperationOld New Disposed of

1995 120 70 50

1996 162

1997 182 152 30 10

1998 222

1999 236 216 20 6

2000 236

10 + 6 = 16 Naya mixer-grinders were disposed of bythe end of 2000.

Hence, option 2.

18. 50 Naya mixer-grinders were purchased in 1999.Hence, option 2.

19. 20 Purana mixer-grinders were purchased in 1999.Hence, option 1.

20. As the number of Purana mixer-grinders purchased in1996 is not known, the ones purchased and disposed of

in 1998 and 2000 cannot be determined.

Hence, option 4.

21. Let one kilogram of potatoes, onions and gourd cost Rs.p, Rs. o and Rs.g respectively. Thenp + o +g < 75.

Consider statement A:

2p +g


4/18

CAT 2004


Rashmis rank is seven.IfKumars rank among boys is 3, 2 or 1, there are 3, 4

or 5 girls in the first 6 rankers.

Rashmis rank is three. Statement A is insufficient.

Consider statement B: There were three boys in the

top 5 and Kumar was 6th

. There were 4 boys and 2 girls in the top 6. Rashmi was not in the top six. Kumar had a better overall rank.Statement B is sufficient.

Hence, option 1.

26. Let Zakibs and Supriyos incomes be z and srespectively.

Consider statement A:

0.2z> 0.25s

z> sZakib and Supriyo spend 0.3z and 0.4s on childrenseducation.

Statement A alone is not sufficient.

Consider statement B:

0.13s > 0.1z

Supriyo spends more than Zakib on childrenseducation.

Statement B alone is sufficient.Hence, option 1.

27. Consider the game against Pakistan (G1).Runs scored by Y, V and K = 40 + 130 + 28 = 198

Total runs scored = 198/0.9 = 220

Runs scored by R (r1) and S (s1), r1, s1 < 28 andr1 + s1 22Consider the game against South Africa (G2).

Runs scored by K, R and S = 51 + 49 + 75 = 175


Runs scored by Y (y2) and V (v2),y2, v2 < 49 andy2 + v2 75

Consider the game against Australia (G3).

Runs scored by R, Y and S = 87 + 55 + 50 = 192


Runs scored by V (v3) and K (k3), v3, k3 < 50,

v3 + k3 48

Rs M-index = 49

Ss M-index = 50

Vs M-index 49

Ys M-index is either 40 or between 41 and 49.

S had the best M-index.Hence, option 2.

28. Ify2 < 40, then Ys R-index = 87 y2 > 47; i.e. 47 < Ys R-index 87

Ify2 > 40, then Ys R-index = 87 40 = 47

47 Ys R-index 87Similarly,

23 Ks R-index 51

33 Rs R-index 55 (r1, s1 < 28 and r1 + s1 22)53 Ss R-index 75 (r1, s1 < 28 and r1 + s1 22)82 Vs R-index 130 (v3, k3 < 50, v3 + k3 48) Any one of Y, K or R could have the lowest R-index.Hence, option 1.

29. From answer to the first question, the M-index of onlyR and S can be exactly calculated.

Hence, option 3.

30. Y scored 127 in G1 and G3. V scored 130 in G1 itself.Ks max score could be 28 + 51 + 48 = 127

Rs max score could be 49 + 55 + 22 = 126

Ss max score could be 75 + 50 + 22 = 147

Only R definitely scored less than Y.Hence, option 2.

31. Let there be x labour experts. Then, the number ofhealth, population and refugee relocation experts will

be 2xeach.

Hence,x+ 2x+ 2x+ 2x= 7x= 21x= 3That is, the number of Labour, Health, Population and

Refugee Relocation experts are 3, 6, 6 and 6

respectively.

Let Australasia have (y+ 1) experts. Then the Americas

have 2yexperts and Africa and Europe have yexperts

each.

y+ 1 + 2y+y+y= 21y= 4That is, Australasia, Americas, Africa and Europe have

5, 8, 4 and 4 experts respectively.

As Australasia has sent at least 2 experts on population

studies, it has sent 1 expert each for the other three

fields.

The Americas and Europe have sent 1 expert each onlabour.

Europe has sent 1 expert each on Health, PopulationStudies and Refugee Relocation.


5/18

CAT 2004


Labour Health

Popula-

tionStudies

Refugee

Reloca-tion

Total

Africa 0 4

Americas 1 8

Australasi

a1 1 2 1 5

Europe 1 1 1 1 4Total 3 6 6 6 21

Number of experts in Refugee Relocation from Africa

cannot be found.

Hence, option 4.

32. If Africa and Americas, each have 1 expert inpopulation studies, the total number of experts in this

field = 5, which is not possible as we know that the

number is 6.

Option 4 is not possible.Hence, option 4.

33. If Americas have 1 expert in population studies, wehave the following.Labour Health

Popula-

tion

Studies

Refugee

Reloca-

tion

Total

Africa 0 1 2 1 4

Americas 1 3 1 3 8

Australas

ia1 1 2 1 5

Europe 1 1 1 1 4

Total 3 6 6 6 21

Option 3 is not true.

Hence, option 3.

34. Since Africa has 4 experts in total and none of them arefrom labour, the number of experts from the other 3

fields should be 4.

Hence, Africas Refugee Relocation experts 2

The total number of Refugee Relocation experts in the

conference was 6. Of these, 1 is from Europe and 1 is

from Australasia.

Hence, Refugee Relocation experts from Africa and

Americas = 4

Hence, Total number of Refugee Relocation experts

from Americas = 2 or 3

Apart from Alex, there is at least one more and atmost 2 more American experts in refugee relocation.

Hence, option 3.

35. Since Pakistans Goals For (GF) and Goals Against(GA) is 2 and 1 respectively, and it won 1 game and lost

the other, the only possible combination of scores for

Pakistan in its two matches will be 2:0 and 0:1.

Similarly, Germanys scores in its two matches will be

2:1 and 1:0; while Argentinas scores in its two

matches will be 1:0 and 1:0.

Hence, we have the following table:

(G stands for Germany, A for Argentina, S for Spain, P

for Pakistan, NZ for New Zealand and SA for South

Africa)

Goals For Goals Against

G1 0

2 1

A1 0

1 0

S

P2 0

0 1

NZ

SA

Since Spain lost to Germany in the opening round, one

ofSpains score could be either 0:1 or 1:2. Since Spains

total GF = 5 and GA = 2 for the first 2 rounds, we have

the following possible scores for Spain:

Possibilities

for SpainGoals For Goals Against

10 1

5 1

21 2

4 0

Since the GF for both South Africa and New Zealand is

1, for each of these teams the GF for one match will be

1 while the GF of the second match will be 0. Hence, the

different possibilities are as follows:

Possibilities

for SAGoals For Goals Against

11 3

0 1

21 2

0 2

Possibilities

for NZ Goals For Goals Against

11 2

0 4

21 3

0 3

31 4

0 2

41 5

0 1


6/18

CAT 2004


Combining the above possibilities for Spain, SA and NZ

with the table showing the scores of Germany,

Argentina and Pakistan, we see that the 1st possibility

for SA is not possible since no possibility for any other

team has the score 3:1. Similarly, the 2nd and 3rd

possibility for NZ can also be eliminated. Hence, we

have,

Against Goals For Goals Against

G1 0

wins, SA 2 1

A1 0

1 0

S0/1 1/2

5/4 1/0

wins, SAP

2 0

0 1

NZ1 2/5

0 4/1

loses, G

SA

1 2

loses, P 0 2

Looking at the GF and GA values, we can guess which

teams played against others, for certain cases. (For

example, SA has a score of 1:2 and Germany is the only

team to have 2:1.) These are filled in the first column of

the above table.

Also, since Germany beats SA with a score of 2:1, it

beats Spain with a score of 1:0. This eliminates the 2nd

possibility for Spain. This implies that Spain beats NZ

with 5:1, eliminating NZs 1st possibility. Hence, we

have,

Goals For Goals Against

wins, SG

1 0

wins, SA 2 1

wins, PA

1 0

wins, NZ 1 0

loses, GS

0 1

wins, NZ 5 1

wins, SAP

2 0

loses, A 0 1

loses, SNZ

1 5

loses, A 0 1

loses, GSA

1 2

loses, P 0 2

Compiling the above information, we have the

following:

Country 1 Goals Country 2 Goals

Germany 1 Spain 0

Germany 2 South Africa 1

Argentina 1 Pakistan 0

Argentina 1 New Zealand 0

Spain 5 New Zealand 1

Pakistan 2 South Africa 0

Argentina beat Pakistan by 1 goal to 0.

Hence, option 2.

36. Germany beat SA by 2 goals to 1.Hence, option 4.

37. The following table gives the distribution of gameswithin each round:

R1 and R2 R3 R4 R5

G versus A - draw - -

G versus S G wins - - -

G versus P - - P won 1:0 -

G versus NZ - - -G won

3:0

G versus SA G wins - - -

A versus S - - S won -

A versus P A wins - - -

A versus NZ A wins - - -

A versus SA - - -A won

3:0

S versus P - draw - -

S versus NZ S wins - - -

S versus SA - - - S won

P versus NZ - - -P won

1:0

P versus SA P wins - - -

NZ versus SA - draw - -

(Note: There is an inconsistency in the question. In

Round 4, only 4 teams have played while in Round 5,

two teams (NZ and SA) have played 2 matches. This, as

we will see later, causes an inconsistency in the

question as well.)

The points table will be as follows:

Points

R1 and R2 R3 R4 R5 Total

G 6 1 0 3 10

A 6 1 0 3 10

S 3 1 3 3 10

P 3 1 3 3 10

NZ 0 1 0 1

SA 0 1 0 1

Since, 4 teams are tied with the same number of points,

the qualifying teams will be chosen based on their Goal

Difference (GD).

The GFs and GAs for the first two rounds is already

given. In the third round, the match of Germany versus

Argentina was drawn. Hence, both their GFs and GAs

will be equal (say, X). In the fourth round, Spain won

the match against Argentina. Hence, if Spains score is

(say) A:B, where A > B, then Argentinas will be B:A.

Following along similar lines, we have the following

table:


7/18

CAT 2004


R1 and

R2R3 R4 R5

GF GA GF GA GF GA GF GA

G 3 1 X X 0 1 3 0

A 2 0 X XB

(


8/18

CAT 2004


43. Let a and d be the first term and the commondifference of the AP.

Sum of the firstn terms of this A.P.

The sum of the first 30 terms = 15 (2a + 29d) (i)

By conditions,

11a + 55d= 19a + 171d 8a = 116d

From (i),

The sum of the first 30 terms = 15 (29d+ 29d) The sum of the first 30 terms = 0Hence, option 1.

Alternatively,If the sum of the firstp terms of an A.P. is equal to the

sum of the firstq terms of the A.P. such thatp and q are

different, then the sum of the first (p + q) terms of the

A.P. is zero.

As the sum of the first 11 and the sum of the first 19terms of the A.P. is equal, the sum of the first (11 + 19)

= 30 terms of the A.P. is zero.

Hence, option 1.

44. Letx hrs be the time required to reach the place at11:00 am

Distance that the man has to cycle = 15xkm

15x= 10x+ 20 5x= 20x= 4 hrs Distance to be travelled = 60 km To reach the place at noon, the man should cycle for

x+ 1 = 5 hrs.

Let the new speed be y.

y= 12 km/hrHence, option 2.

45. Members are added on the first day of every month for6 months before July 2, 2004.

Number of members in S1 on July 2, 2004 = n + 6b

= 64n (as b = 10.5n)

Number of members in S2 on July 2, 2004 = n r6

By conditions, 64n = n r6

r= 2

Hence, option 1.

46. x+y=xy

Thusyis the quotient of two consecutive integers. Asy

is an integer, x can take only the values 0 and 2. The

corresponding values ofywill be 0 and 2.

The only integer pairs satisfying this equation are(0, 0) and (2, 2).

Hence, option 3.

Alternatively,

The only two pairs of numbers whose sum is equal to

their product are (0, 0) and (2, 2).

Hence, option 3.

47. f(x) =x3 4x+pf(0) =p andf(1) =p 3

p 3 0.

p < 3 andp > 0 0


9/18

CAT 2004


Ifa + b + c = 0, a = (b + c)

Hence, option 3.

50.

2y2 + 7y= 3 +y 2y2 + 6y 3 = 0

As all the terms inyare positive,yis positive.

Hence, option 4.

51. f(x) = ax2b|x|x2 and |x| both are positive. Letx 0.

Consider the following cases:

1.a > 0, b > 0f(x) > 0, when ax2 > b|x|

f(x) < 0, when ax2 < b|x|f(x) is neither maximised or minimised whenx= 0.

2.a > 0, b < 0f(x) = ax2 + |b||x| > 0Thusf(x) is greater than 0 whenx 0.

f(x) is minimised whenever a > 0, b < 0.Hence, option 4.

52. The boats together travel 10 + 5 = 15 km in 60 minutes.

Hence, option 3.

53. Letfbe the number of families. The number of adults 2f, children 3fAlso, adults > boys > girls > families

Iff= 2, the minimum possible number of girls and boys

is 3 and 4.

Thus, number of children = 3 + 4 = 7 and number of

adults 4

But as adults > boys,fcannot be 2.

Iff= 3, minimum possible number of girls and boys = 4

and 5.

Thus number of children = 9 and number of adults 6

This is possible. Thus the minimum number of families

in the locality = 3.

Hence, option 4.

54. 100 nuts are produced per minute. Time taken to produce 1000 nuts = 10 minutes.But the machine needs cleaning for 5 minutes after

producing 1000 nuts. Thus effective time taken to

produce 1000 nuts = 15 minutes.

Effective time taken to produce 9000 nuts =

9 15 time taken for the last cleaning

= 135 5 = 130 minutes.

75 bolts are produced per minute.

Time taken to produce 1500 bolts = 20 minutes.But the machine needs cleaning for 10 minutes after

producing 1500 bolts. Thus effective time taken to

produce 1500 bolts = 30 minutes.Effective time taken to produce 9000 bolts = 6 30

time taken for the last cleaning = 180 10 = 170

minutes.

Thus time taken to produce 9000 pairs of nuts and

bolts = 170 minutes.

Hence, option 3.

55. Let the length and breadth of the rectangle be xand yrespectively.

x>y

Hence, option 2.

56.

Let the diameters of I and II be 4xand 3x.

SQO ~ RPO


10/18

CAT 2004


42 = 56 7xx= 2

PQ = 7 cm, OQ = 21 cm PQ : OQ = 1 : 3Hence, option 2.

57. Radius of circle II = 1.5 2 = 3 cm.Hence, option 2.

Alternatively,

We can solve this question and the previous question

together using options as follows:

Consider each of the options in this question.

1.If the radius of circle II is 2, the radius of I is 8/3. PQis then 14/3 and OQ is 70/3.

PQ : OQ = 1 : 5, which is not there in the options ofthe previous question.

2.If the radius of circle II is 3, the radius of I is 4. PQ isthen 7 and OQ is 21.

PQ : OQ = 1 : 3, which is there in the options of theprevious question. This is possible.





The radius of circle II is 3 and PQ : OQ = 1 : 3Hence, option 2.

58. SO2 = OQ2 SQ2 Hence, option 3.

59.

mEBC = 65 mEOC = 130 ( angle subtended by an arc at thecentre is twice the angle subtended by the same arc on

the circumference)

As AC || ED, mOCE = mDECOEC is an isosceles triangle.

mOCE = mOEC = (180 130)/2 = 25

mDEC = 25Hence, option 4.

60.

Quadrilateral ABCD is an isosceles trapezium.

Let AM = DN =x

AD = 8, AO = DO = BO = CO = 4 OM = ON = 4 xBMO and BMA are right triangles.

OB2 = OM2 + MB2 16 = (4 x)2 + h2 (i)Also,

AB2 = MB2 + AN2

4 =x2 + h2 (ii)

From (i) and (ii),x= 0.5

BC = 2(4 x)

BC = 7

Hence, option 2.

61.0 x 1 x 1 1 x< 0 x1

f1(x) x 1 0 0

f2(x) =f1(x) 0 0 x 1

f3(x) = f2(

x)0 0 x 1

f4(x) =f3(x) x 1 0 0

f1(x) =x 0 x 1

= 1 x 1

= 0 1 x< 0= 0 x1

The table is written after defining the given function as

above.

From the table, only f1(x) f2(x) and f2(x) f4(x) are

necessarily zero for everyx.

Hence, option 3.

62. From the table in the previous question,f3(x) = f4(x) =f1(x).

Hence, option 2.


11/18

CAT 2004


63. Let there be a, b and c questions in groups A, B and Crespectively.

Then, a + b + c =100

Total marks = a + 2b + 3c

b = 23a + c = 77a = 77 c

a 0.6a + 27.6 + 1.8c 4a 276 + 18ca 69 + 4.5ca 4.5c 69 77 c 4.5c 69 77 69 + 5.5cc 8/5.5

c = 1Hence, option 1.

Alternatively,

Evaluating options,

If C has 1 question then B and A have 23 and 76

questions respectively.

The total number of marks = 125

Group A has 60.8% marks. Option 1 is possible.If C has 2 questions then B and A have 23 and 75



Group A has 59.05% marks. Option 2 is not possible.If C has 3 questions then B and A have 23 and 74



Group A has 57.36% marks. Option 3 is not possible.Hence, option 1.

64. c = 8a + b = 92

2b 23.2 + 0.2b

b 13Also, as group A carries at least 60% of the total marks,

a 78

b 15b can be 13 or 14.Hence, option 3.

Alternatively,

Consider options.

For c = 8 and b = 11, a = 81. The total marks = 127.

Group B has 17.32% marks, which is not possible.For c = 8 and b = 12, a = 80. The total marks = 128.

Group B has 18.75% marks, which is not possible.


Group B has 20.15% marks and group A 61.24%

marks, which is possible.


Group B has 21.53% marks and group A has 60%

marks, which is possible.


Group B has 22.9% marks and group A has 58.77

marks, which is not possible.

Hence, option 3.

65. Letr=x. The circumference of the circular path = 2x. The sprinter covers 2xmetres in one round. The timetaken to complete each round is as under:

AverageSpeed

TimeDistanceCovered

Round

x 0.5 x/21stRound Time

Required

= 7.5 minutes

x/2 1 x/2

x/4 2 x/2

x/8 4 x/2

x/16 8 x/22stRound Time

Required

= 120 minutes

x/32 16 x/2

x/64 32 x/2x/128 64 x/2

x/256 128 x/23stRound Time

Required

= 1920 minutes

x/512 256 x/2

x/1024 512 x/2

x/2048 1024 x/2

Thus, we see that the ratio of time taken for the second

round to that for the 1stround = 16.

Similarly, ratio of time taken for the third round to that

for the 2nd round = 16 and so on.

Hence, option 3.

66. a1 = 81.33a2 = 19a3 = 100.33

a4 = 81.33

a5 = 19

a6 = 100.33

a7 = 81.33

a8 = 19

We can see that the sequence repeats itself after every

6 terms.

Sum of the first 6 terms of the sequence = 0


12/18

CAT 2004


Thus, the sum of the first 6000 terms of this sequence

= 0

The sum of the 6001stand 6002nd terms = 81.33 19

= 62.33

Hence, option 3.

67. (1523 + 2323) is divisible by (15 + 23) ie, 38. 15

23

+ 2323

= 38x, which is divisible by 19. Remainder when (1523 + 2323) is divided by 19 is 0.Hence, option 3.

68. To reach point B from A, the car has to take anorthward route thrice and a westward route five

times. Thus we can visualise a set of 8 routes out of

which 3 will be northward and 5 westward.

The number of ways in which the car can reach point B

from A is a permutation of 8 routes, 5 (W) and 3 (N) of

which are repeated.

Hence, option 2.

69.

Let the radius of C be r.

and so on.

Thus the areas of circles with diameters P0P1, P1P2,

P2P3, are

Required ratio = 11 : 12Hence, option 4.

70. u = (log2x)2 6 log2x+ 12 (i)xu = 256

Taking log on both sides,u log2x= log2 256 = 8

Let log2x= m

u m = 8Substituting in (i),

m3 6m2 + 12m 8 = 0 (m 2)3 = 0m = 2 log2x= 2x= 4

The given equation has exactly one solution forx.Hence, option 2.

71. The first stripe can be coloured in 4 ways. Then thesecond can be coloured in 3 ways. The third, fourth,

fifth and sixth can be coloured thereafter in 3 ways

each.

The total number of ways in which the flag can becoloured

= 4 3 3 3 3 3

= 12 81 ways.

Hence, option 1.

72. Let the side of the cube be a units.DF, AG and CE are body diagonals each of length aunits.

The triangle is an equilateral triangle of side aunits.

Circumradius of this equilateral triangle

Circumradius = side of cube.Hence, option 1.

73.

A D

CB

K

O


13/18

CAT 2004


AB = AK = 2

Quadrilateral ABCD is a square. Let the centre of the smaller circle be O and let its

radius bex.

Hence, option 4.

Alternatively,

By visual inspection, we can see that the radius of the

smaller circle is less than half the radius of the larger

circle. After finding the approximate values of the fouroptions, we can eliminate options 2 and 3.

Now, the approximate values of options 1and 4 are

0.17 and 0.343 respectively. Also AC = 2.82

The distance between the smaller circle and point C is

less than the radius of the small circle. This distance is

given by

AC AK 2(KO) = 2.82 2 2(KO)

Considering option 1,

2.82 2 2(0.17) = 0.48, which is more than 0.17.

Option 1 is eliminated.Considering option 4,

2.82 2 2(0.343) = 0.134, which is less than 0.343.

Option 4 is the answer.Hence, option 4.

74. In an out-of-season resort hotel, there should be lesspeople. Similarly if the white house resembled this

serene hotel, it should have empty (option 3) corridors.

Hollow is incorrect, as it does not blend with the

context very well.

The corridors could be white but then again, we need a

word which goes with the idea of an out-of-season

hotel.

Striking too goes out of context.

Hence, the correct answer is option 3.

75. If people were speaking in low-pitched voices, theywould not be loud (option 3) or stentorian (marked by

loud voice, option 4).

Quiet goes more with the idea of low-pitched voices,

therefore, we can eliminate faded (option 2) as well.


76. The only colour or choler (anger, irritability) wasprovided by the president; therefore, his temper

(option 4) would easily set off. Since the author

indicates anger, humour and laughter can be ruled out.

Curiously does not go with the idea of anger.


77. The president was not prowling the corridors as thereis no mention of the president wanting to catch hold of

someone (no predatory instinct that is). A stroll is aleisurely walk and in his angry mood, the president

cannot be taking a leisurely walk! Stormed will not fit

where usage is concerned. A person may storm in or

out of a corridor. Paced is the correct word. Pace is a

manner of walking in which a person may stride or

walk back and forth.


78. The statement that the person himself did not filereturns is a straightforward or a blunt statement, with

no deceitfulness (treachery) or tact (diplomacy) or

pretension (to give a false appearance). Therefore,

blunt is the best adjective here.


79. The principal tax has already been mentioned, so wecan eliminate option 3. Ramesh has mentioned that he

has not filed his returns; hence the answer is not

option 4 either. If the 20,000 became 60, 000 it could

be because of interest levied. Therefore, interest is a

more suitable option than taxes.


80. If Ramesh has not paid income tax for the yearsmentioned, most likely, the IT department will levy

charges. The charges could take the form of interests

and fines. One of the options (the precious question)was interest. It follows that the second could be fines.

Working with the options also gives us the same

answer. Ramesh will not get a refund (option 2) unless

he files his returns. IT department does not charge fees

(option 3). There are no sanctions (option 1) involved

in income tax.


81. In legal terms, attach means to seize persons orproperty by legal writ. Impound also has a similar

meaning to seize and retain in legal custody. The

word is generally used in terms of confiscating illegal

possessions. But royalties and trust funds, when seizedby the use of a legal writ, are said to be attached.

Detached being the opposite, does not apply. Nor does

the word closed.


82. The income tax department is a not violent mob whichwould destroy (smash) or dismantle (take apart)

automobiles. Nor will it freeze an automobile. The


14/18

CAT 2004


correct word is seized. It can seize or get hold of

automobiles.


83. The person who does not file his or her IT returnsbecomes an offender. He is neither an investor (option

3) in Income tax nor is he a purchaser (option 1).

Since it is Rameshs fault (by not filing his IT returns),he does not become a victim (option 2).


84. We have preposition errors here. One does not pleadguilty of but guilty to a crime. With B incorrect, we

are left with options 2 and 4.

In sentence D, it should be sentenced to instead of

sentenced for.

Sentences A and C are correct.


85. In sentence B, the preposition of need not followthinking. It should be thinking what to do.

Sentence C is incorrect as well. It requires the article abefore shower ( took a shower). The article a

represents one and is required here.


86. Efforts bear fruit and not give fruit. Therefore,sentence B is incorrect. That itself would give us the

answer.

Sentence C is incorrect as the homophonic equivalent

compliment is to be used instead of complement.

Complement is related to completion, to make whole or

complete. Compliment is to praise or admire.


87. It is easier to tackle this question by eliminating theincorrect options.

Option 2 has a tense error. Instead of have had, use of

have is sufficient to remove the tense inconsistency.

Option 1 is inappropriate as the first that is redundant,

it is not required.

Option 4 has a pronoun error. With the use of

antecedent things, pronoun should be plural,

i.e. - they should be used in place of it.


88. Option 1 can be eliminated because the usage shouldbe estimated to be 3400 years old.Similarly, option 3 is also incorrect. With reasonable

certainty modifies estimated and should be placed

close to it.

Option 2 is awkward. We can rephrase the sentence to

begin with estimated. Also, pottery is singular (plural

is potteries) and therefore, are estimated cannot

apply to singular pottery. Plus, the sentence looks

grammatically inconsistent. One is not sure whether

are estimated applies to archaeologists or the pottery.


89. In option 1, it should be incidents in place ofincidence. There is need for reduction in the number

of incidents of music piracy, therefore, the plural,

incidents is required.

Option 2 has an error of parallelism. Verb suggest is

not consistent in usage with verb advocating in the

same sentence. Both should take the same form.Option 4 can also be eliminated as prices to be ...

should be replaced by should be.

Option 3 is grammatically correct.


90. Bolt in the 1st option means a large roll of cloth of adefinite length, especially as it comes from the loom

and the word has been used correctly.

Bolt in option 3 is similar to a latch or a fastener to

secure doors and the word has been used correctly as

well.

In option 2, bolt means to move or spring suddenly

and has been used incorrectly. The correct versioncould be, he bolted for the gate and not made a bolt

In option 4, bolt shares a similar meaning, to start

suddenly and run away and the word has been used

appropriately (bolt from).


91. Passing marks in option 1 is easily understood to meanfavourable marks or sufficient marks in an exam.

Option 2 is incorrect as, here the word needs to be

followed by a preposition (by). It should be,

everybody passing by her on the road or simply,

passing on the road.

Option 3 is correct. Passing the parcel is the name of agame.

In option 4, passing car is correctly used to mean, a

car going past or moving by.


92. Fallout is the descent of particulate matter which is aresultant of a nuclear explosion or it is an incidental

result (consequence) or side effect.

Option 1 has been used in the sense of the first

meaning (nuclear fallout).

Options 2 and 3 have been used in the second sense of

consequence (political and environmental fallouts).

Option 4 is incorrect, as the word has been used in thesentence to mean failure or dropping out (fallout of his

good students). Fallout does not mean failure.


93. The they in sentence C refers to the two neighbours insentence A. Therefore, AC is a pair. Therefore options 3

and 4 can be eliminated.

Sentence D introduces the concept of a resident joined

by a neighbour fighting an intruder. Thus, D precedes


15/18

CAT 2004


AC making DAC a mandatory sequence. That leaves us

with option 1.


94. Bush was not just fighting the democrats but also theentire congress, at times and therefore, he felt justified

in bypassing congress altogether at times. This

connectivity of ideas makes DBA a mandatorysequence which would get all other options eliminated

except the answer.

To check, sentence E introduces the CEO of white

house having a problem with second guessers and time

wasters.

Sentence C continues the idea of the consequence of

the problem or a solution to it. EC is followed by DBA.


95. Sentence B is the introductory statement, as it insertsthe idea of declining position of Germany in World War

II. The rest of the sentences further this idea.

Therefore, options 1 and 4 can be eliminated (they do

not begin with B).

Sentence B is followed by sentence E, as the discussion

begins with hopelessness for Germany at both ends,

eastern as well as western. Red Army, Russia would be

east and hence D follows E. although, once we have

figured out BE, we already have our answer.

Sentence A discusses matters of the west and therefore

the sequence is BEDAC.


96. Option 1 suggests that one should complain only whenone finds others prejudiced against one, an idea which

is not explicitly or implicitly given in the paragraph.

Option 2 completely presents the points discussed in

the paragraph and is the answer.

Option 3 has missed a main point of avoiding the faults

one sees in others.

Option 4 implies that one should make enemies if they

behave badly with oneself, which has not been talked

about in the passage.


97. A summary does not go out-of-scope. Therefore, option4 can be eliminated. It talks about the likes of people

which has not been discussed in the passage.

Options 2 and 3 are incomplete. Option 2 speaks only

about the requirements and 3 talks more about the

produce.

Option 1 is correct as it takes care of both of these and

takes into account the important points of the passage

like variance of food eaten etc.


98. The author has not criticized executives of automobilecompanies and hence option 1 can be eliminated.

Option 2 is correct. The car that Ford made did 18

miles an hour. Today, in London, cars still manage an

average speed of 17+ miles per hour.

Option 3 goes against the idea expressed in the

passage. Anthropological factors have tried to dampen

the speed of change and not fostered innovation.

According to the author, innovation in jet engines has

been more cosmetic and hence cannot be more thanincremental (option 4).


99. The author takes the example of jet planes andautomobiles to emphasize that structural change has

been incremental (paragraph 6). That takes us to

option 4.

Option 1 is not entirely supported by the passage. The

author states that statements like nothing is

permanent as change (paragraph 2) are no more than

clichs.

Again, with the example of tribalism and other

examples, the author refutes the argument that changeis always rapid. This eliminates option 2.

With the example of Ford motors, the author points out

that with a lot of money invested by automobile

companies, there has been hardly any rapid major

change. That eliminates option 3.


100. To quote from the first paragraph, tribalism protectsfrom fear of change. In another example, the author

quotes the IBM CEO to put forth the idea that we scare

ourselves constantly with the idea of change. Therefore

we can do away with option 1 (Rapid change is usually

welcomed in the society).The author gives examples from the automobile

industry to stress that more innovation does not lead

to rapid change; it may just lead to cosmetic

alterations. Option 3 can also, thus, be eliminated.

Although competition may spur change but there is no

mention of radical innovation (option 4).

Option 2 correctly points out the gist of the passage

Industry is not as innovative as it is made out to be. Jet

planes, automobiles have not changed much in a

hundred years.


101. The last sentence of the passage answers this question,Because auto executives understood pistons and

carburettors, and would be loath to cannibalize their

expertise, along with most of their factories. Because

auto executives (option 1) did not want change, they

did not adapt.

Alternative fuels were discovered and implemented

(option 2 can be eliminated).


16/18

CAT 2004


Change in technology also took place in Germany,

Japan and France. Therefore, options 3 and 4 can also

be eliminated.


102. In an insecure culture, the painter himself has tochoose for the society (last two paragraphs). That

renders option 1 false.Option 2 When a culture is in a state of disintegration

or transition the freedom of the artist increases- but

the question of subject matter becomes problematic for

him: he, himself, has to choose for society. emphasises

the idea of a painter having the freedom to choose a

subject for his painting (its meaningfulness to the

painter).

Option 3 cannot be substantiated from the passage.

According to the passage, either the painter identified

himself with the people or he has to find his subjects

within himself.

There is no mention of the painter using his past

experience or memory to choose his subject. Thiseliminates option 4.


103. The author begins the passage by illustrating thefreedom which painters today enjoy in choosing their

subject for painting. He further says in the first

paragraph that with freedom to choose any subject for

painting, the painters have abandoned other subjects

and have begun to paint abstract pictures. He

questions the connection between these two

developments increase in freedom to choose and

abandonment of other subjects to go in favour of

abstract art.Other two options (1 and 4) can be clearly eliminated

in the light of this information.

The success of artists has not been talked about

(option 2).


104. From the fifth paragraph, for a painting to succeed, itis essential that the painter and his public agree about

what is significant (option 1 can be eliminated).

According to the passage, When the subject has been

selected, the function of the painting itself is to

communicate and justify the significance of that

selection. Thus option 2 is a necessary attribute forthe painter to succeed, and can be eliminated.

In paragraph 5, the author gives an example of

renaissance art and states that it is appreciated

because of its historic significance. That eliminates

option 4.

The subject may have a personal meaning for the

painter or individual spectator; but there must also be

a possibility of their agreement on its general

meaning. This implies that although it is important for

the subject to be meaningful to the painter it loses

significance if the spectator or public do not agree with

the authors concept of meaningful. Thus option 3 by

itself is not necessarily an attribute for a painter to

succeed.


105.

The second last paragraph substantiates option 3. It istoo often forgotten how many of the art scandals of

that time (19th century) were provoked by the choice

of subject (Gericault, Courbet, Daumier, Degas, Lautrec,

Van Gogh, etc.).

Option 2 can be confirmed to be true from paragraph 6

The general agreement about what is significant is

so well established that the significance of a particular

subject accrues and becomes traditional. This is true,

for instance, of reeds and water in China. The author

takes the instance of renaissance art (paragraph 5) to

point out that the agreement on the general meaning of

a painting is influenced by culture and historical

context.Option 1 is not true. To quote from paragraph 3, A

subject does not start with what is put in front of the

easel or with something which the painter happens to

remember.


106. In paragraph 7, the author says that when a culture isin a state of disintegration (insecure), the freedom of

the artist increases. That proves that option 1 is true

and that option 2 (whose idea is opposite to that of

option 1) is contradictory to the passage.

In paragraph 6, the author puts forth this idea that in

secure cultures the artist is unlikely to be a free agentand that he will be employed for the sake of particular

subjects. That negates option 3.

Option 4 cannot be substantiated from the passage.


107. The author quotes, The New Mercantilism facessimilar problems of internal and external division

(paragraph 3). That similar problem refers to

problems faced by New Imperialism. The third

paragraph states the irregular effects of New

Mercantilism. And, on this context the author draws

parallels between the two systems.

Options 1 and 2 are incorrect as origins and othersimilarities have not been explicitly mentioned in this

regard.

Option 3 may be considered as it showcases the

consequences of both systems, but in light of what the

author directly says option 4 is a better answer.


108. Option 1 has been clearly stated in the fifth line of thepassage.


17/18

CAT 2004


Option 3 can be eliminated as the author explicitly

mentions that the empire did not work towards

developing its vast hinterland (end of first paragraph).

Option 4 is only partially true, as the empire wanted to

stop the development of a native capitalist class.

Option 2 goes beyond the scope of the passage.


109. The centre here refers to the new mercantilism,multinational corporate system of special alliances and

privileges, aid and tariff concessions.

In any case since the entire passage deals with

multinational corporate system, it does not refer to a

specific national government (option 1).

Nor does it refer to native capitalists (option 2) or new

capitalists (option 3) as they would not be responsible

for overall functioning of the centre.


110. Option 1 is about native capitalists (who bargain withmultinational corporations) and not about middle

class.

Option 2 is not completely correct, as their (middle

classs) power comes from the metropolis and they

cannot easily afford to challenge the international

system (not that they are dependent on it).

Option 4 can be eliminated as the author does not

speak about this in terms of popular support.

Option 3 is the correct answer, as statements in the

fourth paragraph support this point. Firstly, the fervent

nationalism asks only for promotion with the

corporate structure and not for a break with that

structure (maintaining status quo). Secondly, they

cannot easily afford to challenge the internationalsystem (again they are not in a position to challenge

the status quo).


111. There is now considerable evidence that Type Bmalnutrition is a major cause of chronic degenerative

diseases (paragraph 4, first sentence).

Option 2 is the correct reason for why Type B

malnutrition is a major contributor to illness (chronic

degenerative diseases) and subsequent death. If

developing countries suffer from one type of

malnutrition, it does not apply that developed

countries would suffer from another type (option 1).Option 3 is not correct. It has been explicitly stated in

paragraph 4 that therapeutic medicines have been

developed by the pharmaceutical companies.

Whether national surveys include the newer nutrient

groups or not has not been stated in the passage

(option 4).


112. From the first paragraph, a majority of apparentlyhealthy people are pre-ill. That is because of chronic

degenerative diseases which strike silently. According

to the author, there would be a latency period before

the symptoms appear and a diagnosis is made. But till

that time that apparently healthy person is still ill.

We can easily eliminate options 2 and 3, as they do not

come close to this idea.Option 4 is a lift from the passage and looks attractive

enough. But the option explains about the latency

period.

The option that answers the question why is option 1.

Because so-seemingly healthy people may have

chronic degenerative diseases, therefore they are

deemed pre-ill.


113. According to the author, multiple micronutrientdepletion is a common kind of malnutrition in

developed countries (paragraphs 1 to 4).

This gives rise to chronic degenerative diseases whichcan be managed by repletion of these nutrients. That

straightaway gives us our answer (option 2).

Option 1, 3 and 4 are weak arguments or are irrelevant

for the question in hand.


114. In the last paragraph, it is mentioned that althoughtailoring micronutrient-based treatment plans to suit

individual efficiency is not suitable, the micronutrients

are safe to use and most people consume suboptimal

levels of these nutrients. Both these ideas are summed

up in option 3.

Option 1 can be ruled out because it goes out-of-scope.Option 2 does not make much sense in light of the

passage.

Option 4 is true but that is not the reason the author

quotes.


115. In paragraph 3, the author mentions how the ferocityof Tsavo lions (which are not different from lions

elsewhere) annoys certain scientists as it is a myth and

not a fact. According to the passage: "People don't want

to give up on mythology ... Tsavo's lions are no more

likely to turn man-eater than lions from elsewhere."

The only option which illustrates this idea is option 3that the bestselling book perpetuated a bad name for

the lions in that area.

Their ferocity being same as other lions (option 1) is

not a problem. The scientists or others are not really

jealous about the money made by Patterson (option 2).

Only the narration is not a reason for the annoyance

(option 4).



18/18

CAT 2004

M-PP-01 B1 18 www TestFunda com

116. The lions attacking vehicles and humans (option 4) orthey being more aggressive living in a tough area

(option 2) - are statements definitely contributing to

their image of being savage or ferocious. Therefore

options 4 and 2 are eliminated.

Option 1 too favours this sentiment - Tsavo lions have

been observed to bring down one of the strongest and

most aggressive animals.Only option 3 is a neutral statement and does not

contribute to the popular image of Tsavo lions as being

savage creatures.


117. As per the first paragraph, Craig and West had thoughtthat mane less lions seen by the amateur observers

were adolescents. But once the scientists saw these

lions and saw the colour of their noses, the scientists

understood that these were actually adults and that

they were mistaken. This eliminates options 1, 2 and 4.


118. Gnoske and Peterhans hypothesis is that Tsavo lionsmay be similar to unmanned cave lions of the

Pleistocene.

Option 2 strengths this and hence can be eliminated.

Tsavo lions are known to be ferocious.

Option 1 may weaken the statement slightly but both

option 1 and 4 are not strong arguments. Craigs and

Peytons doubts have not been proved and the

morphological variations if insignificant contribute to

the similarities between the two.

If the Pleistocene lions were less ferocious (option 3),

then that weakens the comparison between the two.


119. Between sentences A and C, sentence C is a moreappropriate introductory sentence. In A, only such a

full-hearted leap will allow is more of a conclusion

than introduction.

Sentence E follows C, as C introduces the idea of fuel

cell economy, and E continues that idea by putting

across that the current efficiency is 30 percent.

Sentence D follows E, the sentence (D) furthers the

idea in E by referring to its efficiency with keyword

that that is twice as good.

Sentence B justifies further improvement and A

concludes the paragraph.Hence, the correct answer is option 1.

120. CB is a mandatory pair. C introduces the idea ofsources of information like pyramids and tombs. B

furthers it by adding even from pyramid temples.

That leaves us with only one option, option 3.

Sentence E begins the paragraph whereas sentence A

ends it, as it sums up the ideas of the rest of the

sentences (talk about pyramids, tombs and graves) by

saying that death was not the only preoccupation for

the Egyptians.

Sentence D follows the introductory sentence E, as it

reasons the idea in E we know more about the rich

because the monuments were made for the rich (E),

whereas we do not know about the poor as their

houses have not been preserved and they were buried

in simple graves (D).Hence, the correct answer is option 3.

121. The passage does not state that research will help infinding out a definitive answer (option 1).

Option 3 too is ruled out, as, we do not (from the data

in the passage) whether research in Germany would

help in finding a definitive answer.

Option 4 goes out of scope and discusses that research

and not debates can get an answer. This has not been

mentioned in the passage.

Option 2 is the most appropriate one out of the four

options.


122. Nowhere does the author mention that Nietzscheurged the decadent and enfeebled modern society

(option 1), although there may be undertones of the

same.

Option 2 is factually incorrect. Nietzsche does not urge

to smother the will with excessive intellectualizing.

Option 3 can be eliminated as well, as Nietzsche does

not criticize intellectuals.

Between options 1 and 4, option 4 is suitable as it

captures the essence of the passage.


123. Option 1 does not highlight that this kind of conflict is adirect action.

Option 2 again fails to mention that it is a new kind of

class conflict.

Option 4 goes in a bit of detail about subsidization.

Option 3 highlights all the major points (preferential

treatment, exacerbation of injustice, direct protests

from the local communities, and results in a new type

of class conflict) and therefore is a more suitable

option than the rest.


cat 2004 detailed solutions

Documents