Cat Zero Expanse

CAT - 2009 CAT Zero EXPLANATORY ANSWERS

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EXPLANATORY ANSWERS SECTION - I 1.

æ 3ö 10 ç - ÷ è 2ø

The required sum can be calculated as follows: The sum of the numbers in the first list

-

31 = 528 2 The sum of the numbers in the second list = 32 ×

The sum of the numbers in the third list = 496 – 2 × 8 = 480 The sum of the numbers in the fourth list = 480 – 2 × 4 = 472 The sum of the numbers in the fifth list = 472 – 2 × 2 = 468

4.

The sum of the numbers in the sixth list

æ 3ö + b ç - ÷ – 63 = 0 è 2ø

– 63 = 0

Let mother’s present age be x years. \ Father’s present age will be

Hence, [3]. Alternatively, Every time the operation is performed, one number is reduced and the total of all the numbers is reduced by 2. Hence to get from the original 32 numbers to a single number it will take 31 operations and the

4x +3 4x + 9 3 = years Daughter’s age will be \ 3 9 Also, the mother’s age – 2 = 5 (son’s age – 2)

æ 32 ´ 31 ö ÷ i.e. 528 will get original sum which is ç è 2 ø reduced by (31 × 2).

\ Son’s age will be =

( x - 2) x +8 +2 = 5 5

Sum of ages is 83

Hence the final sum will be 528 – 62 = 466.

4x 4x + 9 x +8 + + = 83 3 9 5 \ 134x + 117 = 83 × 45 \ x = 27 x +

Just like the last digit, the last two digits also would follow a cyclicity. If we check the powers of the number 43, we see that the last two digits repeat every four steps as shown below: Last two digits of 43 2 = last 2 digits of 43 × 43 i.e. 1849 = 49 Last two digits of 43 3 = last 2 digits of 49 × 43 i.e. 2107 = 07 Last two digits of 43 4 = last 2 digits of 07 × 43 i.e. 301 = 01 Last two digits of 43 5 = last 2 digits of 01 × 43 i.e. 43 = 43 Hence the last two digits of 43 120 will be the same as the last two digits of 43 4 i.e. 01. Hence [5].

\ Son’s present age =

27 + 8 35 = = 7 years. 5 5

Hence, [2]. Answers to questions 5 and 6: f(6) = 36a + 6b + c = 0 ... (i) f(8) = 64a + 8b + c f(4) = 16a + 4b + c 3f(8) = –4f(4) ... (ii) \ 256a + 40b + 7c = 0 Multiplying (i) by 7 and subtracting from (ii), 4a – 2b = 0 \ b = 2a Let m be one root of the equation f(x) = 0. Th e other root is 6.

f(x) = 10x 3 + ax 2 + bx – 63 f(–1) = 10(–1) 3 + a(–1) 2 + b(–1) – 63 = –8 \ –10 + a – b – 63 = –8 ... (i) \ a – b = 65 Now, (2x + 3) is one of the factors i.e., At x = -

135 9a 3b + 4 4 2

2

4x years. 3 According to the conditions, the father’s age + 3 = 3 × the daughter’s present age.

= 468 – 2 × 1 = 466

3.

æ 3ö + a ç- ÷ è 2ø

9a 3b 387 = 4 2 4 9a – 6b = 387 ... (ii) Solving equations (i) and (ii) simultaneously, we have a = –1 and b = –66. Hence, [3]. Alternatively, Using f(–1) = –8, we have a – b = 65. Considering the options, only [3] satisfies this.

= 528 – 2 × 16 = 496

2.

3

3 ; f(x) = 0 2

\ 6 + m =

2

-b = –2 a

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C A T 2 0 0 9 4300 but having all digits distinct = 2520 + 280 + 56 = 2856. Hence, [2].

\ m = –8 \ The equation is f(x) = a(x – 6)(x + 8) = a(x2 + 2x – 48 ) 5.

Answers to questions 9 and 10:

If a = 1, b = 2 and c = –48. But if a changes, the values of b and c will also change proportionately and hence ab/c cannot be a fixed value. Hence [5]

6.

g(x) = (x + 8) 2 = x2 + 16x + 64. Hence, [1].

7.

n th term in Bullu's series = 9 + (n – 1)5 = 4 + 5n. Maximum value of n = 38 mth term in Gullu's series = 11 + (m – 1)3 = 8 + 3m. Maximum value of m = 63 We need, 8 + 3m = 4 + 5n \ 5n – 3m = 4

A

Pool M

R N

5n - 4 3 \ n takes values 2, 5, 8, 11, … , 38 \ Number of common terms

9.

é (38 - 2) ù = ê ú + 1 = 13. Hence, [5]. 3 ë û

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8.

To take the shortest route, Aanchal will travel from A to M, then from M to N taking the pedestrian overbridge and then from N to B. 5! = 5 ways. She can travel from A to M in 4!

7! = 7 ways. Thus, 6! total number of ways = 5 × 7 = 35. Hence, [1].

9, 14, 19, 24, .... 194

10 .

194 - 14 + 1 = 13. 15

To travel from B to C, Aanchal can choose to go via point J or K. 6! Number of ways to travel to J = (4! ´ 2! ) = 15 and thereafter to C = 3 ways. \ Total ways to travel from B to C via J = 45. Number of ways to travel to K =

Case (i): Number is greater than 5000. The number in the thousands place can be selected from 5, 6, 7, 8 and 9 in 5 ways. The hundreds, tens and units digits can then be selected out of the remaining 9 digits in 9, 8 and 7 ways respectively. \ Number of ways = 9 × 8 × 7 × 5 = 2520 Case (ii): The thousands place is 4 and the hundreds place is > 3 The number in the hundreds place can be selected from 5, 6, 7, 8 and 9 in 5 ways. The tens and units digits can then be selected out of the remaining 8 digits in 8 and 7 ways respectively. \ Number of ways = 1 × 5 × 8 × 7 = 280 Case (iii): The thousands place is 4 and the hundreds place is 3. The tens and units digits can be selected out of the remaining 8 digits in 8 and 7 ways respectively. \ Number of ways = 1 × 1 × 8 × 7 = 56 \ Total number of four-digit numbers greater than

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B

She can travel from N to B in

Gullu’s series is ® 11, 14, 17, 20, ..., 194, 194 So, the first common term = 14 & the last common term = 194 Difference between any two common term = 15 \ Total number of common terms =

K J

\ m =

Alternatively, Bullu’s series is

C

6! = 6 and thereafter 5!

to C in way. \ Total number of ways to go from A to C via B = 35(45 + 6) = 1785. Hence, [1]. 11.

f(7, 6) = f(7, = f(7, = f(7, = f(7, Hence, [1].

5) + 7 + 1 = f(7, 5) + 8 4) + 16 = f(7, 3) + 24 2) + 32 = f(7, 1) + 40 0) + 48 = 7 + 48 = 55

12 .

r(4), r(14), r(41), r(22), r(27), r(72), r(39), r(93), r(89), r(98) = 4 Thus there are 10 such numbers with their product roots being 4. Hence, [1].

13 .

Ð BOC = 120. But Ð BAC =

1 ( Ð BOC – Ð EOD) 2

® Ð EOD = 60. Since OBC is isosceles, it will be a 120°-30°-30° triangle

3

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C A T 2 0 0 9 and we can show that BC =

3 r where r is the radius 15 .

of the circle. Similarly EOD can be shown to be a 60°-60°-60° triangle (i.e. an equilateral triangle) and hence ED = r. Now consider the two triangles ABC and ADE. We know that AE × AB = AD × AC i.e.

17 P B

AE AD = AC AB

and also Ð A is a common angle. Hence the two triangles are similar. The ratio of the corresponding

3 r : r i.e. 3 : 1 hence the ratio of the areas for the two triangles will be 3 : 1. Let these areas be 3x and x, then from the given information, area of BCDE = 2x = 48. Hence the required area of D ADE = x = 24. Hence, [3]. Alternatively, By tangent – Secant theorem, AE × AB = AD × AE \ D ADE ~ D ABE (by S-A-S test)

\ A( D ABC) =

BC = DE

Þ

2

=

3

1 [A( D ABC) = 3

=

7056 = 84 sq. units

24 ´ 14 ´ 21

1 × Base × Height 2

3 th of the cherries plus half a cherry 4 and none are left. So when she came in, there must Tandy eats

1 ) × 4 = 2 cherries. 2 When Sandy came in, there must have been

have been (0 +

x 1 = [x = Area of D ADE (say)] x + 48 3 Þ 3x = x + 48 Þ x = 24 \ A ( D ADE) = 24 sq.units. Þ

1 ) × 4 = 10 cherries. 2 And when Mandy came in, there must have been (2 +

1 ) × 4 = 42 cherries. 2 Hence Mandy ate 42 – 10 = 32 cherries. Hence [4]. (10 +

When Ð P = 60 o , Ð Q = Ð R = 60 o (as PQ = QR) i.e., D PQR is an equilateral triangle Þ QR = 5 When, Ð P = 90 o , QR =

24(14)(3)(7) =

x 8-x = Þ x » 5.8 21 8 \ Perimeter or PQRS = 5.8 × 4 = 23.2 units Hence, [2].

A( D ADE) A( BCDE)]

14 .

s(s - a )(s - b)(s - c)

Þ

16 . =

10 + 17 + 21 48 = = 24 2 2

PQ AM \ BC = AN

1 3

A (DADE ) A (DADE ) + A ( BCDE )

C

84 ´ 2 \ h = 8 21 Let side of square PQRS be x. Now, PQ || BC Q AN ^ BC Þ AN ^ PQ Since, D ABC ~ D APQ (by A-A-A test)

\ From equation (i) Þ æ 1 ö A ( DADE ) ÷ ç = ç 3÷ A( DABC ) ø è

NR

\ h =

BC DE = Sin120° Sin 30°

Þ

10

1 1 \ 84 = 2 × BC × AN = 2 × 21 × h

By properties of triangle theorem,

3 2 1 2

Q

=

But, A( D ABC) =

.... (i)

BC BC Sin120° = = Þ Þ DE DE Sin 30°

S 21

M

Semiperimeter of D ABC =

sides BC and ED is

2 A ( DADE ) æ DE ö \ A( DABC ) = ç BC ÷ è ø

A

17 .

52 + 52 = 5 2 .

As the American man sits on seat number 1 and the Chinese woman sits on seat number 15, we have. AM

Thus, we get, 5 £ QR £ 5 2 . Hence, [3].

1

4

CW 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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C A T 2 0 0 9 the midpoints of the respective sides of the square ABCD.

No two men, no two women and no two children are together (as a child must always be between a man and a woman). Also, a woman cannot be to the right of a man, so a man, a child and a woman sit one after the other, starting with a man. Also, it is given that an Indian never sits on a prime numbered seat or a seat that is a cube of a number. So the arrangement would look as following:

4 \ Each quarter circle has radius = 2 = 2 cm. p( 2) 2 = p cm 2 4 \ Area of 8 quarter circles = 8 p cm2 \ Area of square = (4) 2 = 16 cm2 \ Total area of shaded region = 8 p – 16 = 8( p – 2) cm2 Hence, [3]. Alternatively, Area of each quarter circle =

A C M C W M C W M C W M C W M C W 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Thus we see that there is only one possible seat for a child from India i.e., seat number 14. Hence, [3]. 18.

19.

20.

21 .

A

From the answer to the previous question, the Indian child is at seat 14, and since a Indian and a Briton always sit together, the British man sits at seat number 13. As 7 is a prime number, the 7 th seat can be occupied by either a Japanese or a Chinese man only. (1 º American man, 13 º British man, 7 ¹ Indian). If the Japanese man sits at seat number 7, then the Indian and Chinese men have to sit on chairs numbered 4 and 10 respectively. Þ The British child has to sit on chair number 5. Þ There won’t be any place where Indian woman and the British woman can sit together. Hence, the Chinese man has to sit on chair number 7. Hence, [2].

D

A( D DOC) =

O

X

H

D

F

22 .

100t D Aircraft (100 m/s)

C

o

30

B

500 m

500 m 60o

O Gun

A

ground level

Let the bullet hit the aircraft after ‘t’ seconds. \ CD = 100t \ CB = CD sin 30 o =

G

and BD = CD cos 30 o =

C

100t = 50t 2 3 (100t) = 50 3t 2

\ CA = 500 + 50t and OA = 50 3t

Since O is the centre of the square, E, F, G and H are

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1 × 4 × 2 = 4 2

\ The shaded area = 2p – 4 \ The required value = 4 × ( 2p – 4) = 8( p – 2) cm2

B

Y

pr 2 p ´ 2 2 = = 2p 2 2

A(sector F–DOC) =

If there are n rounds in the tournament, the number of players is between 2 n-1 + 1 and 2 n . Statement A: The number of players lies between 129 and 256 i.e. 2 7 + 1 and 2 8 . Thus the number of rounds = 8. Statement B alone is not sufficient to answer the question. Hence, [1]. E

C

F

Ð DOC is a right angle. \ The shaded area will be A(sector F–DOC) – A( D DOC)

One player is eliminated in each match. As only one player is the champion, the number of matches played is one less than the number of players. Statement A: The number of players is 64. Statement A is sufficient to answer the question. Statement B: If there are n rounds in the tournament, the number of players is between 2 n-1 + 1 and 2 n . Hence, [1].

A

B O

Q tan 60 o =

5

CA OA

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SECTION - II

500 + 50t

3 =

\

50 3 t

Answers to questions 26 to 28:

\ 100t = 500 \ t = 5 sec Hence, [3]. Alternatively, Ð COA = 60° Þ Ð DOC = 30° Ð CDB = 30° Þ Ð CDO = 120° \ In D ODC, Ð DCO = 30°, i.e., D ODC is an isoseles trian gle. DC = OD = 50 0 m i.e., the aircraft travelled a distance of 500 m at the speed of 100 m/sec. \ Time taken by the bullet to hit the aircraft is

From (iii), we get the following arrangement.

4

\ From (i) and (ii), two girls cannot sit at M-10 and M-11. \ Two girls must occupy the two seats at the extreme left i.e., M-4 and M-5. Then from (4) we get;

E 4

500 = 5 sec. 100 23 .

2

2 2 4

2

1 169 - 168 ... –

Now

–

1 146 - 145 1 169 - 168

-5 4 -1

1 -1 0

Since, there is only one person sitting between H and F, F must be sitting on M-7 seat. Also, D occupys seat M-10, implies B is on seat M-6 i.e., between H and F. Hence, [1].

28 .

From the previous answer, C is sitting on M-9 seat. \ Number of people between C and E is 4. Hence, [4].

29 .

GDP of Bhutan =

1 168 - 167 +

=

1

+

167 - 166

– ... –

25 .

168 –

–

1

168

146 –

168 –

167 +

167 +

145 +

145 +

144

» $40

13 » $60 0.22 GDP of Sri Lanka = $50 GDP of Malaysia = $110 GDP of USA = $200 GDP of Singapore = $20 GDP of Korea = $125 GDP of Pakistan = $33.3 Only for the pair USA and Singapore the difference is more than 100 mn USD. Hence, [3].

145 - 144 169 +

7 0.18

GDP of Philipines =

So the above expression can be written as

169 +

B/D C / F A F / C D/B G 6 7 8 9 10 11

27 .

\ 2a 3 + 2a 2 – 5a + 1 = (a – 1)(2a 2 + 4a – 1) = 0 This has only one integer root, a = 1. Thus the five original integers are –1, 0, 1, 2, 3. \ k = 1. \ (k + 1) 4 = 16. Hence, [2]. 24 .

H 5

26-[4]

Let the five integers be (a – 2), (a – 1), a, (a + 1), (a + 2). Thus, according to the conditions given, (a – 2)3 + (a – 1)2 + a + (a + 1)2 + (a + 2)3 = 30a + 1 \ 2a 3 + 2a 2 – 5a + 1 = 0 a = 1 is a root. By synthetic division:

1

5

C/F A F/C 6 7 8 9 10 11

166

30 .

GDP is highest for USA and lowest for Singapore. Hence, [5].

31 .

Let the revenue obtained in the current year be ‘x’. Hence revenue obtained for next year is ‘2x’. Let the percentage share is ‘y’ for the current year, hence it will be

=

169 + 144 = 13 + 12 = 25. Hence, [4].

GDP =

Any term will be of the form a pb qcr, where p, q and r are integers between 0 and 10 and p + q + r = 10 So the problem is the same as finding the number of non-negative integer solutions to p + q + r = 10. This can be solved using partitioning logic as 10+3-1C 12C = 66. Hence [3]. 3–1 = 2

GDP =

x y

y 2

for the next year.

(for current year)

4x 2x = y y 2

(for next year)

\ Percentage increase = 300% Hence, [3].

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32 .

Nitu should spend at least Rs.15, Rs.15, Rs.15 and Rs.20 respectively on the 4 items. But, she must spent at least Rs.60 in shop 3, which is possible only if she spends at least Rs.20 on item 2 in shop 3. Thus, the minimum total amount with Nitu could be 15 + 20 + 15 + 20 = Rs.70. Hence, [3].

33 .

The two shops must be shop 2 and shop 4, then Nitu should pay Rs.10, Rs.15, Rs.15 and Rs.15 respectively. Thus, the minimum amount she paid for any item is Rs.10. Hence, [2].

34.

If Nitu decides to spend Rs.14, Rs.14, Rs.30 and Rs.14 respectively on these 4 items, then she will not be able to buy them from any shop, though she had a total of Rs.72. Hence, [4].

Loan approval as a percentage of cumulative approval is given below. 0.5 1. Year 2000 = = 8.33% 6 1.5 2. Year 2001 = = 20% 7.5 1.5 3. Year 2002 = = 16.67% 9 3 4. Year 2003 = = 25% 12 3 = 20% 5. Year 2004 = 15 Thus, maximum growth is in the year 2004. Hence, [4].

Answers to questions 35 to 38: From [iv] and [v], A, B, C and E won at least one match, hence D must have lost all the matches in round 1(From [i]). From [i] and [ii], the number of matches won by the teams must be 0, 2, 2, 3 and 3 (as total 10 matches were played). From [iii], one among the two teams scoring 2 each must have beaten one among the two teams scoring 3 each. From the data for second round, C was among the top two teams in first round, i.e., scored 3 and from [iv], C lost to B, that means B must be the third team going in the second round and scoring 2 in first round.

40 .

Approval to disbursal ratio is maximum in 2003, as is evident from first table. Hence, [4].

41 .

Loans approved in 2000-2004 = 15 – 6 + 0.5 = 9.5 crore. Hence, [4].

42 .

As seen in the first table, loans approved in 2002 = 1.5 crore Loans disbursed = 1.7 crore Therefore, out of 1.7 crore disbursal, 1.5 crore got approved the same year and 0.2 crore got carried over from previous year. Therefore, percentage of loans approved in 2002 which were carried forward from previous years 0.2 × 100 » 12%. Hence, [1]. 1.7

=

Thus for the first round, we get:

Answers to questions 43 to 47: A B C D E

A × A C A E/A

B A × B B E

C C B × C C

D A B C × E

E A/E E C E ×

Wins 2/3 2 3 0 3/2

If Hiten bought the shares at Rs.100 in first week, then we know that the price per unit of the shares are: st

1 week B

The second round can be tabulated as follows:

B A/E C

B × B C

A/E B × C

C C C ×

39 .

36-[5]

37-[3]

2000 2001 2002 2003 2004

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week

rd

3 week

th

4 week

th

5 week

Q

100

150

R

100

150

S

100

150

150

150

81000 = 540 150 As Hiten sold shares of a company in each week, these 540 shares were of the same company, say S. As Hiten bought the shares of company S in fourth week, the per unit price of shares of company S must have been the least in fourth week, i.e., Rs.50. In second week, the per unit price of the shares of company B (i.e., Q) must have been Rs.200 and that in fourth week it must have been Rs.150. Now, in fourth week suppose the per unit price of the shares of company R increased by Rs.100, then the per unit price of the shares of the other two companies must be Rs.150 each in that week.

=

38-[1]

Refer to the following table. Year

nd

100

Now, Hiten earned Rs.81000 after seliing all the shares with him at the end of fifth week. \ The number of shares with Hiten in fifth week

Wins 1 0 2

Now the questions can be answered as follows: 35-[4]

2

P

Cumulative Actual Ratio Approvals Disbursals Approves Disburses Approval/Disbursal 6 4.45 0.5 0.45 1.11 7.5 5.8 1.5 1.35 1.11 9 7.5 1.5 1.7 0.88 12 9.2 3 1.7 1.76 15 12.5 3 3.3 0.91

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C A T 2 0 0 9 Fo r Class 2 : Th e n ew avera ge m emb ersh ip

Thus we get the following: st

1 week B

2

nd

week

rd

3 week

th

4 week

5 week

150

150

P

100

Q

100

150

150

R

100

200

150 (-)

S

100

50

150 (+)

200 (+)

150 (-)

(4 ´ 40 + 4 + 36) = 40 5 Fo r Class 3 : Th e n ew avera ge m emb ersh ip

th

=

(10 ´ 30 + 10 + 24) = 30.36 11 Fo r Class 4 : Th e n ew avera ge m emb ersh ip

=

Now, depending on when the price of the shares of company R increased we get the following cases:

(6 ´ 18 + 6 + 12) = 18 7 Fo r Class 5 : Th e n ew avera ge m emb ersh ip

Case 1 st

P B Q R S

1 week 100 100 100 100

nd

rd

th

=

th

2 week 50 (-) 200 (+) 100 100

3 week 50 150 (-) 200 (+) 100

4 week 150 (+) 150 200 50 (-)

5 week 150 150 150 (-) 150 (+)

2nd week 100 200 (+) 100 50 (-)

3rd week 200 (+) 150 (-) 100 50

4th week 150 (-) 150 200 (+) 50

5th week 150 150 150 (-) 150 (+)

(25 ´ 9 + 25) = 9.6 26 The average membership changes only for Classes 1, 3 and 5. =

Case 2 P B Q R S

1st week 100 100 100 100

1st week 100 100 100 100

2nd week 50 (-) 200 (+) 100 100

Consider Case 1: Hiten had

3rd week 150 (+) 150 (-) 100 100

4th week 150 150 200 (+) 50 (-)

5th week 150 150 150 (-) 150 (+)

8000 × 100 = 20 shares of 4

The total monthly fees (with discount) = [8 × 210 + (300 + 400) × 0.7] × 0.88 = Rs.1909.6 The average monthly fees (with discount) = 190.96 = Rs.191. Hence, [2].

50 .

The monthly fees (with discount) paid by a Class 5 member in January 2009 = Rs.400 Monthly fees paid by the member in January 2012 = 400 × (0.7) 3 = 137.2 The required difference = 400 – 137.2 = Rs.262.8. Hence, [4].

SECTION - III

47-[4]

Fo r Class 1 : Th e n ew avera ge m emb ersh ip =

0.36 30

49.

51.

A, C and E are correct. In B, 'automobiles' is spelt wrongly with an extra 'l'. In D, 'high breathing problems' is incorrect terminology. The correct phrase should be ‘high incidence of breathing problems’. Hence, [3].

52.

B and E are correct. In A, 'Reich' is singular, but 'fanatics', being plural, cannot be used. In D, since '6 million' is a number, the article 'a' before it is inappropriate. C is a fragment of a sentence, since it ends with a comma, but does not continue in the next line. So it is grammatically incorrect. Hence, [2].

53 .

A, B, C and E are all correct. In D, the semicolon used after 'basic question' is incorrect, because a semicolon is used when two related but completely different or independent facts have to be separated. Here, a colon should have been used instead. Hence, [1].

Company A is either company P or company S, then the per unit price of the shares of company A increased in fourth week (case1) or fifth week (case 2). Hence, [5]. 46-[2]

48.

For Class 3: The change =

0.6 9 The change is highest for Class 5. Hence, [5].

each company in first week. In second week, Hiten sells company Q's shares and buys company S's shares. Then he has 100, 0, 20 and 20 shares of company P, Q, R and S respectively. In third week, he sells company R's shares and buys company P's shares. Then he has 180, 0, 0 and 20 shares of company P, Q, R and S respectively. In fourth week, he sells company P's shares and buys company S's shares. Then he has 0, 0, 0 and 540 shares of company P, Q, R and S respectively. Thus, this case is possible. Similarly we can prove that case 2 is possible but case 3 is not possible. Now, we can answer the questions. 43-[4] 44-[3] 45 .

0.67 54

For Class 5: The change =

Case 3 P B Q R S

For Class 1: The change =

(5 ´ 54 + 5 + 48) = 53.83 6

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54 .

55.

56 .

In sentence B, 'on where' is grammatically incorrect - it should be either 'on which' or simply 'where'. The word 'columns' is wrongly spelt as 'columms' in sentence C. In E, the correct prepositional phrase should be 'at anchor', not 'in anchor'. Only sentences A and D are correct. Hence, [2]. 'Insurgency' (A) means rebellion or revolt by a group of people against the government. 'Migration' (B) means travelling from one region to another, usually for permanent residence or to find work. Hence (B). 'Ambience' (A) means the surrounding atmosphere or environment, especially in a public place such as a restaurant, pub, club, etc. 'Ambivalence' (B) is the state of being uncertain or indecisive. Hence (A). 'Grateful' (A) means thankful. 'Graceful' (B) means elegant in looks, manner, dress, etc. Hence (B). 'Vindictive' (A) means revengeful. 'Testimony' (B) means an evidence or proof in support of some fact. Hence (B). Thus the correct sequence is BABB. Hence, [5]. 'Contested' (A) means competed for, or challenged for. 'Contentious' (B) means something that causes argument or controversy. Hence (B). 'Consumption' (A) means the act of using up something, in this case using of goods and services. 'Consumerism' (B) is a modern movement for the protection of the rights of the buyers against exploitation by the sellers. Hence (B). 'Clone' (A) is a term used to describe the creation of identical copies through a biological process. 'Replicate' (B) means reproducing certain conditions or situations. Hence (B). 'Temperamental' (A) means moody, irritable or erratic in disposition. 'Temporal' (B) means worldly in character, the opposite of spiritual. Hence (A). Thus the correct sequence is BBBA. Hence, [5].

57 .

'Smarting' (A) here means to feel humiliated as a consequences of something. 'Hurting' (B) simply means physical pain. Hence (A). 'Consulate' (A) is a place that houses the consul of a foreign country who looks after the interests and well being of the people of the country by which he is appointed. 'Embassy' (B) is the place in a foreign country that houses the ambassador, who represents his government there. Hence (B). 'Contemporary' (A) means belonging to the modern or present time. 'Contemptuous' (B) means scornful, disrespectful towards others. Hence (B). 'Kneejerk' (A) reaction means a thoughtless or spontaneous reaction . 'Un mitigated' (B) mean s that wh ich is absolute. Hence (A). Thus the correct sequence is ABBA. Hence, [1].

58 .

'Intercept' (A) means to overhear or see, or to interrupt or catch something. 'Intercede' (B) means to intervene or mediate. Hence (A). 'Annihilated' (A) means completely destroyed. 'Insinuated' (B) means suggested something. Hence (A). 'Sensationalism' (A) means doing or showing something in such a manner as to cause intense public excitement and debate. 'Sensitization' (B) means the act of making someone sensitive to something. Hence (A). 'Redundant' (A) means superfluous. 'Regressive' (B) means orthodox in character. Hence (B). Thus the correct sequence is AAAB. Hence, [5].

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59 .

[1], [2], [4] and [5] are correct. [3] is incorrect since 'brand' is not the term used to describe a group of people; it makes no sense. Hence, [3].

60 .

[1], [2], [3] and [4] are correct. [5] is wrong because the sentence becomes thoroughly contradictory and absurd if we use 'race'. To 'race' to some place implies running fast. It cannot be done 'slowly and casually'. Hence, [5].

61 .

[1], [2], [3] and [5] are correct. [4] is wrong. 'Breakthrough' is one word; it means overcoming or surpassing a particular obstacle or problem. 'Break through', on the other hand, means to force into or to divide, separate or pierce through something. Hence, [4].

62 .

In [1], 'snap' means to break with a sharp sound; in [3], it means to speak sharply or angrily; in [4] it means a short spell. The phrasal verb 'snap up' means to buy or seize quickly. But in [5], 'snap' is incorrectly used – the correct word here should be 'snippet' (a small part). Hence, [5].

63 .

[1] is inconsistent with the intention of the sentence. Such a terrible incident cannot be described as 'spectacular'. [2] has an emotional appeal rather than a rational one. 'Frightening' is vague. Moreover, 'more unimaginable' is absurd usage, because 'unimaginable' is an unquantifiable term. In [3], though 'repulsive' fits in well, 'direct' looks out of place. 'The attacks were more direct' conveys no exact meaning. [4] is correct. It conveys the nature of the carnage: 'gruesome', and gives an idea of the gravity of the act: 'audacious'. 'More worldwide' in [5] is an incorrect term because 'worldwide' is in itself a term which conveys maximum or all-round coverage. Also, 'embarrassing' and 'worldwide' do not fit together into a logical statement. Hence, [4].

64 .

In option [1] 'considerable' fits well. But 'acclaimed' which means held in high esteem or regard, does not convey any additional meaning here, though it is praiseworthy to be the First Citizen. [2] is correct. 'Exemplary' means worthy of setting an example. The position is 'honourable' meaning one that commands deep respect. It conveys the positive tone of the sen tence very well. In [3 ], 'little' h ard work is contradictory and deprecates the efforts of the First Citizen. 'Talented' position does not make sense. 'Consistent' in [4] is fine. 'Honorary position' means a position for which one does not receive any monetary compensation or remuneration. There is nothing very positive about an 'honorary' position. 'Exuberant' in [5] means high-spirited or lively. Thus 'lively hard work' is absurd. 'Enviable' means something that can cause envy. Hence, [2].

65.

[1] is correct. 'Senseless' violence fits in well. Moral 'turpitude' means depravity or decadence. The two words together form a logical sentence and a coherent link. In [2], 'blatant' which means unashamed, may be acceptable, but 'vapidity' which means dullness, makes no sense. In [3], 'concentrated' violence can be used to mean a high recurrence of violence in a particular place. However, 'moral control' runs contradictory to the tone of the statement which clearly criticizes the situation of the world today. ‘High-level violence’ makes

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C A T 2 0 0 9 no sense, so [4] can be negated. 'Omnipresent' means prevalent everywhere. It can be used here. But a 'lack of moral ability' is absurd. Hence, [1]. 66 .

67 .

68 .

69.

[1] is correct. 'Stance' means position, and here it means the opinion of the USA. 'Disinterested' means having an unbiased, third-party outlook. Thus this sentence implies that the USA has changed its opinion on Indo-Pak conflicts from an unbiased, impartial one to one of conditional approval of India's stand. In [2], 'disinterested' is correct. 'Take' also means opinion, but in an informal, casual way. Here, the sentence talks of the US opinion on the Indo-Pak conflict, which is a serious, international issue, and thus 'take' cannot be used here. 'Opinion' in [3] is fine, and so is 'stance' in [4]. But 'uninterested' which means a lack of interest in something, does not logically link with 'impartial' since the sentence is trying to emphasize that the stand of the US was an unbiased one earlier. 'Take' an d ‘u nin terested’ in [5 ] as mentioned in [2] and [4] cannot be used in the sentence. Hence, [1]. The paragraph focuses on Indian art movies and points out the ways in which these art movies differ from popular films. The last sentence of the paragraph discuses how artistic filmmakers differ significantly from their counterparts in popular cinema. So it is likely that the next sentence will dwell on the aspect of filmmakers of this artistic genre. Only options [1] and [5] mention artistic filmmakers. But [1] focuses on only one such filmmaker, Satyajit Ray, and thus begins a new theme. On the other hand, [5] continues the existing theme by mentioning one more characteristic of artistic filmmakers. The rest of the options fail to discuss ‘artistic filmmakers’, but focus on unrelated issues such as popular cinema and its treatment and techniques. Hence, [5]. The paragraph discusses the importance as well as the difficulties of managing coastal and ocean areas. Citing Brazil and the UK as examples, it discusses the difficulties due to the levels of jurisdiction. Only op tion [2] con clu des the paragrap h logically by discussing the 'fragmentation of responsibility' that makes managing coastal and ocean areas a big challenge. Wh ile op tion [2] an swers th e question, 'wh y is management of coastal and ocean resources so difficult?', options [1], [3], [4] and [5] provide answers to how we can manage coastal and ocean resources better. Hence, [2]. The last sentence of the paragraph offers a clue to completing the theme appropriately. The last sentence mentions that science has advanced in the direction of 'decoding the human genome' and has studied 'geneenvironment interactions' which explore the biological basis of character traits, including the propensity to commit crimes. Hence, it is likely that the next sentence will discuss how nature and not nurture determines the propensity to commit crimes. Only [1] discusses this aspect, while [5] says the exact opposite. Options [2], [3] and [4] can be eliminated since they do not logically complete the theme. Hence, [1].

70 .

The paragraph discusses the frustration felt by individuals on a weight loss program after they seem to have hit a plateau It further tries to analyse the cause for it and the paragraph concludes with a question, focusing on calorie intake. The sentence following it must thus attempt to answer the question posed in the concluding line of the paragraph, i.e., whether one may be eating more calories than one thinks. Only option [3] focuses on the aspect of calorie intake and discusses how people miscalculate their calorie intake, hence leading to an inaccurate assessment of how much they eat. Options [1], [2], [4] and [5] can be eliminated since none of them discuss calorie intake; instead they focus on issues such as exercise and metabolism, both of which do not answer the question. Hence, [3].

71 .

Refer to the last two paragraphs, where the author discusses the failings of the Maya kings and nobles. Options [1], [2] and [5] are stated in the list of ch aracteristics of th e k in gs and n ob les in the penultimate paragraph. [3] is also stated in the same, and it can also be inferred from the example of Maya kings building temples, given the last paragraph. However, [4] is mentioned in context of the Easter Island chiefs, not Maya kings, so it cannot be said to be a failing of the latter. Hence, [4].

72 .

Refer to paragraph 3, the second sentence, where the quoted word occurs. According to the author, warfare was 'already endemic' among the Maya, after which it 'peaked'. This implies that warfare was already present to a certain degree. So [2] can be ruled out, as can [1], as 'taboo' means something forbidden. The word 'endemic' means prevalent in or characteristic of a particular society. So [3] can also be ruled to. Between [4] and [5], [4] is a better answer, as 'endemic' does not necessarily imply something 'extraordinary'. Hence, [4].

73 .

Options [2] and [5] are mentioned in paragraph 2 as the first and second strands respectively. [1] is the third strand, as stated in paragraph 3, and [4] the fifth strand, given in paragraph 4. But [3] does not correctly state the fourth strand: according to the author, the Maya had lived through droughts before, but the one that led to the collapse was the most severe. So, [3], which states that the Maya had never dealt with a drought before, is incorrect. Hence, [3].

74 .

Refer to the third paragraph. Options [1] and [4] reverse the cause-effect relationship mentioned in the passage: the high population density and decrease in resources were the cause of the warfare, not its result. [2] is completely incorrect: the author mentions no relationship between the warfare and the drought. [3] is only partially correct, as it fails to mention how the no-man's lands affected agriculture. This link is explicitly stated only in [5]. Hence, [5].

75 .

According to the third paragraph, the Maya population was 'at least five million people, perhaps many more', and there is no indication that this was the peak, so [1] cannot be inferred. Though the author draws a parallel between the conspicuous consumption

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of the Maya nobles and that of modern American CEOs, he does not imply that the latter are consciously imitating the former, so [2] is wrong. [5] is completely false, as the passage mentions Rwanda and Haiti only as places facing population problems similar to those faced by the Maya, not as the location of the Maya civilization. [4] is neither stated in the passage, nor can it be inferred. However, [3] is true: refer the the last sentence of the first paragraph. Hence, [3]. 76 .

Refer to paragraph 5, where this phrase occurs. The author is discussing those people who allow their children to have two ice-creams cones at once, thereby allowing them to indulge in excess and showing off their nonexistent wealth (since the two cones were priced the same as one pie). Options [3] and [5] are only partially correct, since they fail to mention that the showingoff was of fictitious, not real, wealth. [1] is too general, and does not capture the essence of the quoted statement. [4] is completely out of context. Only [2] correctly captures the meaning of the phrase. Hence, [2].

77 .

Refer to the last sentence of the passage: '... today's morality wants all of us to be Sybarites'. A Sybarite is a person devoted to pleasure. Similarly, a 'voluptuous' person is one who indulges in pleasures of the senses. 'Voluminous' (large), 'voluble' (talkative), 'volatile' (changeable) and 'voluntary' (of free will) make no sense in this context. Hence, [1].

78 .

Refer to paragraph 4: the author says that '... neither mathematics nor economy nor dietetics justified this refusal. Nor did hygiene ...'. So options [1], [4] and [5] are wrong. [3] was the reason stated by the elders, but the author suspects that it was not the real reason - which is given in paragraph 5: '... two ice creams suggested excess ...' and 'looked indecent'. Therefore, only [2] is the real reason. Hence, [2].

79 .

A 'liturgy' is a ritual or rite of worship. In paragraph 3, the author describes in detail how the children who got two cones ate them. This process seems to him almost like a ritual or a 'liturgy'. While [1], [3] and [4] are also true about this process, they have nothing to do with the word 'liturgy'. [5] cannot be inferred. Hence, [2].

80 .

81 .

Refer to paragraph 5, the first sentence - the author contrasts today's society with that of the thirties. Since until that point in the passage he has been talking about his childhood, we can infer that he was a child in the thirties. Option [3] can be inferred from the same sentence. [2] can be inferred from the examples of the radio and car in the last paragraph. [4] is inferable from the first paragraph. But [5] cannot be inferred, since the author does not compare the amount of ice-cream in the cones with that in the pie. Hence, [5].

and the dissemination of the ideas. Both these points are covered only in option [2]. [3] mentions only the first point, whereas [4] and [5] include only the second on. [1] is an incorrect reading, as it seems to imply that the record, not the ideas, would be disseminated. Hence, [2]. 82 .

Refer to the last line of the first paragraph, where the word 'springboard' occurs. Both options [1] and [2] can be immediately rejected, since it is clear that there is no comparison (i.e., an 'analogy') being drawn to anything. [5] is what 'semantic systems' refers to, and has no relevance to th e word 'springboard'. Metaphorically speaking, a 'springboard' is something that provides an impetus or push to get an activity started. In this case, semantic systems are a 'springboard' for 'further exploration', so the word cannot refer to the exploration itself (as in [3]). Only [4] gives the correct interpretation. Hence, [4].

83 .

Refer to the last paragraph: 'As an art movement slips ... possibilities of his own time.' [4] is incorrect, as it uses the word 'fossil' in its scientific, not metaphorical, sense. Similarly, [5] too is incorrect in stating that a fossilized art movement would be of interest to a scientist (as opposed to an artist). [3] completely contradicts the passage - even if the movement is a fossil, it remains useful and interesting. Between [1] and [2], the former is a better answer, as it explains how an art movement can still be useful after it is 'dead'. Hence, [1].

84 .

Refer to the middle of the first paragraph, where Surrealism is discussed. According to the author, 'not all movements were exclusively concerned with innovation', and Surrealism was one such movement. However, we cannot infer that it was not concerned with innovation at all, so [1] is wrong. [2] is an over-generalization, since only one specific example of Surrealist art - a photograph by Atget - is said to be 'mysterious'. The example of the photograph also shows that [5] is wrong. Since the passage deals mainly with twentieth century art, [3] is most likely wrong. According to the author, Surrealism can provide insight into art of any time period, so [4] is inferable. Hence, [4].

85 .

Refer to paragraph 1, the second and third sentences. The author begins by stating that it is possible to see a pattern emerging in (or to impose one upon) art similar to that which exists in science. However, he qualifies this by adding that in this case this pattern can be misleading. This point is present only in option [3]. [4] is incomplete, as it paraphrases only the second sentence. Both [2] and [5] misinterpret the passage, while [1] cannot be inferred from the data given. Hence, [3].

86 .

[1] is incorrect because it expresses uncertainty and debate about whether language is a cultural artifact or a biological adaptation, though the passage clearly opines that language is a biological adaptation and NOT a cultural artifact. [2] looks close, but the passage does not speak about HOW language is an instinctive ability, rather it explains the reasons WHY it is so.

Refer to the first paragraph: 'The ideas generated by these chance meetings ... from their generation.' The twofold consequences mentioned here include a 'corpus of work' which remains a 'record of the events',

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C A T 2 0 0 9 Thus [2] is incorrect. [3] is correct. The passage puts forth the reasons for language being an instinctive ability of mankind. Thus the 'instinctive nature of language' is being discussed here. The fact that the author seeks to 'invert' popular wisdom which believes that language is a learned ability is correct, but it does not form the central theme of the passage and thus [4] cannot be a title for the passage. Once again, though the similarity between species as regards their unique abilities is discussed in the passage, this does not form the central theme of the passage. Hence [5] is incorrect. Hence, [3]. 87 .

88 .

[1] cannot be inferred: nowhere in the passage is it mentioned that man's unique ability of language places him at the pinnacle of existence. [2] is totally contradictory to the passage, which draws a comparison between man and other species by saying that the ability of mankind to use language is instinctive just like the unique abilities of other species. [3] is contradictory to the meaning of the passage and is also inconsistent with itself. The passage DOES state that the ability of humans for voice modulation is indeed unique. [4] is incorrect, because the inference drawn is wrong. Man's ability to use language is indeed unique according to the passage, but other species too have same unique abilities. So, it does not mean that man stands on higher ground compared to other species. [5] is correct. It perfectly describes the intention of the author while he compares the abilities of humans and other species. The passage clearly states that since other species too possess certain unique abilities just as human beings do, this uniqueness is not exclusive to mankind. Hence, [5]. [1] is contradictory to the views expressed in the passage, which states that like the abilities of humans, the abilities of other species too are ingrained in them, not necessarily acquired. But [1] says that spiders learn to spin webs as they grow, which is wrong. [2] is correct in its essentials, but fails to provide a precise answer to the question which asks us to define the relationship between spiders spinning webs and the human instinct for language. [3] is correct. It overcomes the inadequacies of [2]. It provides us a clear, factual relationship between spiders spinning webs and the human instinct for language as is expressed by the author, and thus answers the question very precisely. [4] is totally contradictory. It is emphasized by the author that the human ability for language is instinctive in nature and not necessarily a product of formal training. [5] is wrong. The author clearly states that there is a difference between 'webs and words', meaning the act of spinning webs and language. Thus the former is NOT a perfectly comparable example to the latter. Hence, [3].

89 .

[1] is wrong because it is out of context and unverifiable. Nowhere does the author mention that formal education reduces a child's linguistic ability. [2] is inconsistent with and contradictory to the theme of the passage, which actually explains that formal education is not necessary for the development of linguistic abilities in children. [3] is out of context and unverifiable. Nothing is said about the 'complementary role' that can be played by formal training to instinctive ability. Similarly, in [4], nothing is mentioned about formal teaching having to play a 'secondary role' either. [5] is correct. It properly explain s the quote, by invalidating the gen erally accepted notion that formal education is necessary for the development of language in humans. It identifies the presence of natural instinct as a far more effective factor than training. Hence, [5].

90 .

Refer to the second paragraph. According to the author, humans are not unique in having a unique ability (i.e., the ability to use language), other animals have unique abilities of their own too. To illustrate this, he gives the example of bats using Doppler sonar. So an example that could replace this has to feature a unique ability of a particular animal. This rules out [1], which is not an ability at all, but a reproductive characteristic of the platypus. The ability mentioned in [3] is not unique, but rather the method used is, so it is not a perfect example. [5] is too negative, as it mentions an ability that dogs lack as well as one they have. [4] focuses on the human inability rather than the animal ability. Only [2] mentions a suitably unique animal ability. Hence, [2].

A n s we r Key SECTION I 1-3 2-5 7-5 8-2 13-3 14-3 19-1 20-1 25-3

3-3 9-1 15-2 21-3

4-2 10-1 16-4 22-3

5-5 11-1 17-3 23-2

6-1 12-1 18-2 24-4

SECTION II 26-4 27-1 32-3 33-2 38-1 39-4 44-3 45-5 50-4

28-4 34-4 40-4 46-2

29-3 35-4 41-4 47-4

30-5 36-5 42-1 48-5

31-3 37-3 43-4 49-2

53-1 59-3 65-1 71-4 77-1 83-1 89-5

54-2 60-5 66-1 72-4 78-2 84-4 90-2

55-5 61-4 67-5 73-3 79-2 85-3

56-5 62-5 68-2 74-5 80-5 86-3

SECTION III 51-3 52-2 57-1 58-5 63-4 64-2 69-1 70-3 75-3 76-2 81-2 82-4 87-5 88-3

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