Exam Reports3

8/3/2019 Exam Reports3

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Group Question

Answer the following questions based on the information given below.

A consulting firm carried out a perception mapping exercise for 15 companies andplotted the results as shown below. The perception mapping was done on the basis of two parameters : the trust of products (made by each company) among the customersand the popularity of the company among customers. The consulting firm plottedpopularity on the X-axis and trust on the Y-axis. Each company received a rating from10 to +10 for both the parameters. A rating of +10 was considered to be the highestwhile that of 10 was considered to be the lowest.

Each company was given the result and the consulting firm bagged the contract toimprove the ratings for these companies. To improve the ratings on each parameter, theconsulting firm charged each company as per the tariff structure shown in the tablebelow. It improved the performance of the company based on marketing needs andproduct manufacturing. To improve the trust ratings, the consulting firm suggested amechanism to improve the product while it suggested marketing ideas to improve thepopularity ratings of the company. The tariff worked on the mechanism of pills whereineach pill would improve a certain parameter for the company as shown below. For

example, a White Pill would cost the company Rs. 9 Lakhs and it would improve thepopularity rating of the company by 1 point but would decrease the trust rating of thecompany by 0.5 points.

Collapse All

Section I


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Based on historical data, the consulting firm identified the maximum success rate for each firm as shown by the graph below. Thus, even though a particular Pill couldtheoretically improve a rating up to a certain level, the actual improvement would beconstrained by the success rate shown in the graph below. For instance, if CompanyA took a White Pill then, at the most, the consulting firm could have improved thepopularity rating by 0.8 points (80% of 1) but the trust rating would still go down by 0.5points. Also, the amount charged would still be the same though for all the companies for that pill.

Answer the questions below based on the data given above.

1.3 Marks

What is the maximum percentage increase in the popularity rating of Company E if it takes 2 White Pills and 1 Blue Pill?

1) 37.5%

2) 60%

3) 41.67%

4) 33.33%

Solution:The popularity rating of Company E is currently at 6 points.

If Company E takes 2 Whilte Pills and 1 Blue Pill, its popularity rating canimprove by (2 1) + 0.5 = 2.5 points.


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However, the success rate for Company E is 90%

Therefore, the actual maximum increase in the popularity rating = 0.9 2.5 =2.25 points.

Therefore, the new popularity rating = 6 + 2.25 = 3.75

Therefore, the maximum percentage increase in the popularity rating

= [(6) (3.75)]/(6)} 100

= (2.25/6) 100

= 37.5% Hence, option 1.

2.3 Marks

What is the minimum number of pills that company K needs to take in order toexceed the position of Company C in both the popularity and trust ratings?

1) 8 Pills

2) 9 Pills

3) 10 Pills

4) 11 Pills

Solution:The current popularity and trust ratings of the two companies are as shown

below:

Company C is at 8 on Popularity and 2 on Trust.

Company K is at 9 on Popularity and 8 on Trust.

Since company K wants to overtake company C, the ratings of company Cneed to be static and the success rate of only company K need to beconsidered.

Also, since the number of pills is to be minimised, the pill chosen should besuch that it either improves ratings on both the parameters simutaneously or does not negatively impact the rating on any parameter.

Therefore, company K needs to take either Black, Red or Blue pills.

Now, note that the success rate for company K is 80%.

Also, company K needs more than 6 points on Trust and more than 1 point onPopularity to exceed Company C.


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Therefore, it should take a pill that gives it maximum improvement on the trustrating.

Since a Black Pill does not provide any improvement on trust, company K canonly take a Blue or Red pill to improve Trust.

Company K would require 8 Red Pills to exceed company C on trust i.e 8 0.8 1 = 6.4 points.

However, there would be no inprovement in the popularity ratings.

Now, it would need 2 Blue pills to exceed company C on popularity i.e. 2 0.8 1 = 1.6 points.

Thus, in such a case, company K would need a minimum of 10 pills.

Hence, option 3.

Note: There is a combination where the number of pills required is 9 (7 Red +

1 Blue + 1 Black) but in this case, the trust rating improves by exactly 6 pointsand becomes equal to that of company C. Since the question requirescompany K to exceed company C, the trust rating has to improve by morethan 6 points. Had the question asked for minimum number of pills to ensurethat company K is not inferior to company C on any parameter, we couldhave taken the minimum number of pills as 9.

3.3 Marks

Which of the following statements is definitely true?

I. Both L and J can take 2 White Pills each.II. M needs at least 4 pills to exceed the position of A in both the parameters.

III. The cost incurred by F to exceed B on Trust is less than Rs. 25 Lakhs.

1) I and II only

2) II only

3) III only

4) II and III only

Solution:Consider Statement I:

The popularity and trust rating of company L is 3 and 9 respectively.

Also, its success rate is 75%.

Therefore, if it takes 2 White Pills, its popularity rating would improve by 2 1 0.75 i.e. 1.5 points, while its trust rating would go down by 2 0.5 0.75 i.e.0.75 points.


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Therefore, the new popularity and trust ratings for company L would be 4.5 and8.25, which are both valid values.

The popularity and trust rating of company J is 9 and 5 respectively.

Also, its success rate is 70%.

Therefore, if it takes 2 White Pills, its popularity rating would improve by 2 1 0.7 i.e. 1.4 points, while its trust rating would go down by 2 0.5 0.7 i.e.0.7 points.

Therefore, the new popularity and trust ratings for company J would be 10.4and 5.7.

However, the maximum rating that a company have is +10.

Therefore, company J cannot take 2 White Pills.

Therefore, statement I is false.

Hence, option 1 can be eliminated.

Consider Statement II:

The popularity and trust ratings for M are 8 and 5 respectively while thecorresponding ratings for company A are 7 and 7 respectively.

Thus, M needs to gain more than 2 points on trust and more than 1 point onpopularity.

The success rate of M is 85%.

Thus, it has to take a minimum of 1 Black Pill, 2 Red Pills and 1 Blue Pill toovertake A on both parameters.

Thus, M needs atleast 4 pills to exceed the position of A on both parameters.

Hence, statement II is definitely true.


Consider Statement III:

The trust ratings for F and B are 7 and 5 respectively.

Thus, F need to improve by more than 2 points.

The success rate of F is 80%

To improve the trust ratings, F can use either the Yellow Pills or the Red Pills.


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owever, e e ow s are c eaper an so ey are use .

F will need 3 Yellow pills and the cost of the same would be 3 7 = Rs. 21lakhs.

However, if the Red Pills are used, the cost is 3 12 = Rs. 36 lakhs.

Thus, the cost incurred by F to exceed B on the trust ratings is not necessarilyless than Rs. 25 lakhs. Note that the statement does not mention minimumcost. Had it mentioned minimum cost, statement III would be definitely true. Inthe given scenario, statement III may or may not be true.

Hence, only statement II is definitely true.

Hence, option 2.

4.3 Marks

Each question is followed by two statements, A and B. Select the correct optionbased on the following instructions:

Mark (1) if the question can be answered by one of the statements, but not by theother.Mark (2) if the question can be answered by using either statement, independentlyof the other.Mark (3) if the question can be answered by using both statements together, but notby either statement alone.Mark (4) if the question cannot be answered by either of the statements.

Find the number of factors of N 2 if N is a natural number.

A. N has 12 factors.

B. N 3 has 70 factors.

1) 1

2) 2

3) 3

4) 4

Solution:We know that if a number X = p a qb r c , where p , q and r are prime numbers, thennumber of divisors of X are ( a + 1)(b + 1)(c + 1)

Using statement A alone:

N has 12 factors so N is of the form p 11 or p 5q or p 3q2 or p 2qr .

All the four cases will give different values for the number of factors of N 2.

Thus, the question cannot be answered using statement A alone.


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or n = , we ge a = . ence, e seven num ers w e , , , , ,and 85. Since, this set contains two prime numbers (79 and 83), it is not a feasiblesolution set.

For n =183, we get a = 92. Hence, the seven numbers will be 89, 90, 91, 92, 93, 94and 95. Since, this set contains only one prime number i.e. 89; it is a feasiblesolution set.

For n =281, we get a = 141. Hence, the seven numbers will be 138, 139, 140, 141,142, 143 and 144. Since, this set contains only one prime i.e. 139; it may be afeasible solution set.

But, since we need two multiples of five in the given series, n = 281 will not be apossible value.

Hence, option 3.

6.3 Marks

D and E are the midpoints of sides CA and CB respectively of an isosceles righttriangle ABC, right angled at A. If F is a point on DE in the interior of ABC such that BA= BF, then what is the value of m FCB?

1) 10

2) 15

3) 20

4) 30

Solution:


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Here, ABC is an isosceles right angled triangle with BA = AC

BC 2 = 2BA2

E is the midpoint of BC.

BCF ~ BFE

m BEF = m BFC = 135

Using sine rule in BFE, we can write,

m BFE = 30

And by similarity, m FCB = m BFE = 30

Hence, option 4.

7.3 Marks What is the area of the quadrilateral formed by the solution set of the inequations 5 x

+ 7y 42, x 0, y 0 and x 5?

1) 19 sq. units

2) 18.4 sq. units

3) 25.6 sq. units

4) 21 sq. units

Solution:The region formed by using the given inequations is


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By solving equations 5 x + 7y = 42, x = 0, y = 0 and x = 5, we get the intersectionpoints.

We can figure out that the shaded region is a trapezium.

The lengths of the parallel sides are 6 and 2.4 and the height is equal to 5 units.

= 21

The required area is 21 sq. units.

Hence, option 4.

Group Question


The following charts show the total quantity of paddy production (in Million tonnes), its


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.India over the period 2002-03 to 2008-09.

8.3 Marks

What is the per capita value of production in the year 2005-06?

1) Rs. 470

2) Rs. 250

3) Rs. 240

4) Rs. 390

Solution:Per capita value of production in a year = Annual per capita production for that year Per kg value of production for that year


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e per g va ue o pro uc on n e year - = 10 6 10 3) = Rs. 2.5

Therefore, per capita value of production = 2.5 188 = Rs. 470

Hence, option 1.

9.3 Marks

What is the percentage increase in the population of the given state from

2003-04 to 2004-05?

1) 3.26%

2) 3.7%

3) 3.1%

4) Cannot be determined

Solution:

Percentage increase in population = {[(77.77 75) 107

]/(75 107

)} 100= 3.68%

Hence, option 2.

10.3 Marks

Each question is followed by two statements, A and B. Select the correct optionbased on the following instructions:

Mark (1) if the question can be answered by one of the statements, but not by theother.Mark (2) if the question can be answered by using either statement, independentlyof the other.Mark (3) if the question can be answered by using both statements together, but notby either statement alone.Mark (4) if the question cannot be answered by either of the statements.

The HCF of three numbers, x , y and z is 13 while their product is 21970. What is thevalue of x + y + z ?

A. One of the numbers is less than the other two.


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. .

1) 1

2) 2

3) 3

4) 4

Solution:It is given that the HCF of the numbers x , y and z is 13.

We can say that x = 13 a , y = 13 b and z = 13 c , for some natural numbers a, band c .

xyz = 21970

13 a 13 b 13 c = 21970

abc = 10

The possible values for a , b , and c are 1, 2 and 5 or 1, 1 and 10 (in any order).

The possible values for x , y , and z are 13, 26 and 65 or 13, 13, 130 (again, in anyorder).

Using statement A alone:

One of the numbers is less than the other two.

Therefore, the least number has to be unique.

The numbers cannot be 13, 13 and 130.

The numbers are 13, 26 and 65.

The sum of the numbers is 13 + 26 + 65 = 104

Thus, the question can be answered using statement A alone.

Using statement B alone:

One of the numbers is greater than the other two. |

Therefore, the greatest number has to be unique.

This is true for both the sets obtained earlier.

Therefore, a unique pair of values of x , y and z cannot be found.


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, .

Thus, the question can be answered using statement A alone but not by usingstatement B alone.

Thus, the question can be answered by using one of the statements but not by theother.

Hence, option 1.

11.3 Marks Given a function f defined as f ( x ) = 7 x + 4, what is the value of a b if f (f (f ( x ))) = ax +

b?

1) 78204

2) 78402

3) 68204

4) 68402

Solution:As f ( x ) = 7 x + 4, f (f ( x )) = 7(7 x + 4) + 4 = 49 x + 32

f (f (f ( x ))) = 7(49 x + 32) + 4 = 343 x + 228

a = 343 and b = 228

a b = 78204

Hence, option 1.

12.3 Marks a , b and c are positive numbers. a + b is 60% of a + b + c and ab is 320% more

than a + b + c . Then minimum value of ( a + b + c ) is?

1) 45

2)

3) 46.664) Cannot be determined

Solution:Without loss of generality we can assume that,

a + b + c = x

a + b = 0.6 x and, c = 0.4 x


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Similarly, ab = 4.2 x

Now, ab /(a + b) = 4.2 x /0.6 x = 7

ab 196

Now, for a + b to be minimum, ab = 196 and a = b .

For minimum a + b ,

a 2 = 196

a = 14 (As a , b and c are positive numbers)

Hence, the minimum value of ( a + b) is, 14 + 14 = 28

Now, as a + b is directly proportional to a + b + c , hence, ( a + b + c ) will be minimumif (a + b) is minimum.

Hence, minimum value of ( a + b + c ) = 1/{0.6( a + b)} = (1/0.6) 28 = 46.66

Hence, option 3.

Group Question


The leading automobile dealer from Central India had the dealership for all vehicles of Tata, Mahindra, Maruti, Ford, Nissan and Hyundai.

The table below shows the revenue earned by the dealer from each of these brands as apercentage of the total revenue earned by him in the year 2008.

On analyzing the sales pattern for all these brands, the dealer found that for four brandsviz. Tata, Mahindra, Nissan and Hyundai, 2 nd sales played a significant role.

The revenue generated from 2 nd sales for a brand as a percentage of the totalrevenue earned for that brand was as follows:


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13.3 Marks

What was the total revenue earned by the dealer from 2 nd sales in 2008 as apercentage of the total revenue earned by the dealer in that year?

1) 30.5

2) 35.5

3) 33.5

4) 27.5

Solution:

Let the total revenue earned by the dealer in the year 2008 be 100.

Total revenue generated from Tata (15% of total) will be 15.

and the revenue generated from the 2 nd sales of Tata will be 20% of 15 i.e. 3.

Balance revenue can be calculated as (Total Revenue 2 nd SalesRevenue).

Balance revenue for Tata will be 15 3 = 12

Similarly, the 2nd

sales revenue (and the balance revenue) for the other threebrands can also be calculated as shown in the table above.

From the table, the total revenue earned by the dealer in 2008 from 2 nd sales= 3 + 10 + 6.5 + 11 = 30.5

Therefore, the required percentage = (30.5/100) 100 = 30.5%

Hence, option 1.

14. Which of the followin statements are definitel true?


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3 Marks

I. The total revenue generated from 2 nd sales was less than thetotal revenue generated from Mahindra.

II. The total revenue generated from sales of Nissan in which 2 nd sales did not play anypart was 17.5% of the total revenue generated through the sales of Hyundai in 2008.

III . The percentage point difference between total revenue generated through 2 nd salesin 2008 and the revenue generated from the total sales of Maruti was 20.5%.

IV. The total revenue generated from the sales of Hyundai vehicles which were not from

2nd sales was 40% of the revenue generated from the total sales of Mahindravehicles.

1) I only

2) II only

3) Exactly one out of III and IV

4) More than one statement is true

Solution:Consider the total sales, break-up of 2 nd sales and of balance sales obtainedin the solution to the first question.

Consider statement I:

Total revenue from Mahindra = 25

The total revenue from 2 nd sales = 30.5

Total revenue generated from 2 nd sales > Total revenue generated fromMahindra.

Statement I is not true.


Consider statement II:

The first part of this statement refers to the balance revenue generated from

Nissan.

Balance revenue generated from Nissan = 3.5

Total revenue generated from the sales of Hyundai = 20

The required percentage = (3.5/20) 100 = 17.5

Statement II is definitely true.

Since option IV mentions More than one statement is true, statements III and


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IV need to be checked.

Consider statement III:

Total revenue generated through 2 nd sales in 2008 was 30.5% of the overalltotal sales and the total revenue generated from the sales of Maruti is 17% of the overall total sales

The percentage point difference between the two is 30.5 17 = 13.5%

Statement III is not true.

Consider statement IV:

The first part of this statement refers to the balance revenue generated fromHyundai.

Balance revenue from Hyundai = 9

The total revenue generated from the sales of Mahindra vehicles = 25

The required percentage = (9/25) 100 = 36%.

Statement IV is not true.

Only statement II is definitely true.

Hence, option 2.

15.3 Marks

Following pie-chart shows the percentage distribution of Mr. As investments whilepie chart below it shows the percentage distribution of Mr. As return from theseinvestments.


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If Mr. A decreases his investment in E by 50% then the return from B is what percentof the total return.

Assume Return is directly proportional to the investment.

1) 15%

2) 16.66%

3) 22.5%


Solution:Without loss of generality we can assume that Mr. A invested Rs. 100 and got areturn of Rs. 100.

Now, he gets Rs. 20 after investing Rs. 30 in E.

Hence, if he decreases his investment in E by 50% then his return will be halved i.e.Rs. 10

Hence, his total return will be,

20 + 15 + 15 + 30 + 10 = Rs. 90

Hence, the return from B is 15/90 100 = 16.66%

Hence, option 2.

16.3 Marks The argument, , of a complex number, z = x + i y , where i 2 = 1, is defined as tan

1(y / x ).


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What is the argument of z 2, if the argument of z is given as 22.5.

1) 22.5

2) 45

3) 90

4) None of these

Solution:z = x + i y

z 2 = ( x + i y )2 = x 2 y 2 + 2 ixy

Argument of z 2 = tan 1 (2 xy /( x 2 y 2))

= tan 1 (2(y / x )/ (1 ( y / x )2)

But it is given that the argument of z is 22.5

y / x = tan 22.5

Argument of z 2 = tan 1 (2 tan 22.5/(1 tan 2 22.5))

= tan 1 (tan (2 22.5))

= tan 1 (tan 45) = 45

Hence, option 2.

Alternatively ,

Let, z = a (cos + i sin ), where a is magnitude of z and is argument of z .

Now, by de Moivre's formula,

z 2

= a2(cos 2 + i sin 2 )

Hence, argument of z 2 = 2 = 2 22.5 = 45

Hence, option 2.

17.3 Marks In the figure given below, ABCD is a square with side R units. Sector B-AC is a

quarter of a circle. Point O, which is the centre of the smaller circle lies on thediagonal BD of the square. The line segment PQ makes equal intercepts on thesides AD and CD. What is the area of the shaded region in square units?


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1)

2)

3)

4) None of the above

Solution:

Side of square ABCD = R


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Radius BE = R

Let radius of the smaller circle be r units.

Now, BD = BE + EO + OD

Hence, option 4.

18.3 Marks (a , b) is an ordered pair of positive integers such that a + b = 211. a leaves a

remainder of 2 when divided by 7 and b leaves a remainder of 3 when divided by9. What is the sum of all possible values of a ?

1) 298

2) 300

3) 302

4) 288

Solution:a leaves remainder of 2 when divided by 7.

Let a = 7 x + 2, where x is a positive integer.

b = 211 7 x 2 = 209 7 x


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Now, as b leaves a remainder of 3 when divided by 9,

209 7 x should leave a remainder of 3 when divided by 9 or in other words itshould leave a remainder of 6 when divided by 9.

209 leaves a remainder of 2 when divided by 9. Hence 7 x should leave a remainder of 8 when divided by 9.

Values of x for which 7 x leaves a remainder of 8 are,

5, 14, 23, 32 ...

But 7 32 > 211

Possible values of x are 5, 14, 23.

Corresponding values of a for x = 5, 14, 23, are a = 37, 100, 163

Sum of all possible values of a = (37 + 100 + 163) = 300

Hence, option 2.

19.3 Marks

Rashmi buys a vessel made by joining a cylinder (hollow and open at both ends) and ahollow hemisphere such that the cylindrical part fits above the hemispherical part.She fills the vessel to the brim with water. The depth of the entire vessel is 15 cm.Ravish accidently drops 50 spherical marbles, each of radius 1 cm, into the vessel,due to which some amount of water spills out. What is the approximate ratio of thevolume of water that is spilled out to the total volume of water originally contained inthe vessel if the diameter of the base of the cylinder is 12 cm?

1)

2)

3)

4)

Solution:Let R and r be the radii of the cylinder and a spherical marble respectively and h bethe depth of the entire vessel.

The height of the cylinder = h R = 15 6 = 9 cm

The radius of the hemisphere = R = 6 cm


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Total volume of the container = Volume of the cylinder + Volume of the hemisphere

Hence, option 3.

20.3 Marks

Quadrilateral ABCD is a rhombus with side of length c . BD is the shorter diagonal.The median AE of ABC is drawn on side BC from point A. EF is drawnperpendicular to AC at point F. If the area of AEF = a , then what is the ratio of AC

to BD in terms of a and c ?

1)

2)

3)

4)

Solution:Let O be the point of intersection of BD and AC.

BD AC


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Let (BD) = q and (AC) = p

From the given diagram, consider AEF,

EF AC

EF || BD

Now, E is midpoint of BC. Hence,

Hence EF = (1/4) q

and AF = (3/4) AC = (3/4) p

A(AEF) = 1/2 AF EF

a = (1/2) (3/4) p (1/4) q

Hence, p q = (32/3) a = a (say)

Now, ( p /2)2 + (q/2)2 = c 2

p 2 + q2 = 4c 2

( p + q)2 = 4c 2 + 2 pq

( p + q)2 = 4c 2 +2a

and similarly,

( p q)2 = 4c 2 2 a


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Applying componendo-dividendo,

Hence, option 1.

21.3 Marks

A, B and C start playing a match-stick game with a total of 50 sticks distributedamong themselves, with each having a natural number of match-sticks. As per thegame, A starts by distributing match-sticks to B and C such that the number of stickswith B and C doubles respectively. A continues to do so for 4 rounds, after whichshe has only 2 sticks left and can no longer distribute to keep up the doubling trend

for both B and C. If ( b , c ) represents the possible number of match-sticks that B andC could have at the beginning of the game, then how many combinations of ( b , c )are possible?

1) 1

2) 2

3) 3

4) More than 3

Solution:Let the number of match-sticks with A, B and C initially be a , b and c respectively.

After the 1 st round, B and Cs match-sticks double to 2 b and 2 c respectively, whileAs match-sticks reduce to ( a b c ). Continuing similarly for the first 4 rounds, wehave,


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After 4 rounds, A is left with only 2 sticks. This means that B and C together had 50 2 = 48 sticks after 4 rounds

i.e. 16 b + 16 c = 48

b + c = 3

Possible values for ( b , c ) are (0, 3), (1, 2), (2, 1) and (3, 0).

However, as per the question, the players begin the game with a natural number of match-sticks; thus (0, 3) and (3, 0) are not valid values.

Hence, option 2.

22.3 Marks

1)

2)

3)

4)

Solution:Let P( x , y ) be a point on the line 3 x + 4y 9 = 0

The value of this distance will be minimum if the line joining point P( x , y ) and the

origin O(0, 0) is perpendicular to the line 3 x + 4y 9 = 0 at point P.The distance of a point Q( x 1, y 1) from the line Ax + By + C = 0 is given by,

This distance is the length of the perpendicular dropped from Q( x 1, y 1) to the line Ax + By + C = 0


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when divided by 6?

1) 12

2) 14

3) 15

4) None of these

Solution:f ( x ) = x 3 x + 7

f ( x ) = x ( x 2 1) + 7

f ( x ) = x ( x 1)( x + 1) + 7

For an integral value of x , x ( x 1)( x + 1) represents the product of three consecutivenumbers. Hence, x ( x 1)( x + 1) will be divisible by 6 for all integral values of x .

Hence we can assume that x ( x 1)( x + 1) = 6 k ...(where k is some integer)

Hence, f ( x ) = 6 k + 7 = 6( k + 1) +1

Hence f ( x ) will always leave a remainder of 1 when divided by 6.

Hence there are no such integral values of x for which f ( x ) leaves a remainder of 2when divided by 6.

Hence, option 4.

24.3 Marks

The shrewed owner of Gandhiyan rice bhandar, a no profit organization, wanted toearn some profit so that he could pay off his loans. His friend suggested him thefollowing tricks to do so. Which of the following options should he select to maximisehis profit?

A. Increase the selling price by 25%.

B. Increase the selling price by 14% and also cheat by selling 5% less.C. Add small white particles of sand equivalent to 30% of the weight of the rice and then claim

to sell it at the cost price.D. Weigh 900 gm instead of 1000 gm.

1) A

2) C

3) A or C

4 B or D


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Solution:Out of the ways suggested by his friend, he should use that way that gives himmaximum profit and discard those that yield him lesser profit.

Let the cost price of the rice be Rs. 100 for every 100 kg.

Option A:

S.P. = Rs. 125 for every 100 kg.

Profit = 25%

Option B:

S.P. = Rs.114 for 95 kg

C.P. of 95 kg = Rs. 95

Profit = 100 (114 95)/95 = 20%

Option C:

C.P. = Rs. 100 for 130 kg

S.P. = Rs. 130 for 130 kg

Profit = 30%

Option D:

C.P. is Rs. 90 for 90 kg.

S.P. = Rs. 100 for 90 kg.

Profit = 11.11%

Hence, option 2.

25.3 Marks A milkman adulterates milk using a mixture of water and a milk-like liquid, X. He hadtwo containers of equal capacity filled with milk that he had adulterated. He haddiluted the milk in the first container with a 40% concentrated solution of X in water.The milk in container 2 was mixed with a 30% concentrated solution of X inwater. He mixed the milk in the two containers into a bigger container. If the resultantmixture had 8% X and 16% water then the concentration of pure milk in the firstcontainer was:

1) 86%


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3) 84%


Solution:Without loss of generality we can assume that the volume of the final mixture is 100ml.

Hence the final mixture has 8% i.e. 8 ml of X, 16% i.e. 16 ml of water and 76% of milk i.e. 76 ml of milk. Thus we can say that the mixture has a 33.33% concentratedsolution of X in water. This is formed by mixing two solutions of X and water withconcentration 40% and 30% respectively.

Let w 1 be the volume of mixture with 40% concentration, and w 2 be the volume of mixture with 30% concentration.

Hence, w 1/w 2 = (33.33 30)/(40 33.33) = 1/2

Now, w 1 + w 2 = 24

Hence, w 1 = 8 ml and w 2 = 16 ml.

Hence, the first container has 8 ml mixture with 40% concentration.

Now, the first and second containers have equal capacities. Hence the firstcontainer has 50 ml of adulterated milk.

Hence, container 1 has 50 8 = 42 ml of pure milk.

Hence, concentration of pure milk in container 1 = 42/50 100 = 84%

Hence, option 3.

Group Question


In a Hit-the-Bulls-Eye competition, which consisted of five rounds; namely Round 1,Round 2 and so on , four players - Anushka, Rubina, Prateeksha and Anjali -participated in all the five rounds. The rounds consisted of firing 50 shots in two of therounds, 100 in two other rounds and 150 in one round, in any order.

Each shot that hits the target fetches the player one point.


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26.3 Marks

If, compared to Anjali, Anushka had hit the target more number of times in all

the rounds put together, then which of the following statement/s is/ arenecessarily true?

I. The maximum number of shots permiss ible in Round 3 was 50.II. The number of permissible shots in Round 1 is 150.

1) Only I

2) Only II

3) Both I and II

4) Neither I nor II

Solution:Let the number of shots fired by each person in rounds 1, 2, 3, 4 and 5 be a , b ,c , d and e respectively.

Anushkas conversion rate (percentage of shots that hit the target) for rounds1, 2, 3, 4 and 5 is 40, 60, 50, 70 and 80 respectively.

Anjalis corresponding conversion rate for rounds 1, 2, 3, 4 and 5 is 40, 50,

90, 60 and 70 respectively.

Also, in all, Anushka hit more shots on target than Anjali.

0.4 a + 0.6 b + 0.5 c + 0.7 d + 0.8 e > 0.4 a + 0.5 b + 0.9 c + 0.6 d + 0.7 e

6b + 5c + 7d + 8e > 5b + 9c + 6 d + 7e

b + d + e > 4c (i)


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, .

Therefore, c can take one out of three possible values : 50, 100 and 150.

Also, the only possible values of b , d and e are 50, 100 or 150.

If c = 150, 4 c = 600

In such a case, b , d and e can only be 50 or 100, and their sum can never begreater than 600.

c 150

If c = 100, 4 c = 400

Now, one value out of b , d and e can be 150, one can be 100 and the third hasto be 50 (since the other 100 is already taken by c ).

In such a case, b + d + e = 300

This violates the condition of the obtained inequality.

c 100

c = 50

Thus, the maximum possible number of shots in round 3 is 50.

Therefore, statement I is necessarily true.

Hence, options 2 and 4 can be eliminated.

Now, c = 50

4c = 200

Therefore, for the given inequality to be true, b + d + e > 200

For this, b , d and e can take the following values (in any order) :

(150, 100, 100) ...therefore, a = 50

(150, 100, 50) ...therefore, a = 100

(100, 100, 50) ...therefore, a = 150

Thus, the number of permissible shots in round 1 is not necessarily 50.

Therefore, statement II is not necessarily true.

Hence o tion 1.


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, .

27.3 Marks

If the number of rounds that were fired in Round 4 was 150, then what can besaid about the following statements?

I. Anushka and Prateeksha could hit the same number of targets in all rounds puttogether.

II. Round 2 and Round 5 consisted of 50 shots each.

1) If statement II is false, then statement I is true.

2) If statement I is true, then statement II is true.

3) If statement II is true, then statement I is true.

4) Both, options 2 and 3

Solution:Let the number of shots that were fired in rounds 1, 2, 3, 4 and 5 be a , b , c , d

and e respectively.

Consider statement I to be true:

Both Anushka and Prateeksha had hit same number of targets in all therounds put together we have;

4a + 6b + 5c + 7d + 8e = 7a + 6b + 8 c + 4 d + 5e

3d + 3e = 3a + 3e , i.e. d + e = a + c (i)

Now if round 4 had 150 shots, then d = 150, e = 50 and a = c = 100, implyingthat b = 50

Thus, round 2 and round 5 would have consisted of 50 shots each.

Thus, statement II is true.

If statement I is true then statement II has to be true.

Consider statement II to be true:

b = e = 50 and d = 150, implying that a = c = 100, then,

the number of shots hit on target by Anushka = 4 a + 6 b + 5c + 7d + 8e = 2650

and the number of shots hit on target by Prateeksha = 7 a + 6b + 8c + 4d + 5e= 2650

Thus, Anushka and Prateeksha would have hit the same number of shots on

target in all.


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Thus, statement I is true.

If statement II is true, then statement I is also true.

Hence, option 4.

Group Question


A cricket coach while analyzing the performance of the bowlers of his team Super-Champions has made the following table:

His team is playing a ten-over-a-game tournament and the table shows the number of runs given by a bowler in a particular over.

Each bowler can bowl a maximum of two overs and no bowler can bowl two consecutiveovers.

Assume that for all the questions below, each bowler gives exactly the same number of runs as shown above, if and when used for that particular over. For instance, whenever Akash bowls the 5 th over, he gives away 9 runs in that over.

Answer the following questions based on the information above:

28.3 Marks

In one game, the score of the opposing team was 51 after 7 overs while Anujand Ajay had both bowled out their quota of 2 overs. What is the minimum finalscore that Super Champions can restrict the opposing team to? Assume thatthe 7 th, 6 th and 5 th overs were bowled by Amar, Arjun and Akash respectively.

1) 83

2) 33

3) 324) 84


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Solution:Since the score of the opposing team has to be minimised, the 8 th, 9 th and10 th overs have to be bowled by players giving away minimum runs.

Anuj and Ajay cannot bowl any more overs, as they have exhausted their quota. This also means that between them, they have bowled the first four

overs. Therefore, the 5th

, 6th

and 7th

over is the first over of Akash, Arjun andAmar respectively. All three can bowl one more over.

The 8 th over cannot be bowled by Amar since he bowled the 7 th over.

Therefore, one out of Akash, Avinash or Arjun may bowl the 8 th over.

However, Akash gives away 12 runs in the 8 th over while Avinash and Arjungive away 11 runs each.

Therefore, Avinash and Arjun are better choices to bowl the 8th

over.

Now, no bowler can bowl two consecutive overs.

Therefore, among Avinash and Arjun, the person bowling the 8 th over shouldbe such that he gives away more runs in the 9 th over. This is because we wantsomeone giving away less runs to bowl the 9 th over.

Observe that Avinash gives away 11 and 13 runs in the 8 th and 9 th oversrespectively while Arjun gives away 11 and 12 runs in these same overs.

Also note that Amar and Akash give away 13 runs in the 9 th over.

Therefore, Arjun is the best choice for the 9 th over.

Thus, if Arjun bowls the 8 th over, he cannot bowl the 9 th. This will lead to moreruns being given away.

Therefore, Avinash and Arjun have to bowl the 8 th and 9 th overs respectively.

Now, Arjun has also finished his quota.

One of Amar, Akash and Avinash can bowl the 10 th over.

Amar, Akash and Avinash respectively give away 11, 15 and 10 runs in the10 th over.

Therefore, Avinash should bowl the 10 th over.

Thus, the minimum runs scored overs 8-10 is 11 + 12 + 10 i.e. 33 runs.


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Hence, the final score (minimum) would be 51 + 33 = 84

Hence, option 4.

29.3 Marks

What is the least possible score that the Super Champions can restrict an

opponent to, if Ajay completes his quota within the first four overs?

1) 75

2) 76

3) 77

4) 78

Solution:The least possible score occurs when all the bowlers bowl such that they givethe least numbers of runs in every case such that each bowler bowlsa maximum of 2 overs and does not bowl two consecutive overs.

Also, Ajay has to complete his quota within the first four overs.

Since no bowler can bowl two consecutive overs, consider the bowlers whogive the lowest and second lowest number of runs in two consecutive overs.

Consider overs 1 and 2:

For both these overs, Ajay gives away the least runs (4 in each over) whileAnuj is the second most economical (6 and 7 respectively).

Therefore, Ajay and Anuj have to bowl these two overs.

If Ajay bowls the 1 st over, Anuj has to bowl the 2 nd and the total runs given are4 + 7 = 11.

In the other case, Anuj and Ajay bowl the 1 st and 2 nd over respectively.Therefore, the total runs given away = 6 + 4 = 10.

Thus, Anuj and Ajay bowl the 1 st and 2 nd over respectively.

This methodology can be used for each set of 2 overs. If the same two bowlersgive away the least and second lowest number of runs in a set of two overs,their order should be such that the total for these two overs gets minimised.

Consider overs 3 and 4:

Again Anuj and Ajay should bowl these two overs.


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Mark (3) if the question can be answered by using both statements together, but notby either statement alone.Mark (4) if the question cannot be answered by either of the statements.

If A is the tallest person, then who is the shortest among A, B, C, D and E?

A. B is taller than C and E.B. C is taller than D and E.

1) 1

2) 2

3) 3

4) 4

Solution:Using statement A alone:

A is the tallest and B is taller than C and E.

Hence, one of C, D or E can be the shortest person.

Hence, the question cannot be answered using statement A alone.

Using statement B alone:

A is the tallest and C is taller than D and E.

Hence, one of B, D or E can be the shortest person.

Hence, the question cannot be answered using statement B alone.

Using both the statements together:

B is taller than C and E; and C is taller than D and E.

Therefore, B is taller than C, who in turn, is taller than D and E.

Since A is the tallest, either of D or E can be the shortest.

Hence, the question cannot be answered by either of the statements.

Hence, option 4.

Group Question

Section II


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The passage given below is followed by a set of questions. Choose the most appropriateanswer to each question.

Competitive balance is a relative measure of how closely or dispersed talent levels arein leagues and is one of the major issues in the professional sports market; evidencedby the work stoppages that we see. In fact, as most of us know, the primary focus of the2004 NHL lockout was the dispute over implementing a salary cap instrument into themarket for players. One of the arguments that leagues and owners use to support salarycaps is the necessity to maintain a certain level of competitive balance in leagues. Thetheory is that if the same teams win most of the time that fans will lose interest anddemand will decrease to a point where certain teams cannot remain profitable and if leagues contract there will be fewer jobs for athletes. Theoretically, salary caps with botha price floor and price ceiling, if designed properly, can improve competitive balance.

With the start of the NHL playoff around the corner we thought it would be interesting tolook at how playoff structures affect competitive balance. First, any type of playoffs willimprove competitive balance in leagues; and the more playoff rounds the more it willimprove competitive balance. We can see it in todays market- compare the competitivebalance in MLB and the NHL.

So how it is that playoffs improve competitive balance? Here it is they reduce theincentive for teams to invest in talent because the probability of winning to gain themarginal revenue from the next round decreases with more playoff rounds. For example;if San Jose is favoured to win any round in this years playoffs with a probability of 60%,then the probability of San Jose winning the first round is 60%, the second round is 36%,and going to the Stanley Cup finals is only 22%. So San Jose has to invest a substantialamount to be the best team in the league and will most likely not last far enough in theplayoffs to benefit financially from the revenues. Teams are often better off financially toassemble a team that makes the playoffs and might win a round does this sound

familiar to any cities?

The question really becomes then, why does a team like Detroit win most often? Well,there are a number of reasons that are economically sound. The most of which is thatfans in Detroit demand or are willing to pay so much more to win than in other cities thatthe marginal revenues from the regular season are greater than the marginal cost of thesalaries required.

31.3 Marks

Which of the following can be inferred about MLB and NHL?

1) MLB stands for Middle-borough league of base-ball.

2) NHL has better competitive balance than MLB.

3) MLB has more play-off rounds than NHL.

4) None of these

Solution:The passage says that we need to compare the competitive balance betweenMLB and NHL to see how more play-offs improve competitive balance. But itdoes not say which of the two have better competitive balance, nor is the full-


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form of any of these mentioned in the passage. Therefore, none of the optionscan be inferred from the passage.Hence, the correct answer is option 4.

32.3 Marks

What assumption has the author made regarding the structure of the StanleyCup?

1) Best of three: Team that wins two out of three matches plays in the

final.2) Best of five: Team that wins three or more out of five matches plays

in the final.

3) Knock out: Team that wins each and every game in the playoffsplays in the final.

4) Best of nine: Team that wins nine or more matches plays in the final.

Solution:

The probability of San Jose winning the first round is 60%.Similarly, the probability of San Jose winning the second round is (60% 60%) = 36%The probability of winning the third round is (60% 60% 60%) = 21.6% (or 22% approximately).This implies that if San Jose has to reach the finals, it has to win its first threematches.Hence, option 1 is false.Also, from the above calculations, if a team wins three out of three matches, itreaches the final. Thus it does not need to win or play any more matches toreach the final.Hence, options 2 and 4 are false.If the San Jose team wins each playoff game, it reaches the final.Hence, option 3 is true.Hence, the correct answer is option 3.

33.3 Marks

Each of the questions below consists of a set of labelled sentences. Thesesentences, when properly sequenced, form a coherent paragraph. Choose the mostlogical order of sentences from the options.

A. The simplest sort of discrepancy between subjective judgment and objective reality is wellillustrated by John Lockes example of holding one hand in ice water and the other hand in

hot water for a few moments.B. The objective is characterized primarily by physical extension in space and time.C. Thus, one perceiving mind can hold side-by-side clearly differing impressions of a single

object.D. The subjective is characterized primarily by perceiving mind.E. When one places both hands into a bucket of tepid water, one experiences competing

subjective experiences of one and the same objective reality.F. One hand feels it as cold; the other feels it as hot.

1) DBAEFC


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Akbar : I came from Chiklu. Moreshwar came from Dholu.

Birbal : I came from Dholu. Chandragupta came from Chiklu.

Chandragupta : I came from Piklu. Akbar came from Neelu.

Moreshwar : I came from Chiklu. Birbal came from Piklu.

It is also known that exactly one of the four belongs to the Dabra tribe and at least one of them belongs to the Cabra tribe and at least one of them belongs to the Abra tribe.

35.3 Marks

Who among the following is a Cabra?

1) Akbar

2) Birbal

3) Moreshwar

4) Chandragupta

Solution:There is exactly one person from the Dabra tribe, and atleast one person eachfrom the Cabra and Abra tribes.

Thus, the number of people from the Abra, Cabra and Dabra tibes canrespectively be 2, 1, 1 or 1, 2, 1.

Since a Cabra is to be identified, consider each person to be a Cabra and

verify the other statements.Consider Akbar to be a Cabra.

Therefore, he always tells the truth and so, Akbar is from Chiklu andMoreshwar is from Dholu.

Therefore, Birbal and Chandragupta can be from Piklu and Neelu in any order.

Both of Birbals statements are false and he is a liar i.e. he is a Dabra.

Therefore, there cannot be any more Dabras.

Also, the second statement of Chandragupta and the first statement of Moreshwar is definitely false.

Now Birbal can be from Piklu or Neelu.

In any case one of Chandragupta and Moreshwar has to be a liar.

If Birbal is from Piklu, then both statements of Chandragupta are false and if Birbal is from Neelu then both statements of Moreshwar are false.


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respec ve y.

In that case, the second statement made by Akbar is false.

Therefore, Akbar is a Dabra and Birbal and Moreshwar are Abras.

Hence, option 4.

36.3 Marks

Who has come from Neelu?

1) Akbar

2) Birbal

3) Chandragupta

4) Moreshwar

Solution:

Consider the solution to the previous question.

Akbar has come from Neelu.

Hence, option 1.

37.3 Marks

There are 8 cricketers A, B, C, D, E, F, G and H out of which 4 are to beselected under the given conditions.

1. If A is s elected then B will not be selected.2. If B is selected then C will not be selected.3. If C is selected then D will not be selected.4. If D is selected then E will not be selected.5. If E is selected then F will not be selected.6. If F is selected then G will not be selected.7. If G is selected then H will not be selected.8. If H is selected then A will not be selected.

Find the number of ways in which the cricketers can be selected.

1) 1

2) 23) 3

4) Data Inconsistent

Solution:The given data can be represented by the figure given below, such that thecricketers, who are directly connected with a line, cannot be selected together.


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Since C is younger than D, C could have been born in 1981 or 1971.

But, if C was born in 1971, E would be born in 1969 and D in 1981. This wouldmake D younger than C, which contradicts the given data.

Therefore, C was born in 1981.

Thus, D and E were born in 1971 and 1969 (in no particular order).

Since the youngest person was born on 2 nd Dec, C was born on 2 nd Dec, 1981.

Now, observe that D can be oldest or second-to-oldest.

The birthday of the oldest person is already given.

Therefore, if Ds day of birth is known, the year of his birth is known, and so theorder of their birth can be found.

Since 23 rd July is the only date that is not mentioned in the given data, start with theoption that mentions this date. i.e. option 4.

Consider option 4.

If D was born on 23 rd July, he could not have been the oldest.

Therefore, D would have been born on 23 rd July, 1971 and E was born on 10 th Feb,1969.

Since the person born on 29 th Nov was older than the person born on 12 th Dec, andsince B is older than A; B was born on 29 th Nov, 1975 while A was born on 12 thDec, 1977.

Thus, everybodys date of birth is known.

This cannot be found if the other statements are considered.

Hence, option 4.

Group Question


In the second auction of a cricket league, the three teams, Team A, Team B and Team Cselected their players among the following nine players - Sachin, Bret, Chris, Virat,Rahul, Rohit, Shane, Brad and Ricky.

The maximum number of players selected by any of the three teams was not more than

four. Atleast two players were selected by each of the three teams. No two teams havethe same number of players. The team that selected Chris selected three more players


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, , .and Ricky were not selected by the same team. Brad and Bret were not selected by thesame team. The team that selected Shane also selected Rohit with him.

39.3 Marks

If the team that selected Chris, also selected Rahul. Ricky is selected by TeamA. If Team A selected only two players, then in how many ways can the teamsA, B and C be formed?

1) 42) 6

3) 5

4) None of these

Solution:It is given that Chris must form a team of 4 members only and Virat must forma team of 3 members only.

Thus, Chris and Virat are in two different teams. Let their teams be calledTeam 1 and Team 2 respectively.

The third team should have two persons as shown below.

Now let us take the other conditions and fill the above table.

Chris and Ricky cannot be in the same team.

Ricky will be in the second or the third team. Brad and Bret cannot be in thesame team. Rohit and Shane must be in the same team.

It is given that Chris and Rahul are together, whereas Ricky is in Team Awhich has two members.


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Rohit and Shane must be in the same team. Since Team A has only spot left,

they can go into the first team or the second team.

Let us consider these two cases.

Case 1: Rohit and Shane go into the first team.

Bret and Brad cannot be in the same team,

One of them will go in the third team and the other into the second team.This gives rise to two ways of forming the teams - One with Bret in the secondteam and the other with Bret in the third team.

Case 2: Rohit and Shane go into the second team.

In this case too, one of Bret and Brad will go into the first team and the other into the third team.

Either Team B or Team C can have four players, there are total eight waysof forming the teams. Hence, option 4.

40.3 Marks

If Virat, Rahul and Brad were selected by Team C and Ricky was selected byTeam A, then which of the following must be true?

1) Rohit and Bret are selected by Team B.

2) Team A selected either Bret or Sachin.

3) The three players that are selected by Team B are Rohit, Shane andSachin.

4) More than one of the above are true.

Solution:Since Virat has been selected by Team C, Team C has 3 players in all.

Since Ricky is in Team A, Chris has to be in Team B.

Therefore, Team A and B would have selected 2 and 4 players respectively.

Since Virat, Rahul and Brad have been selected by Team C, no on else canbe in team C.

Now, there are four people left : Rohit, Shane, Sachin and Bret.


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, .

Since Rohit and Shane are in the same team, they have to be in Team B.

Therefore, one out of Sachin and Bret is in Team A and the other is in TeamB.

Therefore, the statement in option 2 is definitely true.

The statement in option 1 may or may not be true.

Since Team B has four players, the statement in option 3 is false.

Thus, only one statement is definitely true.

Hence, option 2.

41.3 Marks

If Virat and Sachin are selected by Team B, then which of thefollowing can never be the only two players selected by Team C?

1) Ricky and Rahul

2) Bret and Rahul

3) Brad and Ricky

4) None of these

Solution:Virat is in the team with 3 players,

Team B is the team with 3 players.

Since the question talks about the only two players in Team C, Team A willhave 4 players.

Therefore, Chris is in Team A.

Virat and Sachin are in Team B, if we take Rohit and Shane as the twomembers of Team C then Ricky has to be in Team B in which case we haveboth Brad and Bret in Team A which is not possible.

Therefore, Rohit and Shane have to be in Team A.

Now, there are 4 people left - Rahul, Brad, Bret and Ricky.

The two people in Team C can be any one from the following combinations -(Ricky, Bret), (Ricky, Brad), (Ricky, Rahul), (Brad, Rahul), (Bret, Rahul).

Thus, the two people who have to be selected cannot be determined.

Hence, option 4.


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42.3 Marks

In each of the following questions, the left hand side column lists four phrases and theright hand side column lists meanings of these four phrases, not necessarily in thesame order. You need to match the phrases with their respective meanings.

Best

1) AF-BG-CE-DH

2) AH-BF-CE-DG

3) AE-BG-CH-DF

4) AG-BF-CE-DH

Solution:At best means under the most favourable circumstances. Therefore, A relates toG.Make the best of means to cope with in the best way possible. Therefore, Brelates to F.Have the best of means to gain the advantage over. Therefore, C relates to E.For the best means to an ultimate advantage. Therefore, D relates to H.Hence, the correct answer is option 4.

43.3 Marks

Fill in the blanks with the most appropriate pair of words from the given options.Many _____ come to India in search of ______ values.

1) businessmen, material

2) tourists, spiritual

3) foreigners, correct

4) businessmen, economic

Solution:The keywords in the sentence are India , and values . Perhaps some backgroundknowledge will help as well. Values means the ideals, customs, institutions, etc., of a society.Options 1 and 4 are eliminated because their second blanks do not make sensewith 'values'.Option 3 is eliminated since correct does not fit into this context.Spiritual is a better fit for the second blank.Hence, the correct answer is option 2.


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Group Question

For each of the passages below, read the passage, and mark the most appropriate answer tothe question(s).

Hypotheses of social evolution and cultural evolution are common in Europe. TheEnlightenment thinkers who preceded Darwin, such as Hegel, often argued thatsocieties progressed through stages of increasing development. Earlier thinkers alsoemphasized conflict as an inherent feature of social life. Thomas Hobbes 17 th centuryportrayal of the state of nature seems analogous to the competition for natural resourcesdescribed by Darwin. Social Darwinism is distinct from other theories of social changebecause of the way it draws Darwins distinctive ideas from the field of biology intosocial studies. Darwins unique discussion of evolution was over the supernatural inhuman development. Unlike Hobbes, he believed that this struggle for natural resourcesallowed individuals with certain physical and mental traits to succeed more frequentlythan others, and that these traits accumulated in the population over time, which under certain conditions could lead to the descendants being so different that they would bedefined as a new species.

However, Darwin felt that social instincts such as sympathy and moral sentimentsalso evolved through natural selection, and that these resulted in the strengthening of societies in which they occurred, so much so that he wrote about it in Descent of Man:The following proposition seems to me in a high degree probable- namely, that anyanimal whatever, endowed with well-marked social instincts, the parental and filialaffections being here included, would inevitably acquire a moral sense or conscience, assoon as its intellectual powers had become as well, or nearly as well developed, as inman. For, firstly, the social instincts lead an animal to take pleasure in the society of itsfellows, to feel a certain amount of sympathy with them, and to perform various servicesfor them.

Social Darwinism, combined with National Efficiency was the main reason for the greatsocial reforms of the early 1900s. After the landslide 1906 election, David Lloyd Georgeand Winston Churchill began to reform society according to the Rowntree Report. Thereport detailed poor people from York and explained that although they tried hard to liftthemselves of their poverty, it was nearly always impossible. This changed the socialview that the poor were lazy and stupid, and new policies were made concerning theDeserving Poor. These social reforms earned the Liberal Party the title Fathers of theWelfare State and were largely down to Social Darwinism.

44.3 Marks Social Darwinism is different from other theories of social change because:1) It distinctly separates Darwins theory of social change from

Darwins theory of evolution.

2) It creates a distinction between the field of biology and socialscience.

3) It interprets Darwins ideas on biology into the social studies.

4) It creates a distinction between the hypotheses of social evolutionand those of cultural evolution.


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Solution:Apart from option 3, the other options are not mentioned in the passage - inthis context, at least.Option 3 is correct from Social Darwinism is distinct from other theories of social change because of the way it draws Darwin's distinctive ideas from thefield of biology into social studies. Hence, the correct answer is option 3.

45.3 Marks

Why has the author quoted Darwin in the penultimate paragraph?

1) To provide evidence for the statements in the previous part of theparagraph.

2) To provide an introduction to the following paragraph in thepassage.

3) To elaborate and support the statements about Darwins opinionsmentioned in the line preceding the quotation.

4) To exhibit the apparent contradiction in Darwins opinion and theidea in the quotation.

Solution:In the penultimate paragraph, the author elaborates on the statements made inthe previous part of the same paragraph. The line preceding the quotationmentions a concept that the quotation further strengthens.The quotation does not provide evidence for any premise. Thus option 1 isincorrect.Option 2 is incorrect because the quotation does not provide an introductionto the following paragraph and is largely not interrelated.There are no apparent contradictions between Darwins opinions and thosepresented in the quote. Thus option 4 is incorrect.Hence, the correct answer is option 3.

46.

3 Marks

What led the Liberal Party to earn the title Fathers of the Welfare State?

1) The social reforms of the Liberal party that concentrated on thepoor, deserving people.

2) The social Darwinism theory that led to the emergence of theworking class and self governance.

3) The stand taken by the Liberal party enabling equitable distributionof wealth and resources.

4) The landslide election of 1906 that brought the poor elected topower.

Solution:The last few lines of the passage talk about the social reforms of the Liberal


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par y. e paragrap s a es a e soc a re orms a ocusse on ebetterment of the poor led to the name Fathers of the Welfare State for theLiberal Party. The passage talks about the fact that poor were not lazy andstupid. This is in consonance with option 1.Option 4 is incorrect as the 1906 election was not directly responsible for thesocial reforms or the title. The author credits both Social Darwinism andNational Efficiency for the great social reforms of the early 1900s.Option 2 is irrelevant as the passage is not relevant to the working class or self governance.Option 3 is incorrect as it mentions the stand taken by the liberal party. Thepassage states that the liberal partys reforms were aimed at the poor.However, it does not mention equitable distribution of wealth and is thusinaccurate.Hence, the correct answer is option 1.

47.3 Marks

Fill in the blanks with the most appropriate pair of words from the given options.

His _____________ at work led to his being _____________ dismissed from the job.

1) inefficiency, slowly

2) ineptitude, summarily

3) efficacy, suddenly

4) failure, gradually

Solution:Dismissed in the context calls for a negative word in the first blank. Efficacy,meaning effectiveness, is incorrect. Eliminate option 3.Dismissal cannot be slowly or gradually. Eliminate options 1 and 4.Summarily, meaning instantly; without notice, fits the blank.Hence, the correct answer is option 2.

48.3 Marks

Each question has five word pairs. Only one of the words in a word pair would fit thecontext of the sentence correctly. Find the option which enlists all the correct wordsfor a question.

The eager (A) / anxious (B) sales person worried about his dwindling (A) /dawdling (B) sales and hence his incentives (A) / inceptives (B) . Besides (A) /Beside (B) he could not understand what exactly was going wrong with the process.With the amount (A) / number (B) of effort and time he had put in, there had to besomething else which was causing the decline in the sales.

1) AAAAA

2) BBBBB

3) AAABA

4) BAAAA


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The salesperson could be either eager or anxious. But, since he was worried, anxious is moreappropriate here.He was worried about his sales going down or dwindling. Dawdling is leisurely, slow or deliberate and does not fit the context of sales.Inceptive means beginning. The third correct word, therefore, is incentives which meansrewards (monetary in this context).Besides is furthermore or also. Beside is incorrect in this context as it means next to (for

example, he was sitting beside her).Number is used for countable nouns. Here effort is not countable, thus amount is to be usedhere.Hence, the correct answer is option 4.

Group Question


Following is the curriculum in math and physics for the next few years for students of auniversity. The number of semesters needed to complete each course is listed alongwith its pre-requisites:

A student is allowed a maximum of 5 courses per semester, provided he has completedthe pre-requisites for the courses.

49.3 Marks

What is the minimum number of semesters required to complete the course?

1) 4

2) 5

3) 6


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4) 9

Solution:Let the student start PHY101 in the first semester, he will finish it in 3semesters.

He can also start MTH101 in the first semester itself but is not eligible for anyother course.

In the third semester, he can do the course MTH102, at the end of which he willbe eligible for both PHY102 and PHY103.

He can start with PHY102 and PHY103 in the fourth semester and thus hecan finish the course in 5 semesters, as PHY102 requires 2 semesters.

Hence, option 2.

50.3 Marks

If a student fails once in each course (he completes the course in n + 1semesters, if the minimum is n semester for that course), what is the minimumnumber of semesters required to complete the course?

1) 5

2) 6

3) 7

4) 8

Solution:The student will take 1 semester more for each subject.

If he starts PHY101 in the first semester, he will finish it in 4 semesters.

He will also start MTH101 in the first semester itself but is not eligible for anyother course.

In the fourth semester, he can start with MTH102, which he will finish at the endof 5th semester.

He can start PHY102 and PHY103 in the sixth semester and thus can finishthe course in 8 semesters, as PHY102 requires 3 semesters.

Hence, option 4.

51.3 Marks

Suppose a student completes the course in 6 semesters, what is themaximum number of subjects he can fail in (If he fails in a subject then he

takes 1 semester more than the minimum number of semesters required)?

1) 1


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2) 2

3) 3

4) 4

Solution:From the solution to the first question we get that, the student can complete all

the courses in minimum 5 semesters.If he has to pass it in six semesters, he can fail in a maximum of three coursesin any one of these two combinations (PHY101, MTH101 and PHY103) or (PHY101, MTH102 and PHY103) or (PHY101, PHY102 and PHY103).

He can fail in a maximum of 3 subjects.

Hence, option 3.

52.3 Marks

The following question consists of a set of labelled sentences. These sentences,when properly sequenced, form a coherent paragraph. Choose the most logicalorder of sentences from the options.

A. The people sti ll in the room were an old man who looked like an artisan, and was extremelydrunk; sitting with his companion, a burly man with a red beard.

B. There werent many people at that time in the room.C. He was dead drunk and was s leeping on the chair.D. Other than the three drunken men she had met at the doorstep, a group of about six men

and two girls had gone out simultaneously.E. Their departure made the room empty and rather quiet.

1) DEBAC

2) BDEAC

3) ABDEC

4) BACDE

Solution:The first statement is statement B. It indicates the time of the actions that take placein the rest of the sentences.Statement C describes the man discussed in statement A (so C follows A)andstatement E indicates the people discussed in statement D (so E follows D).So statements C and E cannot follow B. The only options are statements A and D.Statement A says the people still in the room. The word still indicates that othershave left.Statement D speaks about those who have left. So statement D goes beforestatement A.That is to say statement D follows statement B.

Hence, the correct answer is option 2.Group Question


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Ashok, Babu, Chetan, Durgesh, Firoz, Gaurav and Harsh live in Mumbai. Their professionis one of Accountant, Engineer, Clerk, Musician, Student, Designer and Doctor. Each of them like exactly one of the following genres of music: Punjabi, Folk, Pop, Jazz, Disco,Rock and Classical. Each of them owns exactly one of the following mobile brands: Nokia,Samsung, LG, Huwai, Sony, Spice and Motorola. Each person owns exactly one of thefollowing cars: Audi, Camry, Honda City, Accord, Duster, Ferrari and BMW.

Some more facts known are:

Ashok owns an Audi but doesnt like rock music.Babu is a doctor and likes folk music.The designer likes jazz and owns an LG phone.Durgesh owns a Duster but doesnt like punjabi music.Gaurav is not an accountant but likes classical music and owns an Accord.Harsh owns a Motorola phone and likes disco music.The accountant likes punjabi music and owns a Nokia phone.

The Samsung phone owner owns a Camry.

53.3 Marks

Which statement among the following is definitely not correct?

1) Ashok is an accountant.

2) The doctor owns a Samsung phone.

3) Durgesh owns a Nokia phone.

4) Harsh owns a BMW.

Solution:

The given data can be represented in a table as shown above :

The additional information that we have is:

Ashok doesnt like rock music, Durgesh doesn't like punjabi music and Gaurav is not anaccountant.The accountant likes punjabi music and owns a Nokia phone.The designer likes jazz music and owns an LG phone.


Consider the statement in option 3:


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Durgesh definitely doesnt own a Nokia mobile phone as Durgesh does not likePunjabi music and the owner of the Nokia phone likes Punjabi music.

The statement in option 3 is definitely not correct.

Hence, option 3.

54.3 Marks

If the person who owns a Duster, also owns a Sony phone; and the person who ownsa BMW, also owns a Spice mobile, then who definitely owns a Huwai phone?

1) Ashok

2) Gaurav

3) Chetan

4) Firoz

Solution:

The additional information that we have now is:

Ashok doesnt like rock music, Durgesh doesn't like punjabi music and Gaurav is not anaccountant.The accountant likes punjabi music and owns a Nokia phone.The designer likes jazz music and owns an LG phone.The person who owns a BMW car, owns a Spice mobile.


Gaurav owns an Accord.

He doesnt own a Samsung phone (as the Samsung phone owner owns a Camry)and cannot own a Spice phone (as the Spice phone owner owns a BMW).

Harsh owns a Motorola phone and Durgesh owns a Sony phone.

Gaurav cannot own Motorola or Sony phones.


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The one who likes Punjabi music, owns a Nokia phone; and the one who likes jazz,owns an LG phone. However, Gaurav likes Classical music.

He cannot own Nokia or LG phones.

Gaurav can only own a Huwai phone.

Hence, option 2.

Group Question


A leading management institute recently absorbed a batch of 80 students for its two year PGP course in management.

The criteria for selection were as follows:

I. The candidate should have taken exactly one of the CAT or XAT examinations.II. The candidate must have :

a. Secured atleast 96 percentile in the examination he or she had written. ORb. Secured a rank among the top 10 students in his or her university examination

(university topper).III . The candidate must either be a fresher or have work experience of more than 3 years.

Further information on the students the Institute had absorbed is as follows:

IV. There were 45 students who had secured a rank among the top 10 students in their universi tyexamination. Of these 33.33% were freshers while 66.66% had appeared for CAT.

V. 30 students had taken the XAT examination, of which 15 were freshers.VI. Of the students who had work experience greater than 3 years, 15 s tudents were university

toppers (i.e. in the top 10) and these students had also secured 96 or more percentile in the

examination they had taken.VII. There were 20 students who had taken the CAT examination, had secured a rank among the top

10 students in their university examination, and also had work experience of more than 3 years.VIII. There were a total of 40 students who had work experience of more than 3 years.

IX. No fresher satisfied both the criteria mentioned in (II) above.

55.3 Marks

What was the number of students with work experience that the college hadabsorbed who were also university toppers, had taken the CAT examinationand had secured more than 96 percentile in the examination they had taken?

1) 5

2) 7

3) 3


Solution:Let a be the number of students who have taken the XAT examination,


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secured 96 percentile or more, have work experience of more than 3 years butare not university toppers.

b : (XAT, at least 96 percentile, University topper, Work experience)

c : (XAT, less than 96 percentile, University topper, Work experience)

d : (CAT, at least 96 percentile, not a University topper, Work experience)

e : (CAT, at least 96 percentile, University topper, Work experience)

f : (CAT, less than 96 percentile, University topper, Work experience)

g : (CAT, less than 96 percentile, not a University topper, Work experience)

h : (CAT, at least 96 percentile, not a University topper, Fresher)

i : (CAT, at least 96 percentile, University topper, Fresher)

j : (CAT, less than 96 percentile, University topper, Fresher)

k : (CAT, less than 96 percentile, not a University topper, Fresher)

l : (XAT, at least 96 percentile, not a University topper, Fresher)

m : (XAT, at least 96 percentile, University topper, Fresher)

n : (XAT, less than 96 percentile, University topper, Fresher)

o : (XAT, less than 96 percentile, not a University topper, Fresher)

Every student who has been absorbed by the institute must have secured atleast 96 percentile in the examination he or she has taken, or must be aUniversity topper,


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g = k = o = 0

Also, from (IX), we have i = m = 0

Total number of students = 80

From (I), there were 45 university toppers.

Therefore, the remaining 35 students were not university toppers.

i.e. a + d + h + l = 80 45 = 35 (i)

Also, of these 45 university toppers, 33.33% (i.e. 15 students) were fresherswhile 66.66% (i.e. 30 students) had taken the CAT examination. This meansthat the remaining 30 students had work experience of more than 3 years, andthat 15 students had taken the XAT examination.

j + n = 15 (ii)

and b + c + e + f = 30 (iii)

and e + f + j = 30 (iv)

and b + c + n = 15 ... (v)

From (VII), we have e + f = 20 (vi)

Using (iv) and (vi), we have j = 10 (vii)

Using (ii) and (vii), we have n = 5 (viii)

From (V), 30 students had appeared for XAT and of these 15 were freshers.


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.3 Marks

. .the top 10) but did not secure 96 percentile in the examination they had taken,then how many of the selected students had taken the XAT examination,secured more than 96 percentile in the examination they had taken, and wereamong the toppers in their respective university examinations?

1) 4

2) 7

3) 9

4) 0

Solution:Consider the solution to the first question.

There were 24 students who had taken the CAT examination and wereuniversity toppers but did not secure 96 percentile in the examination they hadtaken,

i.e. (15 c ) + 10 = 24

c = 1

The number of students who had taken the XAT examination, had securedmore than 96 percentile in the examination they had taken, and were amongthe toppers in their respective university examinations is (10 c ) + 0 = 10 1= 9

Hence, option 3.

57.3 Marks

How many of the students who had taken the XAT examination, managed tosecure at least 96 percentile in the examination they had taken, but wereneither university toppers nor freshers?

1) 5

2) 3

3) 8

4) 2

Solution:Consider the solution to the first question.

Students who had taken the XAT examination and secured at least 96percentile in the examination they had taken, but were neither university

toppers nor freshers are represented by a.

From the solution to the first question, a = 5


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Hence, option 1.

58.3 Marks

What percent of the total students absorbed by the Institute were Universitytoppers who had also secured more than 96 percentile in the XAT?

1) 3

2) 1

3) 5


Solution:Consider the solution to the first quetion.

The absorbed students who were University toppers and had also securedmore than 96 percentile in the XAT are represented by (10 c ).

The value of c is not known,

The required percentage cannot be determined.

Hence, option 4.

59.3 Marks

In a certain electric network there are 5 components namely bulb, fan, computer,music player and a switch. The electrical connection is such that the variouscomponents can be connected to each other and the switch controls the operationof the remaining components in such a way that once the switch is turned ON, the

other four components get switched ON in sequence. The components are placedsuch that the switch and the computer are 1 m apart, the computer and music player are 2 m apart while the fan and switch are 2 m apart. The bulb is 2 m away from theswitch, while the computer and the music player are 2 m and 1 m away from the bulbrespectively. The distance between the bulb and the fan is 2 m and the fan is at adistance of 2 m from the music player. If the cost of wiring all the components is Rs.20/m, what can be the minimum cost of wiring?

1) Rs. 160

2) Rs. 140

3) Rs. 120

4) Rs. 180

Solution:The distance between the various components is as shown in the figure below.


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Since the components turn ON in sequence, the minimum cost of wiring is incurredwhen the network is selected such that it covers the least distance.

Thus, the shortest possible network is from the switch to computer to bulb (or musicplayer) to music player (or bulb) to fan i.e. 1 + 2 + 1 + 2 = 6m

Minimum cost of wiring = 6 20 = Rs. 120

Hence, option 3.

60.3 Marks

4 teams participate in a tournament such that each team plays every other teamtwice. The points system is such that a win results in 2 points, a loss in zero pointsand a draw in 1 point to each team. If no team wins or loses all its matches andthere are at least 3 draws in the tournament, what is the maximum score of the 2 ndhighest team?

1) 12

2) 11

3) 10

4) 9

Solution:Since every team plays the other three teams twice, there are 12 matches possiblein all and each team plays 6 matches.

Now, no team has won or lost all its matches.

Also, there are atleast three draws in the tournament.

To maximise the score of the team with the 2 nd highest score, it should not lose anymatch.

Also, the team with the highest score has to win maximum mathces and draw theremaining matches.

Now, to maximise scores, the team with the highest score will draw both its matcheswith the team having the 2 nd highest score and will win the remaining 4 matches.

Its maximum score = (2 4) + (1 2) = 10


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Therefore, the team with the 2 nd highest score will have a score less than this.

It has already had 2 draws (with the highest ranked team).

Therefore, to maximise its score, it will win 3 games and draw 1 more game.

Its maximum score = (2 3) + (1 3) = 9

Hence, option 4.

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