16927911 Data Interpretation

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DATA INTERPRETATION

Dr. T.K. Jain.

AFTERSCHOOOLCentre for social entrepreneurship

Bikaner

M: 9414430763

[email protected]

www.afterschoool.tk




What was the ratio of males tofemales in the rural area of

Ganga Nagar in theyear 2001?

(chart on next slide)







Answer

72% of males + 47.27 of females = 60.39% of (males + females)

OR

85.34% of males +68.54% of females = 77.80%of (males + females) Solve these and get the answer: .72 m + .4727f = .6039 m + .6039 f

1.1376m = 1.27754 f M / F = 1.27754/1.1376 Or : 1277: 1136 answer




Percentage urban population of

males in Bikaner is what per cent of the percentage

female population of rural areathere in theyear 2001?

(chart on next slide)







Solution«

% of male population in rural areas :

(average ± female%) / (male % - Female %)

= (46.38 ± 28.83) / (61.92 ± 28.83) =53%

Thus female are 47% in rural areas.

Similarly for urban areas :

= (76.17 ± 65.62)/(85.38 ± 65.62) = 53.4%

Thus 53.4% / 53% gives answer : 1.0072answer




In a certain code, ELEPHANT

is written asWLDFSCOC. How will

AGGARWAL be writtenin the same code?

First of reverse the word ELEPHANT : it is : TNAHPELE. Add 3 infirst digit and deduct 2 from next digit and so on. We get :LAWRAGGA from AGGARWAL. Now solve it :

OYZPDEJY. Answer




What is the trend in the number of retirees(who have opted for VRS) in the age group 50

- 55 from 1994 to 1996?




solution

In 1994, 55+ are 2000 which is 60% and in1996, 55+ are 1000, which is 40%. Thus totalnumber of retirees in 1994 and 1996 are :

2000*100/60 = 3333 and 1000*100/40 = 2500 The number of retirees in 50 to 55 are 20% of

total number in each of these years : thus it is666 in 1994 and 500 in 1996. thus there is atrend of decrease in these two years. Answer




What was the percentage

change in the break-up figurefrom 1990 to 1998 of the

retirees under VRS in the 55 +age group?

Solve it based on the graph of theprevious question.




Solution.

It was 80% (or .8) in 1990 and it reached30% in 1998. thus it decreased by .5 from.8.

The change in % is .5/.8 *100 = 62.5%answer




Which group showed the largest

percent change in per cent break-up from 1990 to 1998?

(solve from the graph of the previousquestion).

The group in 55+ age group showed the

largest % change from 1990 to 1998.answer (solve by observation).




How many more employees in the 46 - 50 agegroup had opted for VRS in 1996 as compared

to 1990?




SOLUTION.

IN 1990, 55+ ARE 2400, WHICH IS 80%OF TOTAL, THUS 5% WILL BE 2400*5/80

=150 IN 1996, 55+ ARE 1000, WHICH IS 40%,

SO 15% (46 TO 50 ARE 15%) WILL BE :1000*15/40 = 375

THUS THERE IS INCREASE OF (375 ±150) = 225 ANSWER







In which match did we have maximumdifference in the scores of the two teams?




Solution«

In the 9th match, the first innings score was200 and the second innings score was140, thus the difference was 60 runs,which is the highest difference out of thegiven data. Answer




What is the number of engineering studentsappearing in CAT in 2008. Compare this

with the data of 2004?




Answer «

In 2008, the number of engineeringstudents was 70,000 in 2004, it was also70000. thus there is no change in the dataof the two year, but the students fromother discipline have increased and so the% of students from engineering faculty has

decreased out of the total number of students




If the revenue of the company increases by 100% from

1998 to 2003 and revenue from biscuits is 100 crores

more than any other product in 2003, then what is the

revenue earned by company by selling shampoo

products in 1998?




solution

Sale in 2003 of biscuits is 20% more thanother items. Thus difference of 20% isequal to 100 crores. Thus total of 2003 is500 Crores.

The sale in 1998 = 500 * 100/200 = 250.be 9

Thus sale of shampoo in 1998 should be10% of 250 = 25 answer



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24




25

During which year were the sales as

a proportion of equity the highest?




26

Solution«

In 1991, the sales was 90 crores, butequity was only 10 crores, thus sales was10 times equity. Thus this is the highestout of all the 4 years that we have for review here.




27

What is the total distance travelled bythe train over this 3-hour period?




28

Solution«

Distance travelled =

= UT + ½ FT ̂ 2

U = starting speed = 35 T = time

F = total acceleration / total time.

= (71 ± 35) / (3 hours)= 12

= 35*3 + ½ (12 * 3*3)

= 159 ANSWER




29




30

What is the growth rate of sales at primary

level as per the table below (75 ± 80 )




31

Solution«

It has increased from 42 to 68000 andthere is growth of approx. 26000/42000which is 60% approx.

Thus per annum growth rate is 12%approx. answer




32

by what percent was the total investment in the two

districts more in 96 as compared to 95?




33

Solution

The total investment (combined in the twodistricts) was approx. 10000 in 1995,which increased by 1800 approx.

Thus growth rate is 18% answer




34

The total number of silver-coloured cars sold

in Metro H is approximately what percentage of

that in Metro M?




35

Solution «

Total sale of silver cars in metro H is 172and in metro M it is 192,

172/192 * 100 = 90% approx. answer




36

By what percentage production of other states

is more than that of the of Mãharashtra?




37

Solution

It is 25000 in other states and 20000 inMaharastra.

Thus it is more by 5000. Thus it is 25% of maharastra answer




38

Approximately what perceptage of the total

producation is shared by the other states




39

solution

Total production is 143000 approx.

Production in other states is 25000

25000/143000 * 100 = 17.5% approx.




40

If 85% of E type cars produced during 1996 and

1997 are being sold by the company, then how

many E type cars are left by the company




41

solution

In 1996 90000 cars of E type wereproduced and in 1997 we had productionof 50000 cars of type E.

Thus 15% of this 21000 is left out with thecompany.

Th t t l d ti b fi i i 1997




42

The total production by five companies in 1997

is what per cent of the total production by

companies B &.D in 1996?




43

solution

Total for 1997 for 5 companies = 185

For 1996 : for

B + D = 95 Thus 185/95 * 100 = 200% approx.




44

Which year had the highest per cent increase inproduction over the previous year?



11/12/2010 AFTERSCHOOOL centre for

social entrepreneurship

45

Solution«

In % the highest growth is in 1999, whichis 75% appro.





46

Cars of which colour are 20% lesspopular than white coloured cars?





47

Solution«

White car is 26% in demand 20 less (it isabsolute ± not comparative), = 6%, thusgolden car is the car which is having 6%popularity. Answer

If i 1997 th l ti f ill D i i d b 10%





48

If in 1997 the population of village D is increased by 10%

and the population of village G is reduced by 5% from

1995. population of village G in 1995 was 9000, what is the

total population BPL of villages D and G in 1997?





49

solution

Population of D + 10200 + 1020 = 11220

Take 58% of it : 6500

Population of G = 9000 ± 450 = 8550 Take 51% of this : 4300

Add these : 10800 answer

In which years was the amount of





50

In which years was the amount of profit the maximum?





51

Solution «

Try for 1998 and 1997, it is 27.5% 0f 150in 1998 and 20% of 190 in 1997, thus it ishighest in 1998. answer.

H th i d th 10





52

How many months experienced more than 10 per

cent increase in crude oil price over the earlier

month?





53

Solution«

We find 4 months with more than 10%increase

Answer





54

lb. numbers of torture eases exceeded the

number of molestation cases by:





55

Solution«

The number of cases of molestation isapproximately : 24000 approx.

The number of cases of torture is : 25000approx. Thus this number is 1000 morethan the cases of molestation.

Thus this is : 1000/24000 * 100

= 4% approx. answer





56

Numbers of ITPA (Immoral Traffic

Prevention Act) cases registeredin A.P. exceeded the casesregistered in Rajasthan by:

See the graph and solve it :





57

Graph :





58

Solution «

The number of cases in Rajasthan isapprox. 8000 but in AP it is approx. 10000.

Thus the number of cases in AP is 2000more than those in Rajasthan.

2000/8000 *100 = 25% answer





59

Consumption of cola in 1984: 75million, in 1998 : 115 million.

If Coke¶s sales for 1998 had been





60

If Coke s sales for 1998 had been30 million bottles, then, with the

distribution shown in the chartremaining the same, the total salesin 1998 would be greater or lower

than the actual value by whatpercentage?





61

Solution «.

Coke were sold 14% of total sales. Totalsale was 115 million, so the sale of cokewas : 14% of 115 = 15.6 million approx.

Sale as per chart : 15.6 million but actualsale (as per question): 30 million.

Thus sales as per chart is less by 14.4

million in comparison to the actual sales.

Thus it is : 14.4/30 *100 = 48% approx.





62

lf Coke¶s share were to increase by

10% in 1999 with total salesremainiaig the same, what would

be the percentage reduction in the

total share of other. Sale of coke in 1998 was 16.1, it increased by

10% so sale in 1999 should be : 17.71 thus it

would increase by 1.61 million. The sale of others would reduce by 1.61, which is 1.61/88.9* 100 = 1.62% ans





63

If kinetic shows same growth for





64

If kinetic shows same growth for next 2 years, then what would be

the sale in 2000?





65

Solution

Sale of kinetic in 1997 was :

104000,

Sale of Kinetic in 1998 :

113580

Growth rate is : 9580/104000 * 100

= 9.2% the same growth will continue in

next 2 years also 113580 * 1.092 *1.092 = 135440 answer





66

assuming the scooter market grows

by 5% for next 2 years and marketshare of LML and others remain

the same, then the market share of

Bajaj shall be

61%





67

assuming the scooter market

grows by 5% for next 2 yearsand market sale of LML andothers remain the same as in

1998, then the market share of Bajaj shall be

Total sale in 1998 was : 1262699 and itwill increase by 5% so it will increase to :1262699 +631349 = 1894048.





68

Solution «

The increase in sale is solely due to salein Bajaj, so the market share of Bajajshould be :

(61% of 1262699 + 631349)/ 1894048*100

74% answer

Which company has the maximum





69

Which company has the maximumratio of ad spend to cigarette sales?





70

Solution

For godfrey philips :

Ad spent : 50 against sales of : 1300

Thus it is : 3.84% For ITC it is 173/ 6700 = 2.58%

VST : 15/1400 = 1.05% approx.

STC = 19/600 = 3.166% Thus highest is in Godfrey Philips. Answer

I hi h h i f





71

In which year was the ratio of denudation the highest?





72

Solution

1996 : 1.2/3.2 * 100 = 33%

1993 : 2/8 *100 = 25%

1995 : 2/5.2 *100 = 38% So highest ratio is in 1995 answer

Which year witnessed the least





73

Which year witnessed the leastincrease in reserve against the

previous year?





74

Solution

Solve by observation. It is the least in1991 when it is close to 10% the least.

The highest growth is in 1990, when itgrows by 66% over the previous year. Answer

C it tili ti hi h t f





75

Capacity utilisation was highest for which vehicle and when?





76

Solution

By observation : motor cycles in 1999have capacity utilisation about 98%, whichis the highest for all. Answer.

What is the rate of growth of share





77

What is the rate of growth of shareof Asia in total business of

Kingfisher as per data given below





78

solution

Earlier Asian region accounted for :

5.4 + 11.1 = 16.5%

Now Asian region accounts for : 7.6 + 17.9 = 25.5%

It has grown from 16.5% to 25.5% that

means it has increased by 9%.

If 6(A¶s capital) = 8 (B¶s Capital) =





79

( p ) ( p )10 (C¶s Capial), what is the ratio of

their capital ?

Take LCM of 6, 8 and 10. The LCM is :

120 Now 6A = 120, so A = 20

8B = 120, so B = 15

10C = 120, so C = 12 Ratio is : 20: 15:12 answer.





80

If A :B = 3:4, B:C =5:6, C :D =11:9, what is the ratio of A:D?

A/B * B/C * C/D = A/D,

SO WRITE :

¾ * 5/6 * 11/9

WE GET : 55/ 72 OR 55: 72 ANSWER





81





82

Which of the following stocks had most variationsbetween opening and closing stocks?

Stocks Open High Low Close

7UP 49.16 49.8 49.16 49.16

ABATEX 0.91 0.91 0.91 0.91

ABCTRANS 3.3 3.39 3.14 3.35

ACADEMY 9.46 9.93 9.93 9.46

ACCESS 15.98 16.4 15.36 15.52

ACENINS 0.95 0.95 0.95 0.95





83

Solution

Access has the most variation betweenthe opening and closing stocks : variationsof .46 answer.

The result of an exam is given below Out of 1000





84

The result of an exam is given below. Out of 1000students who appeared(i) 658 failed in Physics

(ii) 166 failed in Physics and Chemistry(iii) 372 failed in Chemistry, 434 failed in Physics

and Maths

(iv) 590 failed in Maths, 126 failed in Maths andChem Assume all students failed in at least one subject.

How many failed in Physics but not in

Mathematics? Physics : 658, Physics+maths = 434

Physics but not maths : 658-434= 224 ans.

If proteins and sugar are consumed in the ratio





85

1:4, how many grams of proteins will be

required for a 200m jog?





86

Solution«

If we take 100 gram protein, we will take400 gram suger. The calorie intake is : 125+400 = 525

650/525 * 100 = 123.8

Thus 123.8 gram of protein must beconsumed for 600 m jug.

In the previous question, which





87

p qfood has the least number of

calorie per kg? A,B,C and D are the four foods. D has

maximum share of suger, but B has least

share of Fat which gives least calorie per gram. On calculation, we find that B givesthe least calorie per kg.





88

Based on previous table, how

many more kg of food C isrequired for a 100 m. run than

for 100 m. walk?

4.3 times

Food A and C are mixed in ratio of





89

1:2, what % of calorie come from

protein ?

26.67%

(take 100 g A and 200 g C, total proteinyou get is 40 + 40 = 80. thus you are ableto get 80 g protein out of 300 gram of totalintake. This is 26.67% answer)

In which year was actual Net revenue as a





90

ypercentage of estimated plan size highest?





91

Solution

Solve it and find that it is highest in 1994-95 which is 58% approx.

3808/6515*100 =58% approx.

A survey of moviegoers from five cities A to E : first





92

A survey of moviegoers from five cities A,to E : first

column gives the percentage of viewers in each city

who watch less than 1 movie a week. The second

column gives the total number of viewers who watchone or more movies per week. How many viewers in

city C watch less than one movie a week?





93

Solution

85/100 * 2400 = 2040

How many students with 2-3 years of work





94

y y

experience did not prefer marketing?





95

solution

Total students in 2-3 year experience :1080

Total students who opted for marketing :

(270 + 150 ) = 420

Thus there were 660 (1080 ± 420)answer.

The export of diamonds in 1996-97 was _______timesthe export of all other gems and jewellery put together





96

the export of all other gems. and jewellery put together including sales to foreign, tourist.





97

Solution «

14917/3300 = 4.5 times approx.

What is the change (in percentage) in the share of public issues in between August µ97 and





98

public issues in between August 97 andDecember µ97?





99

Solution

In august it was 24% approx.

(207 / 852 * 100)

In December it was 545/5042 * 100 =10.8%

Thus there is decline of 13.2 points.

With reference to the table below what is the cost





100

With reference to the table below, what is the costincurred in the new µcoding¶ stage?

S





101

Solution«

18 * 10 * 1000 = 180000 answer





102

Excluding Latin America, what was the sale of





103

electronics items in 2003 (figures in bracket show

annual growth rate)?

l ti





104

solution

114200 US$ million answer.

(add 13000 * 100/ 90 + 42000 * 100/95 +49000 * 100/98 + 9000 * 100/92) answer

What part of the total electricity produced in 2002





105

What part of the total electricity produced in 2002was contributed by Nuclear power plants?

S l ti





106

Solution:

13.32%

=312 / (980+1050+312) * 100 answer

For which crop, we had maximumi d ti d





107

area, maximum production and

maximum change in 94-2004?

S l ti





108

Solution..

Maximum area : maize (UL), maximumproduction : cant be determined, andmaximum change in area in maize (UL).

We cant know about production from thisgraph.

In which year is the profit per rupee





109

In which year is the profit per rupeeof equity the highest?

S l ti





110

Solution«

Divide profit by equity:

It is highest in 1991 : 6/10 = .6, which isthe highest. Answer.





111





112





113

What was average yearlypopulation of Argentina (in millions)





114

population of Argentina (in millions)

from 1995 through 1997?Population of South America in1995 = 150 millions

Population in 1995 : 37.5 million. Add16.7% growth, it becomes : 43.7 and add

14% growth, it becomes 49.88. theaverage of these three numbers is 43.7.answer.

Use relevant data from last





115

Use relevant data from last

question and tell : What is thefemale population of Peru (inmillions) in the year 2000?

Peru¶s population in 1995 is 12 million (8%of 150). We add growth it it. Thepopulation of 2000 is 22.36 ml. Now sex

ratio is 46%, so female population shouldbe 10.28 million. Answer.

The diagram in the left show marketing in green

and systems in blue. Marketing is further





116

y g

classified in right pie chart. Green and maroon

colour on right are what % of the systems?

11

if in the previous graph, the actual





117

p g p ,values are reduced by half, then

the maroon and blue combined isby what % more than red in the

left pie chart?

28% approximate.





118

The result of an exam is given below. Out of 1000students who appeared

(i) 658 failed in Physics

(ii) 166 failed in Physics and Chemistry

(iii) 372 failed in Chemistry, 434 failed in Physics andMaths

(iv) 590 failed in Maths, 126 failed in Maths and Chem

Assume all students failed in at least one subject.

Th number of students who failed in all the threesubjects is (1) 178 (2) 73 (3) 106 (4) 126

Solution





119

Solution«.

=1000- ((658 - (166+434)) +(372 -(166+126)) +(590 -(434+126))+(166+434+126)) = 106

answer.

solution





120

solution

Which of these had least cost per





121

room?

Solution





122

Solution..

Divide the cost by the number of rooms

We get Royal Holidays with minimum costof .41.

FEI: black: 1997, white : 1998.Which country had maximum





123

Which country had maximum

changein FEI?

soluton




124

soluton

Just by observation, we find the answer :China

Graph shows market shares, what




125

is the growth rate of company A?

Solution




126

Solution

Data inadequate ± as we don¶t know aboutvolume or price.

Graph shows market shares, what isthe growth rate of company A if total




127

the growth rate of company A, if total

volume has increased by 100% andvalue by 50%?

solution




128

solution

Inadequate information ± as we don¶tknow whether the growth rate is in termsof volume or price?

Graph shows market shares, what is theannual growth rate of company A (in terms




129

annual growth rate of company A (in termsof volume), if total volume has increased by

100% and value by 50%?

Solution




130

Solution«

Suppose total volume was 100 in 1991,then the company A had 25. in 2001 totalvolume should be 200, company A should

have 50. Thus there is growth of 25 on 25= 100% growth. Divided by 10 years, weget annual growth rate of 10%. Answer.




131

A, B, C and D are 4 villages on a straight road inthat order, given that B is equidistant from A andC while C is equidistant from B and D. Two girlsReena and Sheena decide to walk from A to D,covers the distance walking at 3 km/hr and

Sheena covers the first lap (upto B) at either 1 or 4 km/ hr and then walked at the other speed till

she meets Reena. Thereafter they walk together to D at Reena µs speed. Where did Sheena meetReena?

Solution




132

Solution«

Suppose the total distance is 120 km. We have threegaps of 40 km each.

The average speed of seena from A to C is : ¼ + 1/1= 5/4 multiply it by ½, we get 5/8 reverse it : 8/5 = 1.6km per hour. Thus Seena should first travel by 1 kmper hour and then by 4 km per hour. Till Seena reachC, (80/1.6) = 50 hours ± Reena should cover 50 * 3 =150 km. Thus as per the logic they will never be ableto meet (If she starts with the speed of 1 km per hour) Thus there is inadequate information. If shestarts with the speed of 4 km per hour, there is apossibility that she can meet from B to C. «

Continued




133

Continued«

If Seena starts at 4 km per hour, then she isahead of Reena. Seena will take 10 hours tocover the distance from A to B. now she willmove at 1 km per hour. And now Reena willmeet her. By the time Reena reaches B, Seenais at : 3.33 km from B. Now Reena will meet her at 3.33 / (3-1) = 1.66 hours. Thus they will meetbetween B and C. Now they will move @ 3 kmper hour. Thus from B to D, they will take 80/3 =

26.6 hours to complete the journey as per our asumptions. We need exact distance tocalculate the point where they met.

Data sufficiency question:




134

In terms of m, y is what percent of x?

(A) m > 0

(B) x is m percent of y

(1) (A) or (B) alone, but not by other statement

(2) Either statement

(3) Both statements together (4) Cannot be answered

Rolling 6 dice it is found that :




135

Rolling 6 dice, it is found that :

1. 3 dice show same numbersand rest show different numbers2. only one dice show 6

3. only 1 dice show 1, what ismaximum and minimum no.

greater than 3? Minimum = 1, maximum = 5.

A watch reads 4.30. if minute handpoints east in which direction will




136

points east, in which direction will

the hour hand point?

North east

.333 of a number is .001 of




137

another number, what is theratio of the two numbers?

Let us assume the 1st number to be 3, it

.33 is 1. now the second number is 1000 Thus ratio is 3: 1000 or 1:333 answer.

Or

Let us assume the 1st

number to be x. thefirst solution is .33X the second number is: .33x / .001, solving it we get : 333 x

Thus the ratio is 1: 333 answer.

1.5 of a number is 6 times another number, what is the ratio of the two




138

number, what is the ratio of the two

numbers?

Let us assume the first number to be 100.

1.5 of this number is 150. This is 6 times another number, so divide

it by 6, we get : 25

The ratio is 100 : 25 Or 4:1 answer.

Shabnam wants to go to IIM, shestarts from her home which is East




139

starts from her home, which is East

facing. She comes to a crossing.The road ahead takes to a hospital,

the road to left takes to Gujarat

University, in which direction is IIMfrom her home?

South ± East

A taxi goes 20 Km north, turns right




140

and goes 30 km then turns rightagain and goes 35 km. Now

turning left goes 15 km. Finally

turns left and again goes 15 km. inwhich direction and how far is thetaxi from the original starting

position? 45 km east from the starting point.

a to f are 6 members in a family.There are 2 couples D is brother




141

There are 2 couples. D is brother

of F and both are lighter than B,who is mother of D and lighter thanE. C is a lady and is neither the

heaviest or the lightest in thefamily. E is lighter than C. the

grandfather is the heaviest. E is a

man. Show the family diagram andas per weight also.

Solution«




142

Solution«

The grandfather is A, and couples are AC(A is man, C women), EB (E is man and Bis woman) and we have two kids : F and

D. The relation as per weight is clear. The

heaviest is A, followed by C, E B and then

we have D and F. we don¶t know who islighter among D and F.

A t F b f f il Th




143

A to F are members of a family. There are

1doctor, 1advocate, 1engineer, 1housewife,2 students in the family. There are 2

couples. F is the father of E and is doctor. Ais girl student and her husband is not an

advocate. B is the grandmother of D and ishousewife. Her husband is an engineer. Dis sister of E. What is the profession of A¶s

husband?

Solution«




144

Solution«

A¶s husband is a doctor by profession.

P starts crossing the fielddi ll ft lki h lf




145

diagonally after walking half way

he turns right. Walks samedistance turns left. Which direction

is he facing now?

p

q

R

S

NORTHSOUTH

From the original position, P & Qmove clock wise and cover half




146

move clock wise and cover half

distance. R & S move anticlockwise and move one side distance.Both the groups then cross over

diagonally opposite direction. If original configerationis PSQR, what

is new configuration?p

S

R

Q

Solution«




147

RQSP

From the original position, P & R




148

move diagonally opposite corners.

Then they move one side anticlockwise and clock wise respectivley. S

and Q move two sides each clockwise and anticlock wise. Where isP now?

pr

QS

NORTHSOUTH

SOLUTION




149

SOUTH WEST CORNER POSITION.

From the original position, P & Rmove diagonally opposite corners




150

move diagonally opposite corners.

Then they move one side anticlockwise and clock wise respectivley. Sand Q move two sides each clock

wise and anticlock wise.Who is atnorth west corner now?

p

s

R

Q

NORTH SOUTH

SOLUTION




151

R

Is X > 3?1. x^2 ± 8x +12 < =0




152

2. x^2 ± 2x ± 8 < = 0 No answer is possible as we cannot draw

the answer from either statement.

Formula :[ - b + - sqrt (b^2 - 4ac) ]/ 2a

= 8 + 4 / 2 and ( 8 ± 4) / 2

We get x = 6 and 2

(2 + sqrt(4 +32) /2 = 4 and - 2 we get x = -2 and 4 from second equation.

Is sqrt x > 1/x ?




153

q

1. x > 0

2 x < 0

Try from .04 and 4 we cant get the

answer.

Answer cannot be drawn from either statement.

The sum of an infinite GP : p,1,1/p, 1/p^2 «. Is a / 2, what is the




154

value of p? Sum of infinite GP = a / (1 ± r)

P / ( 1 ± 1/p) = a / 2

2p = (ap ± a) /p

2p^2 = ap ± a

P^2 = ap ± a / 2

P = sqrt ((ap ± a ) / 2 )

If : (3+5+7««nth term) /(5+8+11«.10th term) = 7 , what is




155

n ? Sum of AP = n/2 (2a + (n-1)d)

A = first term

D = difference = sum of the denominator series is 185

Numerator series / 185 = 7, so numerator

series total = 1295 =n/2 (6 + (n-1) 2) = `1295

Continued«




156

n/2 (6 + (n-1) 2) = ̀ 1295 =n (6 + 2n ± 2) = 2590

=6n + 2n^2 ± 2n = 2590

2n^2 +4n ± 2590 = 0 [ - b + - sqrt (b^2 - 4ac) ]/ 2a

= (( -4 + sqrt(16 + 20720)) / 4

=( - 4 + 144) / 4 =35 answer




157

A vending machine has 5 switchesfor coke,7up,maza,limca,pepsi.




158

, p, , ,p p

Each switch gives 2 differentdrinks. Each drink can be obtainedfrom 2 switches. If two switches are

pressed, if there is common drink,nothing will come out, otherwise

you will get the drink desired. Press

the right combination for getting thedrink. .

1+3 = 7up and maza, 1+2 =k i 1 4 li k




159

coke, pepsi, 1+4 = limca,coke,maza, pepsi switch 1,2,3,4,5don¶t give 7up, limca,coke,

maza, pepsi respectivley.

What is 2+3?

Maza + Limca+ 7up c,m,p,7up Coke maza pepsi, limca, 7up

Answer : pepsei, limca, 7 up

Solution «




160

Prepare a matrix of rows and columns withdrinks in one side and switch in one sideto know the right combination.



What should you turn on for limca +coke ?




162

coke ?

2,3

1,2,3,5

1,3,4

2,3,4

Answer : 1,2,3,5




163

7up pepsi coke maza limca

1 x x y Y x

2 y x x x

3 Y x x x y

4 x y x x Y

5 x x y y x




164




165

How many integers N are theresuch : r < n < s?




166

1. s-r = 5 2. r & s are not integers

Both the statements are required.

What is the time differencebetween NY and London?




167

between NY and London?

1. departure time at NY is 9 amand arrival time at London is 10

am (both local times)2. flight time is 5 hours.

Both the statements are required.

X says to Y : ³ I am 3 times as oldas you were 2 years ago.´ how old




168

y y g

is x?1. Y¶s age 17 years from now is

same as X¶s present age

2. X¶s age nine years from now is 3times Y¶s present age

Answer can be drawn only from the 1st

statement.

In a row of poles, one pole is 11th




169

from either side. How many polesare there is in the row :

10 poles before and 10 after

Total we have 10 + 10 + 1 = 21 answer.

A,B,C are standing in a queue.




170

g q

There are 5 persons between A andB and 8 persons between B and C.if there are 3 persons ahead of C

and 21 persons after A, what couldbe the minimum number of persons

in the queue?

Answer is : 28 answer



Maximum 36 vehicles are markedin a parking lot in a single row




172

in a parking lot in a single row.

After the first car, there is onemore bike. After the 2nd car thereare 2 bikes and after 3rd car, thereare 3 bikes and so on. How manybikes are there in the second row?




173

A performance review table isincomplete with some more

d t il




174

details«

Additional information




175

Half the workers were either excellent or good.

40% of the workers were females.

One third of the male workers wereaverage.

How many students are both female and

excellent

Solution«




176

avg good

excelle

nt total

male 16 22 10 48

female 24 8 0 32

total 40 30 10 80

answer




177

Zero

In which month was the greatest absolute changein market value for any share recorded?

(black bar = XYZ white bar = ABC )




178

(black bar = XYZ, white bar = ABC )

SOLUTION«




179

MARCH (by observation, we find the shareprices of XYZ have increased by some17 points)

The average market value of XYZ.shares is, by what percent less or

th th f ABC? (bl k




180

more than the same for ABC? (black

bar = XYZ, white bar = ABC )

SOLUTION




181

ABC is approx. 75

XYZ is approx. 103

The difference is : 28

28/75 *100

=36% approx. answer.

(black bar = XYZ, white bar = ABC ), market capitalisation

means no. of shares * market price. Both companies have

1000 shares. What is the maximum market capitalisation of




182

any company over the period?

Solution«




183

The highest price visible is of ABC of 68 inthe month of April.

68 *1000 gives us 68000. thus highest

market capitalisation possible is 68000 for ABC.

Which Lok Sabha had minimumseats?




184

Solution«




185

We have to calculatethe number for eachloksabha. We findthat it is least in the

first lok sabha itself. Itis 499 for the firstyear.

498.8662132500

502.9585799

523.6486486521.3270142

544.4126074

543.6893204

550

517.2413793

544.6927374





What will be next in the series:4, 5, 9,18,34 «




188

Options:

43, 59, 50, 49

Solution«

4 + 1, = 5, 5 + 4 = 9, 9 + 9 = 18«. So on,we can see that only square values inseries are added ± thus the next value to

be added will be 25, so 34 + 25 = 59 .

What will be the next in the series :66,36,18 «




189

Options: 3,6,8,9 Solution:

6 * 6 = 36,

3 * 6 = 18

1 * 8 = 8

So next number will be 8 .

What will be the next in the series :21,25,33,49,81,..




190

Options: 145,111,113,127 Solutions

Look at the differences : 4,8,16,32 so on. Itis a series :

Thus next number will be : 81 + 64 = 145

ans

What will be the next in the series :12,32,72,152 «




191

Options : 313, 312, 315, 512

Solution:

Look at the difference :

20,40,80,160«

Thus next number shouold be :

152 + 160 = 312 answer.

DATA SUFFICIENCY QUESTION: Vishaltakes morning train to his office from Bikaner to




192

takes morning train to his office from Bikaner to

Delhi. His colleague Tarun joins him on theway. There are three stations A,B,C on the way

(not necessarily in this order), What is the

sequence of these stations?

STATEMENTS: `1. Tarun joins at B 2. Mr. Jitesh who travels between A & C is

with Vishal and never travels with Tarun.

Solution«




193

Both the statements are inadequate toanswer : as we don¶t know out of A and Cwhich comes earlier. There is not

confirmed information in the question.

Data sufficiency question«What is the value of prime number

X?




194

X?

X ^2 + x is a two digit number greater

than 50 X^3 is a three digit number

Solution«

Both the statements are required to givethe answer. ± as 7 is the only primenumber which fulfills both the conditions.

DATA SUFFICIENCY QUESTION: Vishaltakes morning train to his office from Bikaner

to Nokha and was delayed by 40 minutes




195

to Nokha and was delayed by 40 minutesdue to engine trouble. What is the distance

beteween bikaner and Nokhastatements :

1. Engine trouble developed after 40 kmfrom Bikaner and speed reduced by 1/4th of

the original speed2. engine trouble developed after 2 hours of

journey and speed reduced by 1/4th.



Read this table carefully and answer: Whatper cent of Karnataka¶s railway network has

broad gauge tracks?




197

solution




198

Total rail network in Karnakatak : 552 Thus 365/552 *100 gives 66.12% answer.

Read it and answer If the share of system software in the

total remains same 1990 as in 1988; and in 1990, the total

exports is Rs. 9,000 the system software export in 1990 is




199

Solution«




200

2800 / 6300 * 9000 = 4000 answer

Read it and answer If the share of system software in

the total remains same 1990 as in 1988; and in 1990,

the total exports is Rs. 9,000 the financial software

export in 1990 is




201

Solution




202

Answer cannot be determined.

y ow many mes as s o vbharati and Primary channel) commercialearnings increased over the given period?




203

Solution«




204

AIR revenue increased from 6.26 to 81over the period of time.

Thus it has increased by : 12.9 times.

81 has been arrived by adding 37.3 and43.7 (both the channels).

If 50 units each of A and B areproduced, which machine has been

poorly utilised?




205

poorly utilised?

solution




206

Except in machine 2nd, all the macines arehaving 100% capacity utilisation.

You can see this for machine 1 as : 50 * 3

+ 50 * 4 = 350 Answer = 2nd machine

I go 2 km towards east, I turnright and go 1 KM then I




207

g gagain turn right and I go 1

KM. In which direction am I

now from my starting point? Answer: south east

A three CM cube has beenpainted red on all its sides. It is cut




208

into one CM cubes. How manycubes will be there with one side

painted red?

26 cubes will have one or more sides painted,

out of these, some will be having 2 sides paintedand some 3 sides painted. The number of cubeshaving only one side painted will be : 6 answer.

X+y+z > 0, is Z > 1?Data sufficiency:

1) : Z > x +y, 2) : X+Y < 1




209

) y, )

Both the statements are not sufficient

X+y+z > 0, is Z > 0?Data sufficiency:

1) : Z > x +y, 2) : X+Y < 1




210

) y, )

1st statement alone is sufficient to answer the question.

Question on assumptions




211

: ³If you are beautiful, we will catch your beauty. If you are not, we will make

you beautiful.´ ²An advertisement of a

photo Studio.

I. How to look beautiful, is a problem

of youngsters?

II. Nobody desires to be beautiful

Answer «.




212

Only the first assumption is validassumption.

Question on assumption«




213

The integrated steel plants in India would no longer have to depend on imports for

continuous casting refractories.

I; Continuous casting refractories are.needed by India.

II. Continuous casting refractors are in

demand.



What is the missing number?




215

Solution«




216

Based on logic : 4+ 1 ± X = 4

SO X = 1.

FIND THE MISSING VALUE (hereinstead of 41 read 42)




217

SOLUTION«




218

The answer is 7, 7 * 4 = 28 and 7+4 = 11. answer




219

On rolling 6 dice, it is found that: I. Three of the dice show the same

number. The rest show different numbers.

II. Only one dice shows 6. III. Not more than 3 dice show 4 or more.

What is the minimum possible total of

numbers on the faces if the three diceshow the same number 2?

Answer«




220

The answer should be 21 with thefollowing breakup :

Three dice of 2 each One dice each of 4,5,6.

Total them up = 21. answer.

Question on puzzle




221



II. Only one dice shows 6. III. Not more than 3 dice show 4 or more.

What is the maximum total if 4 of the dice

show less than 4?

Solution«




222

Answer is 22 with the followingcombination:

Three 3 = 3* 3 = 9 One each of 2,5,6 = 13

Total 22. answer.

Puzzle«




223

On rolling 6 dice, it is found that:

I. Three of the dice show the same

number. The rest show different numbers. II. Only one dice shows 6.

III. Not more than 3 dice show 4 or more.

If only 1 dice shows 1, what is themaximum number of dice with numbersgreater than 4?

Solution«




224

Answer is 2.

Puzzle «




225



II. Only one dice shows 6. If only 1 dice shows 1, what is the

maximum number of dice with numbers

greater than 4?

Solution«.




226

We can take as under :

6,5,5,5,4,1,

Thus answer is 4.

After his.oftlce, in the evening, aman walks facing the sun. He turns




227

first to his right, then to his left andagain to his left and then to hisright. In which direction is he

moving now?

Solution«




228

He is moving towards west. You cancancel two left movements and two rightmovements by each other.

Starting from a point, Jitendrawalked 12 m towards North, he




229

turned right and waked 10 m, heagain turned right and walked 12m,

then he turned left and walked 5 m.How far is he now and whichdirection from the starting point?

Solution«




230

15 m. east

What is the all India annual growth rate

in demand of X as the following table?




231

Solution«




232

A compound growth rate of 14.14 willmake 146.54 to 283.9 in 5 years.

146.54* (1.1414)^5 = 283.9

Out of these, which region hadhighest growth rate?




233

Solution




234

The highest growth in the East section (in%)

In absolute terms, the highest growth rate

is in South region

WHAT IS THE NET DEMAND ATB?




235

SOLUTION




236

THE NET DEMAND AT B IS 1200 ± (250 + 550) = 400. ANSWER.

FOUR FRIENDS ARE SITTING IN A ROW TO BE PHOTOGRAPHED.




237

D IS TO THE RIGHT OF B. C IS NEXTTO B. A IS AT ONE EXTREME. B IS NOTIN MIDDLE. THERE IS ONLY ONEPERSON TO THE LEFT OF C.

WHAT IS THE EXACT ORDER OFSITTING ARRANGEMENT?

SOLUTION

ND




238

PUT C IN 2ND POSITION FROM LEFT AND A AND B IN EXTREME POSITIONS

ADCB Answer.

Four friends are beingphotographed?

D IS TO THE RIGHT OF B C IS NEXT




239

D IS TO THE RIGHT OF B. C IS NEXTTO B. A IS AT ONE EXTREME. B IS NOTIN MIDDLE. IN THE PHOTO THAT WETAKE, THERE IS ONLY ONE PERSONTO THE LEFT OF C.

WHAT IS THE EXACT ORDER OFSITTING ARRANGEMENT?

SOLUTION

NOW WE HAVE TO PUT C AT 2ND




240

NOW WE HAVE TO PUT C AT 2ND

POSITION FROM LEFT FROMOBSERVER¶S PERSPECTIVE.

A AND B ARE AT THE TWO ENDS. SITTING ARRANGEMENT IS :

ACDB.

ANSWER.

There were 6 cars in an exhibition. Alto was to the immediate right of

Swift. Spark was between

b d d I di I10 t




241

ambassador and Indica. I10 was atone of the extreme ends. If youtake the third car from your right(when you observe these cars),then you find a car whose name

starts from I. What is the 3rd

car from your left?

Solution«

It ill b ith k ift




242

It will be either spark or swift (draw the maps and solve it).

6 friends are getting photographed.They are sitting in a row. A and C

itti t th D i t th




243

are sitting together. D is to theimmediate right of B. C is in the 2nd

position from left (when you

observe them), E and F are in themiddle. There are three persons to

the left of E. A is to the right of

maximum number of persons.What is the correct sitting order?

SOLUTION«.

Th t l ti i




244

The correct solution is : ACEFDB

ARGUMENT«.

Sh ld th b ld t?




245

Should there be world government? A 1. yes, it will help in eliminating tensions

A 2: no ± then only developed countries

will dominate. ANSWER :

Both the arguments are logicalarguments«

QUESTION ON BLOODRELATION«

R ³h i th h b d f X h i




246

Ram says: ³he is the husband of X, who isthe daughter of Y, who is daughter of Z,who is my father.´. What is the relationbetween Ram and Y.

ANSWER :

Ram and Y are brother and Sister.

QUESTION ON CODING :

A COMPUTER USES FOLLOWING




247

A COMPUTER USES FOLLOWINGSYSTEM WHILE SOLVING:

Input : 23, 09, 320, 90, 12,

1st step: 320, 23, 09, 90, 12 2nd step : 320,90,23,09,12

3rd step & Output: 320,90,23,12,09

In how many step will following input besolved : 90,121,94,23,233,898,22,400?

Solution«

I t 90 121 94 23 233 898 22 400?




248

Input : 90,121,94,23,233,898,22,400? 1st step: 898, 90,121,94,23,233,22,400

2nd step: 898,400, 90,121,94,23,233,22,

3rd

step: 898,400,233, 90,121,94,23,22, 4th step: 898,400,233,121,90,94,23,22.

5th step: 898,400,233,121,94,90,23,22

Thus the question is solved in 5 steps. Answer.

SYLLOGISM

1 ll t




249

1. : all rooms are stones 2. all stones are diamonds

Conclusion:

1. All rooms are diamonds2. All diamonds are rooms

3. All stones are rooms

4. No conclusion can be drawn

Answer

Onl 1st concl sion can be dra n




250

Only 1st conclusion can be drawn



Answer





252


Read the information carefully: A,D, F,M are girls

A,D,E,F,G,H, are intelligentB C D E F G h d ki




253

B,C,D,E,F,G, are hardworkingC,D,E,G,H,M are honest

A,B,C,D,E,F,M,H are ambitiousBoys play Cricket, Girls playChess

name the persons, who areambitious chess players.

solution

A D F M are the ambitious chess players




254

A,D,F,M are the ambitious chess players


A D E F G H are intelligent




255

A,D,E,F,G,H, are intelligentB,C,D,E,F,G, are hardworkingC,D,E,G,H,M are honest

A,B,C,D,E,F,M,H are ambitious

Boys play Cricket, Girls play Chessname the persons, who are the chessplayers, who are neither honest, nor

hardworking, ambitious , intelligent?

Answer

None




256

None


A D E F G H are intelligent




257

A,D,E,F,G,H, are intelligentB,C,D,E,F,G, are hardworking

C,D,E,G,H,M are honest

A,B,C,D,E,F,M,H are ambitiousBoys play Cricket, Girls play Chessname the persons, make a cricket team

of hardworking, intelligent and honestplayers

Solution«

E and G




258

E and G.

2^a = 3^b = 6^-c , what

is value of 1/a +1/b +1/c?

L t l hi h





259www.afterschoool.tk

Let us assume a value which we can equate with all these values. (use log table for solving this question).

Let us take all these values equal to 1. thus value of A, B and C are equal to Zero. Thus the answer is Zero.

We can also assume these values to be equal to 6.

A = 2.6, B =1.65 and C = -1

Now putting these values: ½.6 +1/1.65 ² 1

Log T + Log (T-3) = 1,

what is T?

We know that Log 10 = 1 (Log 10 )






We know that Log 10 = 1. (Log 10

10 )

In log, we multiply, where the symbol is +.

Thus t * (t-3) = 10 ; T^2 -3T =10;

T^2 -3t -10 = 0

T^2 ² 5T + 2T -10 = 0

T (T-5) +2 (T-5); T-5 = 0 or T =5; T+2 =0

T = 5 or -2

Thus T = 5 answer.

Sum of 2 numbers is 52 and their difference is 2.

what are the numbers?X Y 52






X + Y = 52

X ²Y = 2

A

dd these: 2

X =54; X =

27

Y = 25 answer.

Diagonal of rectangle is 5 CM. One of its side is 4

CM. Its area is ?L t fi d th th id






Let us find the other side.

As per pythogorus rules, other

side is sqare root of (5^2-4^2) =

square root of (25-16) = square

root of 9

Other side is 3.

Area = 4*3 =12 answer.

Fourth part of a number exceeds the sixth part by

4. what is the number?






X / 4 ² X /6 = 4

(6X-4X) / 24 = 4

2X = 96 X = 48 answer.

twice the smaller number is

less than twice the greater

one by 18 and 1/3 of smaler






one by 18 and 1/3 of smaler and 1/5 of greater number

are together 21. What are

numbers? Bigger number = X , smaller no. = Y

2X-2Y = 18; 1/5 X + 1/3Y = 21

Let us multiply second eqation by 10, we get: 2X + 10/3

Y = 210. Subtract this equation from 1st. We get -16/3 Y

= -192 Y = 192 *3/16 = 36. thus smaller number is 36. Putting

this in first equation, we get 2X = 90 or X = 45 answer.

.

is five times the sum of its

digits. If 9 is added to it,

digits are reversed What is






digits are reversed. What is the number? Let us assume unit digit to be X & digit

at tenth place to be Y.

The number is : 10Y +X

10Y +X= 5 (X +Y)

(10Y +X ) +9 = 10X +Y or 9y-9X = -9 or

Y-X =-1 10Y ² 5Y=5X-X or 5Y = 4X or Y = 4 and

X = 5 thus number is 45.

Solve such uestion b o tions.

Find the fraction which is equal to ½ when both its

numerator and denominator

are increasd by 2 and is






are increasd by 2 and is equal to ¾ when both are

increased by 12? Options: 3

/8,

5/8, 3

/8,

2/3

Try from options. First option

gives you answer. If you add 2 in

each, you get 5/10 (which is ½)

and if you add 12 in both the

digits, you get 15/20 (which is ¾).

Thus option 1 gives answer.

If X: Y = 3:4, value of

x^2y +xy^2 :x^3+y^3?

Putting X = 3 and Y = 4






Putting X = 3 and Y = 4.

36+48: 27+64

84:91

(divide b

oth the numb

ers by 7).

= 12:13 answer.






2s-p:3t-p then which is true:

p^2= 6st or p =6st or 2p

=3st






=3st Try from options.

Let us assume that P = 6. and as

per first option, St = 6. Let us try putting values in s and t and if we get correct answer , we get answer. S = 2, T = 3 or 4:9

We get next ratios as : -2: 3(which is subduplicate ratio of 2s:3t) thus this is the answer.

ABOUT AFTERSCHOOOL

Afterschoool conducts three year integratedPGPSE ( ft l 12th l ith IAS / CA /






y gPGPSE (after class 12th along with IAS / CA /

CS) and 18 month PGPSE (Post GraduateProgramme in Social Entrepreneurship) along

with preparation for CS / CFP / CFA /CMA /

FRM. This course is also available online

also. It also conducts workshops on social

entrepreneurship in schools and colleges all

over India ² start social entrepreneurship

club in your institution today with the helpfrom afterschoool and help us in developing

society.

Why such a programme?

To promote people to take up






To promote people to take up

entrepreneurship and help develop

the society

To enable people to take upfranchising and other such options

to start a business / social

development project

To enable people to take up social development as their mission

To enable people to promote

Who are our supporters?

Afterschoolians our past






Afterschoolians, our past

beneficiaries, entrepreneurs

and social entrepreneurs are

supporting us.

You can also support us ² not

necessarily by money ² but by

being promotor of our concept and our ideas.

About AFTERSCHOOOL PGPSE ²

the best programme for

developing great entrepreneurs

Most flexible adaptive but rigorous






Most flexible, adaptive but rigorous

programme

Available in distance learning mode

Case study focused- latest cases Industry oriented practical

curriculum

Designed to make you entrepreneurs

² not just an employee

Option to take up part time job ² so

earn while you learn

Workshops from

AFTERSCHOOOL

IIF, Delhi






IIF, Delhi

CIPS, Jaipur

ICSI Hyderabad Branch

Gyan Vihar , Jaipur

Apex Institute of Management,Jaipur

Aravali Institute of Management,Jodhpur

Xavier Institute of Management,Bhubaneshwar

Pacific Institute, Udaipur

Engineering College, Hyderabad

Flexible Specialisations:

Spiritualising business and society






p g y

Rural development and transformation

HRD and Education, Social Development

NGO and voluntary work

Investment analysis,microfinance and inclusion

Retail sector , BPO, KPO

Accounting & Information system (with CA / CS /CMA)

Hospital management and Health care Hospitality sector and culture and heritage

Other sectors of high growth, high technology and social relevance

Salient features:

The only programme of its kind (in the whole world)






No publicity and low profile course

For those who want to achieve success in life ² not just a degree

Indepth knowledge and expertise

Professional approac: World class approach Strong intellectual and business capabilities

Flexible ² you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes

Scholarships for those from poor economic b

ackground Latest and constantly changing curriculum ² keeping pace with the time

Placement for those who are interested

Admissions open throughout the year

Latest and most advanced technologies, books and

Components

Pedagogy curriculum and approach based on IIMAhmedabad and ISB Hyderabad (the founder is alumnus






Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad)

Meditation, spiritualisation, and self development

Essential softwares for business

Business plan, Research projects

Participation in conferences / seminars Workshops on leadership, team building etc.

Written submissions of research projects/articles / papers

Inter view of entrepreneurs, writing biographies of entrepreneurs

Editing of journals / newsletters

Consultancy / research projects Assignments, communication skill workshops

Participation in conferences and seminars

Group discussions, mock inter views, self development diaryng

Mind Power Training & writing workshop (by Dr. T.K.Jain)

Pedagogy

Case analysis,






y ,

Articles from Har vard Business Review

Quiz, seminars, workshops, games,

Visits to entrepreneurs and industrial visits

Presentations, Latest audio-visuals

Group discussions and group projects

Periodic self assessment

Mentoring and counselling

Study exchange programme (with institutions out of India)

Rural development / Social welfare projects

Branches

AFTERSCHOOOL will shortly






AFTERSCHOOOL will shortly open its branches in important cities in India including Delhi,

Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and

developing these branches ² and for promoting social entrepreneurs.

Case Studies

We want to write case studies






We want to write case studies

on social entrepreneurs, first

generation entrepreneurs,

ethical entrepreneurs. Please help us in this process. Help us

to be in touch with

entrepreneurs, so that we may develop entrepreneurs.

Basic values at

afterschoool

Share to learn more






Interact to develop yourself

Fear is your worst enemy

Make mistakes to learn

Study & discuss in a group

Criticism is the healthy route to mutual support and help

Ask fundamental questions : why,

when, how & where? Embrace change ² and compete with

yourself only

www.afterschoool.tksocial entrepreneurship for

better society



Date post:	10-Apr-2018
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16927911 Data Interpretation

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