statistics & business problems 8 oct

www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

QUANTITATIVE APTITUDE AND MATHEMATICS

AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS

CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –

World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship

OPEN FOR ALL FREE FOR ALL

QUANTITATIVE APTITUDE AND MATHEMATICS

Dr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

Bikaner M: 9414430763

tkjainbkn@yahoo.co.in

www.afterschool.tk, www.afterschoool.tk

The Area of a right angle triangle is 1/2X^2 +2x +3/2, what is its height, if it is given that height is more than

• We know that the area = ½ * base * height

• Let us look at the area: • ½ X^2 +2X+3/2 or ½ (X^2 +4X+3)

• Or ½ (X^2 +3X +X +3)

• =1/2 (X(X+3) +1(X+3))

• =1/2 ((X+3)(X+1)) thus base and heights are (x+1) and (X+3) respectively. Ans.

If (X+1) is HCF of (AX^2+bX +C) and (BX^2 +AX+C), then what is

the value of C? • Both the numbers are divisible by (X+1)

because it is HCF (Heightest Common Factor).

• X = -1. thus if we put the value of X as -1, it will equate the equation to Zero

• AX^2+bX +C = 0 (if X = -1)• A – B +C =0 • BX^2 +AX+C or B – A + C = 0 OR C=0

IF (X-1) IS HCF OF (X^2-1) AND (PX^2-Q(X+1)) THEN WHAT IS P?• X = 1, so if we put the value of X as 1, it

will make the equation equal to zero.

• (PX^2-Q(X+1)) = 0• P – Q- Q = 0

• P – 2Q = 0

• P = 2Q answer.

If 6/X + 3/Y = 7 and 3/X +9/Y =11, then what is the value of X?

• Let us assume that 1/X = W and 1/Y = U

• 6W+3U = 7

• 3W +9U= 11 (Multiply 2nd equation by 2)• 6W +18 U = 22

• By comparing the first and 2nd equation, we get : 15U = 15 or U = 1 or Y=1; putting the value in first equation, we get:

• 6W +3 = 7 or 6W = 4 or W = 2/3; X = 3/2

3X+5Y = 0 and KX+10Y = 0, what is the value of K, if there are more

than 1 solutions? • Take 3 from first equation and K from 2nd

equation and 5 from first equation and 10 from 2nd equation.

• 3/K = 5/10• Solving this, we get:

• 5K = 30

• OR : K = 6 answer.

2X+3y – 5 = 0 ; 4X+KY-10 =0 AND THERE ARE

INFINITE NUMBER OF SOLUTIONS, THEN WHAT IS K?

• 2/4 = 3/k = -5/-10

• K = 6

2X+3y – 5 = 0 ; 4X+KY-Z =0 AND THERE NO

SOLUTION, THEN WHAT IS K & Z?

• A1/A2 = B1/B2 IS NOT EQUAL TO C1/C2

• =2/4 = 3/K is not equal to -5/Z

• Thus K = 6, but Z should not be equal to 10 , Z can take any other value. Ans.

2X+3y – 5 = 0 ; 4X+KY-10 =0 AND THERE IS A

UNIQUE SOLUTION, THEN WHAT IS K?

• A1/A2 SHOULD NOT BE EQUAL TO B1/B2

• THUS 2/4 SHOULD NOT BE EQUAL TO 3/K

• THUS K CAN TAKE ANY OTHER VALUE OTHER THAN 6 ANSWER

WHAT IS THE VALUE OF (8)^5/3 ?

• LET US SOLVE IT AS : ((8)^1/3)^5

• = ((2*2*2)^1/3)^5

• =2^5• =2*2*2*2*2 = 32 ANSWER.

WHAT WILL YOU GET BY SOLVING 625^-3/4?

• In order to solve the power of negatives, we will solve it as:

• (1/625) ^3/4• Now we will first solve ¼ and then 3

• =((1/625) ^1/4)^3

• =1/5^3

• =1/125 answer.

There are 50 tickets from 1 to 50. One ticket is drawn at random,

what is the probability that it is in multiple of 2 or 3?

• 50/2 = 25

• 50/3 = 16.66• 50/6 = 8.3

• Thus add 25+16 – 8

• = 33 / 50 answer.

In how many ways 5 persons sit on a round table containing 5 chairs? • (n-1)!

• =4*3*2*1

• =24 answer.

Which is the biggest: (2)^1/2, 3^1/3, 5^1/5 answer?

• 3^1/3 answer.

A,B,C start with equal capital. A leaves the business after 4 month. B doubles his capital after 6 month.

After 12 month, what is the profit sharing ratio among A,B,C for the

year? • Let us assume that each had 1 Rupee. • A = 1*4 month• B = 1*6 + 2*6 month

• C = 1*12 month = 4: 18: 12 or • =2:9:6 answer.

ABOUT AFTERSCHO☺OL

Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme 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 – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.

Why such a programme?

• To promote people to take up entrepreneurship and help develop the society

• To enable people to take up franchising 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 spirituality and positive thinking in the world

Who are our supporters?

• Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us.

• You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.

About AFTERSCHO☺OL PGPSE – the best programme for developing great

entrepreneurs• 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 – not just

an employee• Option to take up part time job – so earn while

you learn • The only absolutely free course on internet

Workshops from AFTERSCHO☺OL

• 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• 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 – not just a

degree• Flexible – 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 background• Latest and constantly changing curriculum – keeping pace

with the time• Placement for those who are interested• Admissions open throughout the year • Latest and most advanced technologies, books and study

material

Components • Pedagogy curriculum and approach based on IIM 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• Interview 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 interviews, self development diaryng • Mind Power Training & writing workshop (by Dr. T.K.Jain)

Pedagogy

• Case analysis,• Articles from Harvard 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

• AFTERSCHO☺OL 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 – and for promoting social entrepreneurs.

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 AFTERSCHO☺OL

• 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 – and compete with yourself

www.afterschoool.tk social entrepreneurship for better

society

statistics & business problems 8 oct

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