Quantitative Aptitude & Mathematics 11 October

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MAGIC MATHSDr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

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If 4^(2x) – 2^(2x) = 12, what is X?

• 2^(4x) – 2^(2x) = 12

• Let us assume 2^(2x) = Y

• Y^2 – Y = 12

• Y^2 – Y – 12 = 0

• Y^2 -4Y +3Y – 12 = 0

• Y(Y – 4) +3(Y – 4)

• Y = 2^(2x)=4 Thus X = 1 answer.


If 2^(X+4) – 2^(X+2) = 3, what is X?

• (2^X+2^4) – (2^X+2^2 )= 3

• 2^x (2^4 – 2^2 ) = 3

• 2^x (16-4) =3

• 2^x *12 = 3

• 2^x = 3/12

• 2*^X = ¼

• 2^(-2) = ¼ thus X = -2 answer.


Sqrt (5 +X ^1/3 ) = 3, what is X?

• Sqrt = Square Root

• Let us square both the sides

• 5+ X^1/3 = 9

• X^1/3 = 4

• Let us make cubes of both the sides

• (X^1/3 )^3= 4^3

• X = 64 answer .


What is the unit digit in the product of 7^35 * 3^21 * 11^55

• We know that 7^4 gives (2401) a unit digit of 1. Thus 7^32 gives unit digit of 1. 7^3 gives unit digit of 3.

• 3^4 gives (81) unit digit of 1, thus 3^20 gives unit digit of 1. 3^1 = 3. thus 3^21 gives unit digit of 3.

• 11^55 gives unit digit of 1.

• Thus 3*3*1 gives unit digit of 9 answer.


Which of the following is the largest number?

• 3^1/3• 5^1/5 • 2^1/2• 7^1/7• Solution: • Let us find LCM of 3,5 it is 15. Let us find out

3^ (1/3*5/5) and 5^(1/5*3/3) • 3^(5/15) and 5^(3/15) ; let us solve

numerator.


Solution . . .

• 3^5 (1/15) = 243 ^1/15• 5^3(1/15) = 125 ^1/15• Thus first number is bigger• 3^1/3 v/s 2^1/2• Take LCM of 3 & 2 it is 6• 3^ (1/3 *2/2) and 2^ (1/2*3/3) Thus we have 9^1/6 and

8^1/6. Again the first is bigger• 3^1/3 V/S 7^1/7; LCM of 7 & 3 = 21• 3^ (1/3*7/7) and 7^(1/7*3/3) • Thus we have 2187^1/21 and 343^1/21. Thus again

3^1/3 is bigger. Answer.


One eighth of a pencil is black. Half of remaining is yellow and

remaining 7/2 CM is blue. What is the total length of the pencil?

• Let us assume that the length of the pencil is X. 7/8 X * ½ = 7/2 CM

• 7/16 X = 7/2 or X = 8 answer.


If 2^(X-1) + 2^(X+1) =320, what is X?

• 2^(X-1) + 2^(X-1)^2 =320

• 2^(X-1) (1 + 2^2) =320

• 2^(X-1) *5 =320

• 2^(X-1) =64

• 2^6 = 64

• Thus X – 1 = 6

• X = 7 answer.


If 2^(2x-1) = 1/ (8^(X – 3)), then what is X?

• 2^(2x-1) =8^(-X +3)

• 2^(2x-1) =2^3(-X +3)

• Let us take base 2 as common.

• 2X-1 = -3X + 9

• 5X = 10

• X = 2 answer.


3^(4x-2) = 729, what is X?

• We know that 3*3*3*3*3*3 = 729

• 3^6 = 729

• 4X – 2 = 6

• 4X = 8

• X = 2 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

only


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