29 July Quantitative Aptitude Ii

QUANTITATIVE APTITUDE AFTERSCHOOOL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL

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QUANTITATIVE APTITUDE Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Squares of two consecutive positive integers differ by 1987, what is the sum of those two numbers?  X^2

– Y^2 = 1987  (X+Y) (X-Y) = 1987  Let us take factors of 1987  We are not able to find such numbers, which can be factors of 1987, therefore, there are no such numbers.

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Squares of two positive integers differ by 1100, what is the sum of those two numbers?     

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X^2 – Y^2 = 1100 (X+Y) (X-Y) = 1100 Let us take factors of 1100 The factors are 11*2*5*2*5 X +Y can be any of the sub factors like 11*2*5 or 11*5*5 or 11*2*2 or 11 or 11*2 or 11*5. Let us try with 11*2*5, thus X-Y = remaining factors = 2*5. We can have 110 and 10 as two factors X +Y = 110, X – Y = 10. solving, we get 2X = 120, X = 60, and 2Y = 100, Y = 50. thus their sum is 110 answer.

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The interior angles of a polygon are in arithmetic series with A = 120, and D = 5. How many angles are there in the polygon?  We

know that in triangle, the sum of angles is 180, in square, it is 360, in pentagon, it is 540, in hexagon it is 720, in septagon it is 900, for Octagon 1080 nanagon 1260 and so on.  Let us start with series : 120+125+130+135+140+145+150+155+ 160 = thus there are 9 angles. www.afterschoool.tk

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We have one defective weight in X number of weights. We know that we can check it in only 3 wighings. Can you tell us, what is the maximum value of X?  

Options: 24,25,26,27 Let us try with maximum from these, the maximum is 27. in first weight, we will compare the in three groups as 9,9, 9. the group with different weight will be taken away. Now we will form groups of 3,3,3, and the group with different weight will be taken away, now we will compare 1,1,1 and the weight with different weight will be identified. Anwwer.

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What is the number of integers that can be formed from 0,2,2,3,3,3,4. The integer must be more than 1 million.     

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1 million contains 7 numbers. We can have numbers like 2233340 etc. Formulae : N! / (Similar numbers)! =7! / (2! *3!) =5040/ 12 = 420 However, it contains numbers starting from 0 also. Thus we have to remove all those numbers also from this. Let us take 0 in the start now we have for remaining 6 numbers solution : 6! / (2!*3!) = 720/12 =60. Thus we have 420-60 = 360 numbers. Answer.

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There is a series. The series is 1!, 2!, 3!, 4! And so on. Suppose we add N terms of this series. This sum is always divisible by which of the following?  Options:

2,3,4,5,6,7  Solution: every factorial from 3! Onwards is always divisible by 3. 1! +2! Is also divisible by 3. Thus this sum is always divisible by 3 answer.

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ABO UT A FTERSCH OOO L 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.

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Why such a programme? 

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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

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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.

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About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs     

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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

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Workshops from AFTERSCHOOOL         

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

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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

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

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  Indepth knowledge and expertise  Professional approac: World class approach  Strong intellectual and business capabilities  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 www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS 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)

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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

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Branches  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 – and for promoting social entrepreneurs.

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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.

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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 – and compete with yourself only

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www.afterschoool.tk social entrepreneurship for better society

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AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS