Quantitative Aptitude And Mathematics 14 October
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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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
QUANTITATIVE APTITUDE AND MATHEMATICS Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted? a. 16 b. 8 c. 12 d. 24
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION . • There are (12/3) *(12/3) * (12/3) = 64 cubes made by cutting the big cube. • However, now there are 8 cubes, which don’t have any colour on any sides ( they are in the centre of this cube).
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage? www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION . . • Let us take LCM of 80 and 120. it is 240. Now let us assume that cloth is 1 Rupee per CM. So the cost is 200 (for 240 CM – because while buying, he uses 120 CM for 100 CM). Now when he goes for selling this, he will sell 240/80 *100 = 300 CM , so he will get Rs. 300. However, he gives 20% discount. He will get Rs. 240. Thus his profit is 40 on 200 or 20% profit on cost. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion? a. 1 : 3 b. 4 : 1 c. 3 : 1 d. 4 : 3
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution. . . • • • • • • •
Area of big cirle : (22/7)*20*20 =1257 or 400pi The total area of 4 small circles: 4* (22/7) *5*5 =314 or 100 pi Thus the ratio of uncut to cut area is : 943:314 or 300pi : 100 pi Or 3:1 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimetres? a. Re 0.7 b. Re 0.5 c. Re 0.13 d. Re 0.2 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution . . . • Total bottom surface area : (adjust for thickness) e.g. length =21 – (.5+.5) =20 • 20*10 = 200 • Total of 4 sides : • Longer sides: 20 * 5.5 = 110*2 =220 • Width wise side: 10*5.5 = 55*2 =110 • Add all these: 530 rate = 70/530 = .13 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four • pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution ….. • The weights are in the ratio : 1:2:3:4 • Let us assume that the total weight initially was 10X and now it is 1x, 2x, 3x and 4x • Square it : • 100X^2 = x^2+4x^2+9x^2+16x^2+70000 • 100X^2 – 30X^2 = 70000 • X ^2 = 1000 thus total original price is 100*1000 = 100000 answer. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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 • • • • •
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's 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 • 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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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)
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
– DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
QUANTITATIVE APTITUDE AND MATHEMATICS Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted? a. 16 b. 8 c. 12 d. 24
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION . • There are (12/3) *(12/3) * (12/3) = 64 cubes made by cutting the big cube. • However, now there are 8 cubes, which don’t have any colour on any sides ( they are in the centre of this cube).
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage? www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
SOLUTION . . • Let us take LCM of 80 and 120. it is 240. Now let us assume that cloth is 1 Rupee per CM. So the cost is 200 (for 240 CM – because while buying, he uses 120 CM for 100 CM). Now when he goes for selling this, he will sell 240/80 *100 = 300 CM , so he will get Rs. 300. However, he gives 20% discount. He will get Rs. 240. Thus his profit is 40 on 200 or 20% profit on cost. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion? a. 1 : 3 b. 4 : 1 c. 3 : 1 d. 4 : 3
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution. . . • • • • • • •
Area of big cirle : (22/7)*20*20 =1257 or 400pi The total area of 4 small circles: 4* (22/7) *5*5 =314 or 100 pi Thus the ratio of uncut to cut area is : 943:314 or 300pi : 100 pi Or 3:1 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimetres? a. Re 0.7 b. Re 0.5 c. Re 0.13 d. Re 0.2 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution . . . • Total bottom surface area : (adjust for thickness) e.g. length =21 – (.5+.5) =20 • 20*10 = 200 • Total of 4 sides : • Longer sides: 20 * 5.5 = 110*2 =220 • Width wise side: 10*5.5 = 55*2 =110 • Add all these: 530 rate = 70/530 = .13 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four • pieces with weights in the ratio 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Solution ….. • The weights are in the ratio : 1:2:3:4 • Let us assume that the total weight initially was 10X and now it is 1x, 2x, 3x and 4x • Square it : • 100X^2 = x^2+4x^2+9x^2+16x^2+70000 • 100X^2 – 30X^2 = 70000 • X ^2 = 1000 thus total original price is 100*1000 = 100000 answer. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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 • • • • •
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's 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 • 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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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)
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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