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Statistics For Management 16 October

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Statistics For Management 16 October

  2. 2. QUANTITATIVE APTITUDE FOR BUSINESS MANAGEMENT Dr. T.K. Jain. AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email_address] www.afterschool.tk , www.afterschoool.tk
  4. 4. WHAT IS THE PROBABILITY OF GETTING A TOTAL OF 10 OR MORE WHEN I THROW 2 DICE? <ul><li>The total possibilities are : 6*6 = 36 </li></ul><ul><li>Possibilities when total is 10: </li></ul><ul><li>6+4, 5+5, 4+6 </li></ul><ul><li>For 11: 6+5, 5+6, </li></ul><ul><li>For 12: 6+6. Thus we have 6 possibilities. </li></ul><ul><li>6/36 = 1/6 answer. </li></ul>
  5. 5. There are 10 prizes and 25 blanks in a lottery, what is the probability of getting prize? <ul><li>10/35 </li></ul><ul><li>= 2/7 answer. </li></ul>
  6. 6. Rectangle =females, Triangle = educated, Circle = urban, Square =Civil Servants, what is the number of uneducated male civil servants?
  7. 7. Answer: <ul><li>17 answer. </li></ul>
  8. 8. Each of Goti and Hari has a peculiar habit in making statements. goti lies on Mondays, Tues days and Wednesday but speaks the truth on the other days of the week, whereas Hari lies on Thursday, Friday and Saturdays but speaks the truth on the other days of the week. Monu is a common friend of Goti and Hari. Today, Monu wanted to find out what day of the week it is and he got the following responses from his friends to his query. Goti Yesterday was one of my lying days. Hari : Yesterday was one of my lying days. What day of the week is today?
  9. 9. Solution . . . <ul><li>Today is Thursday – then Hari has to lie today and so Hari would speak that yesterday was my lying day. </li></ul><ul><li>Goti has to speak tructh that “yesterday was my lying day” </li></ul><ul><li>Thus it is Thursday. </li></ul>
  10. 10. Log sqrt(8) X = 10/3, what is X? <ul><li>X = (8)^1/2 ^10/3 </li></ul><ul><li>X = 2^3/2 ^10/3 </li></ul><ul><li>X = 2^5 </li></ul><ul><li>X = 32 answer. </li></ul>
  11. 12. <ul><li>Which of the following health drinks would be needed in least quantity to obtain its mixture with 15 liters of F such that, its lime water and vitamin percentage is less than 50 and greater than 40 respectively? </li></ul><ul><li>(1) B </li></ul><ul><li>(2) C </li></ul><ul><li>(3) D </li></ul><ul><li>(4) G </li></ul><ul><li>(5) A </li></ul>
  12. 13. Solution .. . <ul><li>In the first option, we mix up B. B contains 3 liters of lime water and F has 15 liters of lime water, thus their combined share is 15 liters out of 25 liters. However, we need only less than 50% mixture as lime water. Thus we can do with only 1 liters of B. which will give us .3 liters of lime water. Ans. </li></ul>
  13. 14. DATA SUFFICIENCY QUESTION <ul><li>A box containing only 50 paise coins and 25 paise coins has a total sum of Rs. 20. What is the number of each of these coins? </li></ul><ul><li>I. The total number of coins is 50. </li></ul><ul><li>II. If there were 10 more 50 paise coins, the sum will in crease by 25% </li></ul>
  14. 15. SOLUTION . . . <ul><li>You can find the answer from the first statement alone. As we can see that if we assume the number of coins to be X and Y. we can frame two equations: </li></ul><ul><li>X + Y = 50 </li></ul><ul><li>.5X + .25Y = 20 </li></ul><ul><li>Solving these we get: .5y = 10 or Y = 20 and X = 30. The 2 nd statement is not required in the process. </li></ul>
  15. 16. Data Sufficiency question <ul><li>Tom pluck apples. He sells some of the apples, distirbutes some of them among his friends, eats some and takes the rest home. How many apples did Tom eat? </li></ul><ul><li>I. He distributes 6 apples among his friends, which comes to be 3/5 th of what he has eaten and sold. </li></ul><ul><li>II. He eats l/3 of the plucked apples, which is 12 less than what he has plucked. </li></ul>
  16. 17. Solution . . . <ul><li>From the second statement we can prepare an equation: </li></ul><ul><li>1x -1/3x =12 </li></ul><ul><li>2/3 X = 12 </li></ul><ul><li>X = 12*3/2 </li></ul><ul><li>X = 18 </li></ul><ul><li>That means he had plucked 18 apples. Thus answer can be obtained from 2 nd statement alone. </li></ul>
  17. 18. DATA SUFFICIENCY QUESTION <ul><li>What is the value of X? </li></ul><ul><li>I. X and Y are unequal even integers less than 10, and X/Y is an odd integer. </li></ul><ul><li>II. X and Y are even integers, each less than 10, product of X andYis 12. </li></ul>
  18. 19. SOLUTION <ul><li>Only first statement is sufficient to answer the question. There is only one such possibility that is 6 and 2 thus 1 st statement alone gives the answer. </li></ul><ul><li>Similarly answer can be obtained from second statement also. Because only one such possibility is there 6*2 = 12 answer. </li></ul>
  19. 20. 16 log 4 5 ? <ul><li>=4^2 log 4 5 </li></ul><ul><li>=4 log 4 5^2 </li></ul><ul><li>=1 * 5^2 </li></ul><ul><li>=25 answer </li></ul>
  20. 21. Solve the following <ul><li>If the quater of the sphere is divided into two equal halves then </li></ul><ul><li>the ratio of surface area of each part with the surface area of </li></ul><ul><li>sphere will be. </li></ul><ul><li>5 : 16 </li></ul><ul><li>1: 16 </li></ul><ul><li>1:8 </li></ul><ul><li>1:4 </li></ul><ul><li>5:8 </li></ul>
  21. 22. Solution . . <ul><li>Total surface area = 4 pi * r^2 </li></ul><ul><li>Let us assume the r = 7 </li></ul><ul><li>=4*22/7 * 7*7 </li></ul><ul><li>=616 </li></ul><ul><li>Now we will multiply it with 1/8 </li></ul><ul><li>=77 </li></ul><ul><li>Thus ratio is 1:8 </li></ul>
  22. 23. FIND THE PROBABILITY THAT A 4 DIGIT NUMBER MADE FROM 2,5,6,7 IS DIVISIBLE BY 4? <ul><li>Any number is divisible by 4 only if the last 2 digits are divisible by 4. If the last 2 digits are 56, 76, 72,52 then the number will be divisible by 4. Keeping these as last 2 digits, we can make 2 numbers from each of these. Thus we have 8 possibilities. </li></ul><ul><li>The total number of possibilities are 4! = 24. Thus required probability is 8/24 or 1/3. </li></ul>
  23. 24. A committee has to be formed of 7 members from 8 boys and 5 girls. What is the probability that the committee will have 2 girls? <ul><li>13C7 gives total possibilities: </li></ul><ul><li>13!/(7! * 6!) = 13*12*11*10*9*8/6*5*4*3*2*1 =1716 </li></ul><ul><li>Selecting 2 girls means: </li></ul><ul><li>8C5*5c2 = 8!/(5!*3!) * 5!/(3!*2!) = 560 </li></ul><ul><li>=560/1716 = .326 </li></ul>
  24. 25. A dice is rolled twice, what is the probability that you get a difference of 2 points? <ul><li>6^2 =36 are total possibilities </li></ul><ul><li>Difference of 2: (6,4), (5,3) (4,2) (3,1) (1,3),(2,4), (3,5), (4,6) </li></ul><ul><li>Thus there are 8 possibilities </li></ul><ul><li>8/36 = 2/9 answer. </li></ul>
  25. 26. For 2 events A and B, P(b) is .3 and P (A but not b) =.4 P (not A) =.6, what are A & B? <ul><li>Total of P(A) and P (B) is .7, that means they are not exhaustive (if they had been exhaustive, their total should have been 1). </li></ul><ul><li>P(notA) and P(A but not b) together are 1 that means there is no common area between A & B. Thus these are mutually exclusive events. </li></ul>
  26. 27. 30%, 40%, 50% failed in Accounts, Maths and at least one of these 2 papers
  27. 28. What is P(AUB), if P(A) = ½, P(B) = 2/3 and P( Ā UB) =5/6 <ul><li>A + B = ½ + 2/3 = 7/6 </li></ul><ul><li>From this we have to deduct the common area of A & B. </li></ul><ul><li>Let us add P( Ā UB) =5/6 + P(A) =1/2 </li></ul><ul><li>This is = 8/6 thus 8/6 -1 = 2/6=1/3 </li></ul><ul><li>1/3 is intersection of A &B. </li></ul><ul><li>7/6 -1/3 = 5/6 is the answer. </li></ul>
  28. 29. 7^ (2n+2) -48n -49 must be divisible by ? <ul><li>Let us try for n =0, 1, 2, 3 and find the answer: </li></ul><ul><li>49 – 49 = 0 </li></ul><ul><li>N = 1 </li></ul><ul><li>2401 – 48 – 49 = 2304 </li></ul><ul><li>N = 2: </li></ul><ul><li>117649 -96 – 49 = 117504 </li></ul><ul><li>Thus 2304 is the answer. </li></ul>
  29. 30. 41,31,23,17,11. . ? <ul><li>Options 6,5,8,10 </li></ul><ul><li>Answer: We have prime numbers at interval of one. Thus next prime number is 5 ans. </li></ul>
  30. 31. 2,9,28,65,126 . . ? <ul><li>options; 261,217,198,180,.. </li></ul><ul><li>1^3+1 = 2 </li></ul><ul><li>2^3 +1 = 9 </li></ul><ul><li>3^3 +1 = 28 </li></ul><ul><li>4^3 +1 = 65 </li></ul><ul><li>5^3 +1 = 126 </li></ul><ul><li>6^3 +1 = 217 answer. </li></ul>
  31. 32. What is the slope of the line: A (-3,5) and B(4,2) is ? <ul><li>Slope = (Y2 – Y1) / (X2 – X1) </li></ul><ul><li>= (2-5) / (4-(-3)) </li></ul><ul><li>=-3/7 answer. </li></ul>
  32. 33. ABC is a triangle with A (7,-3), B (3,-1), C (5,3), then what is the length of the median AD? <ul><li>D is mid point between B and C. Mid point of B and c is: </li></ul><ul><li>8/2 = 4 and 2/2 = 1 thus we have to find distance from A to (4,1) </li></ul><ul><li>Thus distance is sqrt ((7-4)^2 + (-3-1)^2) </li></ul><ul><li>Thus answer is 5. </li></ul>
  33. 34. Three circles of radius 3 CM each are tangent to each other. Find the area between them (surrounded by these circles, but don’t include the area of circles) ? <ul><li>Find the area of equilateral triangle joining the 3 circles: (1.732/4 *6*6) =15.58 </li></ul><ul><li>Find the area of half circle : ½*22/7*3*3 </li></ul><ul><li>=14.14 </li></ul><ul><li>Thus the area is : 1.44 ans. </li></ul>
  34. 35. Two circles touch each other externally, the sum of their areas is 130 pi. Distance between their centres is 14. What is the radii of these circles? <ul><li>Let us assume one radius is r and other (14-r) </li></ul><ul><li>Pi*r^2 +pi* (14-r)^2 = 130 pi </li></ul><ul><li>R^2 +196 -28r +r^2 = 130 </li></ul><ul><li>2R^2 -28R + 66 = 0 or R = solve it: 11 or 3 answer. </li></ul>
  35. 36. What is the ratio of revenue of Telecom & health care to that of e-business?
  36. 37. Solution <ul><li>1:2 </li></ul>
  37. 38. In the previous question, what is the ratio of revenue of Telecom & health care to that of education? <ul><li>6: 55 answer. </li></ul>
  38. 39. For how many countries, the figures are less than average in 2000 and 2004?
  39. 40. Solution <ul><li>5 in each. </li></ul>
  40. 41. Mixture of 40 liters of milk and water contains 10% water. How much water should be added to make water 20%? <ul><li>Water is 4 and milk is 36 now 36 is 80 % </li></ul><ul><li>36*100/80 = 45 </li></ul><ul><li>Thus 5 liters water should be added. </li></ul>
  41. 42. Data sufficiency question
  42. 43. Solution <ul><li>Both the statements are required together and then we can find that Y = 75 degrees. </li></ul>
  43. 44. ABOUT AFTERSCHO☺OL <ul><li>Afterschoool conducts three year integrated PGPSE (after class 12 th 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. </li></ul>
  44. 45. Why such a programme? <ul><li>To promote people to take up entrepreneurship and help develop the society </li></ul><ul><li>To enable people to take up franchising and other such options to start a business / social development project </li></ul><ul><li>To enable people to take up social development as their mission </li></ul><ul><li>To enable people to promote spirituality and positive thinking in the world </li></ul>
  45. 46. Who are our supporters? <ul><li>Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. </li></ul><ul><li>You can also support us – not necessarily by money – but by being promotor of our concept and our ideas. </li></ul>
  46. 47. About AFTERSCHO☺OL PGPSE – the best programme for developing great entrepreneurs <ul><li>Most flexible, adaptive but rigorous programme </li></ul><ul><li>Available in distance learning mode </li></ul><ul><li>Case study focused- latest cases </li></ul><ul><li>Industry oriented practical curriculum </li></ul><ul><li>Designed to make you entrepreneurs – not just an employee </li></ul><ul><li>Option to take up part time job – so earn while you learn </li></ul><ul><li>The only absolutely free course on internet </li></ul>
  47. 48. Workshops from AFTERSCHO☺OL <ul><li>IIF, Delhi </li></ul><ul><li>CIPS, Jaipur </li></ul><ul><li>ICSI Hyderabad Branch </li></ul><ul><li>Gyan Vihar, Jaipur </li></ul><ul><li>Apex Institute of Management, Jaipur </li></ul><ul><li>Aravali Institute of Management, Jodhpur </li></ul><ul><li>Xavier Institute of Management, Bhubaneshwar </li></ul><ul><li>Pacific Institute, Udaipur </li></ul><ul><li>Engineering College, Hyderabad </li></ul>
  48. 49. Flexible Specialisations: <ul><li>Spiritualising business and society </li></ul><ul><li>Rural development and transformation </li></ul><ul><li>HRD and Education, Social Development </li></ul><ul><li>NGO and voluntary work </li></ul><ul><li>Investment analysis,microfinance and inclusion </li></ul><ul><li>Retail sector, BPO, KPO </li></ul><ul><li>Accounting & Information system (with CA / CS /CMA) </li></ul><ul><li>Hospital management and Health care </li></ul><ul><li>Hospitality sector and culture and heritage </li></ul><ul><li>Other sectors of high growth, high technology and social relevance </li></ul>
  49. 50. Salient features: <ul><li>The only programme of its kind (in the whole world) </li></ul><ul><li>No publicity and low profile course </li></ul><ul><li>For those who want to achieve success in life – not just a degree </li></ul><ul><li>Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes </li></ul><ul><li>Scholarships for those from poor economic background </li></ul><ul><li>Latest and constantly changing curriculum – keeping pace with the time </li></ul><ul><li>Placement for those who are interested </li></ul><ul><li>Admissions open throughout the year </li></ul><ul><li>Latest and most advanced technologies, books and study material </li></ul>
  50. 51. Components <ul><li>Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) </li></ul><ul><li>Meditation, spiritualisation, and self development </li></ul><ul><li>Essential softwares for business </li></ul><ul><li>Business plan, Research projects </li></ul><ul><li>Participation in conferences / seminars </li></ul><ul><li>Workshops on leadership, team building etc. </li></ul><ul><li>Written submissions of research projects/articles / papers </li></ul><ul><li>Interview of entrepreneurs, writing biographies of entrepreneurs </li></ul><ul><li>Editing of journals / newsletters </li></ul><ul><li>Consultancy / research projects </li></ul><ul><li>Assignments, communication skill workshops </li></ul><ul><li>Participation in conferences and seminars </li></ul><ul><li>Group discussions, mock interviews, self development diaryng </li></ul><ul><li>Mind Power Training & writing workshop (by Dr. T.K.Jain) </li></ul>
  51. 52. Pedagogy <ul><li>Case analysis, </li></ul><ul><li>Articles from Harvard Business Review </li></ul><ul><li>Quiz, seminars, workshops, games, </li></ul><ul><li>Visits to entrepreneurs and industrial visits </li></ul><ul><li>Presentations, Latest audio-visuals </li></ul><ul><li>Group discussions and group projects </li></ul><ul><li>Periodic self assessment </li></ul><ul><li>Mentoring and counselling </li></ul><ul><li>Study exchange programme (with institutions out of India) </li></ul><ul><li>Rural development / Social welfare projects </li></ul>
  52. 53. Branches <ul><li>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. </li></ul>
  53. 54. Case Studies <ul><li>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. </li></ul>
  54. 55. Basic values at AFTERSCHO☺OL <ul><li>Share to learn more </li></ul><ul><li>Interact to develop yourself </li></ul><ul><li>Fear is your worst enemy </li></ul><ul><li>Make mistakes to learn </li></ul><ul><li>Study & discuss in a group </li></ul><ul><li>Criticism is the healthy route to mutual support and help </li></ul><ul><li>Ask fundamental questions : why, when, how & where? </li></ul><ul><li>Embrace change – and compete with yourself only </li></ul>
  55. 56. www.afterschoool.tk social entrepreneurship for better society