7 June Mock Test
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MOCK TEST Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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How many prime factors can you identify in 2310? • Ans: 2,3,5,7,11
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When we divide 4150 by some number, the quotient is 55 & remainder is 25, what is the divisor?
• Ans: (4150-25)/55 • =75 ans.
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The smallest number, when subtracted from 43079 makes it divisible by 9? • The total of 4+3+0 +7+9 =23, which is not divisible by 9. In order to make this number divisible, deduct 5 from this. • To be divisible by 9, the total of the number (all digits) should be divisible by 9. • Ans: 5
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What least value must be put in place of # in 91876#2 so that it becomes divisible by 8? • Any number is divisible by 8 only if its last three digits are divisible by 8. • By hit and try, we can try for 612, 622, 632 and so on. 632 is divisible by 8. Thus the least number is 3 ans.
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What least value must be put in place of # in 91876#2 so that it becomes divisible by 11? • Any number is divisible by 11 only if the sums of alternate digits is having a difference of 0 or 11 or in multiple of 11. • Sum of : 9+8+6+2 = 25 Sum of : 1+7 is 8. the difference of 25 & 8 is 17. in order to make this difference 11, we will put the value of # as 6. now the sum of second group is: 1+7+6 = 14 . • Ans = 6
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How will you convert this number into a rational number (use smallest possible number)? • 2^1/2 • Solution: • Multiply this number by 2^1/2, ans.
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What will you always get if you divide a natural number by another natural number? • Rational number ans. • Rational numbers are in the form of p/q. we may get integers also – but we will always get rational number. So answer is rational number.
www.afterschoool.tk
Mention 2 prime factors, by which 111,111,111,111 is always divisible? • • • •
Answer: 3 & 11 (by observation) Any number is divisible, if the sum of its digits is divisible by 3. similarly, any number is divisible by 11, if the sum of alternate digits is divisible by 11.
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What is the largest number of 4 digits, which is divisible by 88? • 88= 11*8 • The largest number divisible by 11 is 9999. – but this is not divisible by 8. • If we divide 9999 by 88, we get 55 as remainder. Thus the largest 4 digit number is 9999-55= 9944 ans.
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The (minimum) number of digits in the smallest number, which when multiplied by 7 gives all nines is? • Let us start dividing 9 by 7 in continuation . . . • 9/7, - gives 2, add, 9, we get 29, again divide it by 7, we get 1, add 9, we get 19, again divide, we get 5, add 9, we get 59, again divide, we get 3, add 9, we get 39, again divide, we get 4, add 9, the remainder is Zero. Thus we can get our answer: ( we had divided by: 142857) • The number of digits is 6 Ans. • Answer is 6 ans.
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The sum of n different positive integers is less than 100. What is the greatest possible value of n? • By hit and trial, if we take first 9 digits, the sum of those digits is : • (9*10) / 2 = 45. • If we take 14, the total is (14*15)/2 = 105 – it cannot be answer. • If we take 13, (13*14) / 2 = 91. Thus the greatest possible value of n is 13 ans.
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What will be the smaller angle of hands of a clock at half past six in degrees? • When the minute had reaches 6, hour hand goes ahead by 2.5 • 2.5/60*360 = 15 approx
www.afterschoool.tk
In an apartment, 1/3 flats have 2 bedrooms, 1/7th of 2 bedroom flats have front flats. Which of the following may be total number of flats: 42,56,50, 57
• The total number of flats must be divisible by 1/3 and 1/7 consecutively. Thus this number can be in multiple of 21 only. Thus the answer is 42 Ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 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
About AFTERSCHOOOL 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
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
www.afterschoool.tk
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 Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who wants to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approach • Strong intellectual and business capabilities • World class approach • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business 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 • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
How many prime factors can you identify in 2310? • Ans: 2,3,5,7,11
www.afterschoool.tk
When we divide 4150 by some number, the quotient is 55 & remainder is 25, what is the divisor?
• Ans: (4150-25)/55 • =75 ans.
www.afterschoool.tk
The smallest number, when subtracted from 43079 makes it divisible by 9? • The total of 4+3+0 +7+9 =23, which is not divisible by 9. In order to make this number divisible, deduct 5 from this. • To be divisible by 9, the total of the number (all digits) should be divisible by 9. • Ans: 5
www.afterschoool.tk
What least value must be put in place of # in 91876#2 so that it becomes divisible by 8? • Any number is divisible by 8 only if its last three digits are divisible by 8. • By hit and try, we can try for 612, 622, 632 and so on. 632 is divisible by 8. Thus the least number is 3 ans.
www.afterschoool.tk
What least value must be put in place of # in 91876#2 so that it becomes divisible by 11? • Any number is divisible by 11 only if the sums of alternate digits is having a difference of 0 or 11 or in multiple of 11. • Sum of : 9+8+6+2 = 25 Sum of : 1+7 is 8. the difference of 25 & 8 is 17. in order to make this difference 11, we will put the value of # as 6. now the sum of second group is: 1+7+6 = 14 . • Ans = 6
www.afterschoool.tk
How will you convert this number into a rational number (use smallest possible number)? • 2^1/2 • Solution: • Multiply this number by 2^1/2, ans.
www.afterschoool.tk
What will you always get if you divide a natural number by another natural number? • Rational number ans. • Rational numbers are in the form of p/q. we may get integers also – but we will always get rational number. So answer is rational number.
www.afterschoool.tk
Mention 2 prime factors, by which 111,111,111,111 is always divisible? • • • •
Answer: 3 & 11 (by observation) Any number is divisible, if the sum of its digits is divisible by 3. similarly, any number is divisible by 11, if the sum of alternate digits is divisible by 11.
www.afterschoool.tk
What is the largest number of 4 digits, which is divisible by 88? • 88= 11*8 • The largest number divisible by 11 is 9999. – but this is not divisible by 8. • If we divide 9999 by 88, we get 55 as remainder. Thus the largest 4 digit number is 9999-55= 9944 ans.
www.afterschoool.tk
The (minimum) number of digits in the smallest number, which when multiplied by 7 gives all nines is? • Let us start dividing 9 by 7 in continuation . . . • 9/7, - gives 2, add, 9, we get 29, again divide it by 7, we get 1, add 9, we get 19, again divide, we get 5, add 9, we get 59, again divide, we get 3, add 9, we get 39, again divide, we get 4, add 9, the remainder is Zero. Thus we can get our answer: ( we had divided by: 142857) • The number of digits is 6 Ans. • Answer is 6 ans.
www.afterschoool.tk
The sum of n different positive integers is less than 100. What is the greatest possible value of n? • By hit and trial, if we take first 9 digits, the sum of those digits is : • (9*10) / 2 = 45. • If we take 14, the total is (14*15)/2 = 105 – it cannot be answer. • If we take 13, (13*14) / 2 = 91. Thus the greatest possible value of n is 13 ans.
www.afterschoool.tk
What will be the smaller angle of hands of a clock at half past six in degrees? • When the minute had reaches 6, hour hand goes ahead by 2.5 • 2.5/60*360 = 15 approx
www.afterschoool.tk
In an apartment, 1/3 flats have 2 bedrooms, 1/7th of 2 bedroom flats have front flats. Which of the following may be total number of flats: 42,56,50, 57
• The total number of flats must be divisible by 1/3 and 1/7 consecutively. Thus this number can be in multiple of 21 only. Thus the answer is 42 Ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 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
About AFTERSCHOOOL 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
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
www.afterschoool.tk
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 Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who wants to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approach • Strong intellectual and business capabilities • World class approach • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business 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 • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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