BASIC ALGEBRA FOR ENTREPRENEURS  by :  DR. T.K. JAIN AFTERSCHO ☺ OL  centre for social entrepreneurship  sivakamu veterina...
My words..... My purpose here is to give a few questions on fundamentals of Algebra .  I welcome your suggestions. I also ...
If (x^3 – 1/x^3)= 14, what is (x-1/x) ?  Options :  5,4,3,2 let us assume 1/x = y x^3 -y^3 = 14 (x-y)^3 = x^3 -3x^2y+3xy^2...
What must be added to 1/x to make it equal to x ?  X – 1/x  = (x^2 -1) / x answer
Is (x^3 – 5^3)  divisible by (x-3) ?  Yes
Is (x^3 – 5^3)  divisible by (x+3) ?  No it will be divisible only if the power is even example :  (x^4 – 5^4) is  divisib...
Is (x^3+ 5^3)  divisible by (x+3) ?  Yes,  but only when power is odd
Is (x^3 + 5^3)  divisible by (x-3) ?  Never
X^3 -3x^2+4x+k contains (x+6) as factor, what is the value of k ?  X+6 = 0, so x = -6  Take x=-6  -216 -108 -24 +k = 0 k =...
(x+2) and (x-1) are factors of (x^3+10x^2+mx+n), what is the value of m and n ?  Options :  5,-3 17,-8, 23,-19,  7,-18 sol...
If 5^x /125 = 1, what is X ?  We know that 5^3 = 125,  125/125=1, so x=3 answer
If 3^x – 3^(x-1) = 18, what is x^x  Options : 3,8,27,216  try with 27, x should be 3 let us put the value of x in the equa...
If 2^x – 2^(x-1) = 16, then what is the value of  x^4 ?  Options : 16, 81, 256, 625  let us try with option 625, here x = ...
If (a+b+c) = 0, then a^3+b^3+c^3 is equal to what ?  Options : 0, 3abc, abc, (ab+bc+ac)  answer : = 3abc  formula :  (a+b+...
a+b = 5, and ab = 6, what is  (a^3+b^3) ?  (a-b)^2 = (a+b)^2 – 4ab ab =6, a+b = 5 (a-b)^2=25-24 = 1  (a+b)^3 = a^3 +b^3 +3...
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What will you get from (.4)^(1/2) ?  Options :  1.  .2 2.  .-2  3.  .02  4 none of these  answer : square root of .4 will ...
What will you get from (.8)^(1/3) ? a.  .2 b  .02 c  .04 d  none of these  answer : answer will be more than .9, so answer...
What will you get from the following :  (.9)^(1/2)  a.  .3 b.  .03 c.  between .8 and .9 d. none of these  answer : none o...
Due to  clerical mistake , + is written as *,  / is written as - , * is written as +, - is written as =. what will you get...
What should we add or subtract or multiply or divide  from  13333 to make it a perfect square ? Find minimum digit  If we ...
(149)^2 – (78)^2 – (737) – (98)^2 = ? 22201 – 6084 – 737 – 9604 = 5776 answer
Which of these is highest :  2/5, 15/18 ,  223/226, 1202/1205 ? Here difference between denominator and numerator is same ...
What is the .the sum of first 20 terms of series is 1/5*6 +1/6*7+1/7*8----- We can write it as : 1/30, 1/42, 1/56 we can w...
The least among the following :- a. 0.2 b.1/0.2 c. 0.3^2 d. 0.22 a. 0.2 b.1/0.2 = 5  c. 0.3^2  =.09 d. 0.22 so the answer ...
If 1/3.718 =0.2689,then find value of 1/0.0003718 ? =2689  just shift the decimals as per the question
4.036 divided by 0.04 = ? 100.9 answer
(0.96)3 – (0.1)3/  (0.96)2 +0.096 +(0.1)2 =? (a^3 – b^3) / (a+b)^2  = a-b a = .96 b = .1 answer = a-b = .86 answer
(a+b) * (a-b) =?  = a^2 – b^2
(a+b)^3 = ?  A^3  + 3a^2b + 3ab^2 +b^3
(a-b)^3 =? A^3 - 3a^2b + 3ab^2 -b^3
What is .000000001 in scientific notation ?  = .000000001*10^9 / 10^9 =1*10^(-9)
What is .000000001234 in scientific notation ?  = 1.234* 10^(-9)
What will you get from :  .3879999999.......?  Here 9 is repeating and 387 is non-repeating  deduct 387 from the number an...
What will you get from  .358585858.....? Here 58 are being repeated  we will deduct 3 (non repeating) from 358 and divide ...
Put these in ascending order :  2/3, 25/39, 18/-19, 55/70, .04555..? Ascending means from small to big  the smallest numbe...
What will you get from (91.9432)^2 – (41.9432)^2 ?  (a^2 – b^2) = (a-b) * ( a+b)  = (91.9432 – 41.9432) * ( 91.9432+41.943...
.49*.98*2+.76*.38*2-.98*1.52 = ? Simplify it :  .98*.98+.76*.76-2*.98*.76 (a-b)^2 = a^2 +b^2-2ab =(.98-.76)^2 =(.22)^2  =....
What is the remainder when (2x^3 +5x^2 -4x  -6) is divided by (2x -1) ?  2x-1 = 0 so x = ½ or .5 put this value in the equ...
Which of these is / are factor of (x^2  +4) ?  (x+2) , (x-2) ,  (x^2 -2), (none of these )  answer = none of these
Which of these is a factor of (X^3 -5x^2+8x-4) ?  (x-1), (x-2)^2, (x+2), (x+1) , (none)  answer = (x-1)
What is the remainder when  (x^11 +1) is divided by (x+1) ?  Answer = zero
(x+1/x) = 3, what is the value of (x^6 +1/x^6) ?  Options : 927, 414, 364, 322 let us assume y = 1/x  find its cube : x^3+...
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Basic algebra for entrepreneurs

  1. 1. BASIC ALGEBRA FOR ENTREPRENEURS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india FOR – PGPSE / CSE PARTICIPANTS [email_address] mobile : 91+9414430763
  2. 2. My words..... My purpose here is to give a few questions on fundamentals of Algebra . I welcome your suggestions. I also request you to help me in spreading social entrepreneurship across the globe – for which I need support of you people – not of any VIP. With your help, I can spread the ideas – for which we stand....
  3. 3. If (x^3 – 1/x^3)= 14, what is (x-1/x) ? Options : 5,4,3,2 let us assume 1/x = y x^3 -y^3 = 14 (x-y)^3 = x^3 -3x^2y+3xy^2-y^3 (x-y)^3 =14 -3xy(x-y) (x-y)^3 +3xy(x-y)=14 (x-Y)^3 +3(x-y) – 14=0 (we can cancel xy, as y is 1/x) at this stage put the options, when you put x-y = 2, you are able to solve it so answer is 2
  4. 4. What must be added to 1/x to make it equal to x ? X – 1/x = (x^2 -1) / x answer
  5. 5. Is (x^3 – 5^3) divisible by (x-3) ? Yes
  6. 6. Is (x^3 – 5^3) divisible by (x+3) ? No it will be divisible only if the power is even example : (x^4 – 5^4) is divisible by (x+3)
  7. 7. Is (x^3+ 5^3) divisible by (x+3) ? Yes, but only when power is odd
  8. 8. Is (x^3 + 5^3) divisible by (x-3) ? Never
  9. 9. X^3 -3x^2+4x+k contains (x+6) as factor, what is the value of k ? X+6 = 0, so x = -6 Take x=-6 -216 -108 -24 +k = 0 k = 348 answer
  10. 10. (x+2) and (x-1) are factors of (x^3+10x^2+mx+n), what is the value of m and n ? Options : 5,-3 17,-8, 23,-19, 7,-18 solution : take x = 1 1+10+mx+n or m+n = -11 take x = -2 -8+40-2m+n or -2m+n = -32 or 3n=-54 or n=-18 so last option is correct
  11. 11. If 5^x /125 = 1, what is X ? We know that 5^3 = 125, 125/125=1, so x=3 answer
  12. 12. If 3^x – 3^(x-1) = 18, what is x^x Options : 3,8,27,216 try with 27, x should be 3 let us put the value of x in the equation we find : 27 – 9 = 18 so X = 3 and x^x = 27 answer
  13. 13. If 2^x – 2^(x-1) = 16, then what is the value of x^4 ? Options : 16, 81, 256, 625 let us try with option 625, here x = 5 so put the value of X in the equation, we get : 32 – 16 = 16 so x= 5, and x^4 = 625 answer
  14. 14. If (a+b+c) = 0, then a^3+b^3+c^3 is equal to what ? Options : 0, 3abc, abc, (ab+bc+ac) answer : = 3abc formula : (a+b+c)=0 then a^3+b^3+c^3 = 3abc
  15. 15. a+b = 5, and ab = 6, what is (a^3+b^3) ? (a-b)^2 = (a+b)^2 – 4ab ab =6, a+b = 5 (a-b)^2=25-24 = 1 (a+b)^3 = a^3 +b^3 +3a^2b+3ab^2 or : (a+b)^3 = a^3 +b^3 +3ab(a+b) (5)^3 = a^3+b^3 +3*6(5) 125 – 90 = a^3+b^3 a^3+b^3 = 35 ans
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  17. 17. What will you get from (.4)^(1/2) ? Options : 1. .2 2. .-2 3. .02 4 none of these answer : square root of .4 will be close to .6, so answer is none of these
  18. 18. What will you get from (.8)^(1/3) ? a. .2 b .02 c .04 d none of these answer : answer will be more than .9, so answer is none of these
  19. 19. What will you get from the following : (.9)^(1/2) a. .3 b. .03 c. between .8 and .9 d. none of these answer : none of these
  20. 20. Due to clerical mistake , + is written as *, / is written as - , * is written as +, - is written as =. what will you get from this : 2 of 2 =4 * 6- 3 (2+4-2) Solution : first remove clerical mistake : 2 of 2-4 + 6 / 3 (2*4/2) first solve bracket : 2 of 2-4+ 6 /3 * 4 solve of 4 -4+2 * 4 now solve multiply 4 – 4 + 8 = 8 answer
  21. 21. What should we add or subtract or multiply or divide from 13333 to make it a perfect square ? Find minimum digit If we add 125, we get : 13458, which is square of 116 if we deduct 108, we get 13225 so we should deduct 108
  22. 22. (149)^2 – (78)^2 – (737) – (98)^2 = ? 22201 – 6084 – 737 – 9604 = 5776 answer
  23. 23. Which of these is highest : 2/5, 15/18 , 223/226, 1202/1205 ? Here difference between denominator and numerator is same in each case, so the answer will be 1202 / 1205 answer
  24. 24. What is the .the sum of first 20 terms of series is 1/5*6 +1/6*7+1/7*8----- We can write it as : 1/30, 1/42, 1/56 we can write it as (1/5-1/6)+(1/6 – 1/7)+ (1/7-1/8) . . . . here you can see that in first bracket we have -1/6 and in 2 nd bracket we have + 1/6 and so on.. when we open bracket, we get : 1/5+1/25 we get 6/25 answer
  25. 25. The least among the following :- a. 0.2 b.1/0.2 c. 0.3^2 d. 0.22 a. 0.2 b.1/0.2 = 5 c. 0.3^2 =.09 d. 0.22 so the answer = C
  26. 26. If 1/3.718 =0.2689,then find value of 1/0.0003718 ? =2689 just shift the decimals as per the question
  27. 27. 4.036 divided by 0.04 = ? 100.9 answer
  28. 28. (0.96)3 – (0.1)3/ (0.96)2 +0.096 +(0.1)2 =? (a^3 – b^3) / (a+b)^2 = a-b a = .96 b = .1 answer = a-b = .86 answer
  29. 29. (a+b) * (a-b) =? = a^2 – b^2
  30. 30. (a+b)^3 = ? A^3 + 3a^2b + 3ab^2 +b^3
  31. 31. (a-b)^3 =? A^3 - 3a^2b + 3ab^2 -b^3
  32. 32. What is .000000001 in scientific notation ? = .000000001*10^9 / 10^9 =1*10^(-9)
  33. 33. What is .000000001234 in scientific notation ? = 1.234* 10^(-9)
  34. 34. What will you get from : .3879999999.......? Here 9 is repeating and 387 is non-repeating deduct 387 from the number and divide by 9000 we use as many 9 as there are repeating digits we use as many 0 as we have non-repeatig digits. =(3879-387)/(9000) =3492 / 9000 answer
  35. 35. What will you get from .358585858.....? Here 58 are being repeated we will deduct 3 (non repeating) from 358 and divide it by 990 (as many 9 as there are repeating digits and as many 0 as there are non repeating digits) = (358 – 3) / (990) =355/990 =71/198 answer
  36. 36. Put these in ascending order : 2/3, 25/39, 18/-19, 55/70, .04555..? Ascending means from small to big the smallest number is 18/-19 (as it is in negative). Then we have .04555..... now compare 2/3 and 25/39, in order to compare these, let us multiply the numerators of these by denominators of the other numbers, we get : 78 and 75, the bigger number is 78 so 2/3 is bigger. Now compare it with 55/70. We get : 140 and 165, 165 is bigger so final order : -18/19, .45555.., 25/39, 2/3, 55/70 answer
  37. 37. What will you get from (91.9432)^2 – (41.9432)^2 ? (a^2 – b^2) = (a-b) * ( a+b) = (91.9432 – 41.9432) * ( 91.9432+41.9432) (50) * (133.8864) =6694.32 answer
  38. 38. .49*.98*2+.76*.38*2-.98*1.52 = ? Simplify it : .98*.98+.76*.76-2*.98*.76 (a-b)^2 = a^2 +b^2-2ab =(.98-.76)^2 =(.22)^2 =.0484 answer
  39. 39. What is the remainder when (2x^3 +5x^2 -4x -6) is divided by (2x -1) ? 2x-1 = 0 so x = ½ or .5 put this value in the equation .25+1.25-2-6 =1.5 – 8 = -6.5 answer
  40. 40. Which of these is / are factor of (x^2 +4) ? (x+2) , (x-2) , (x^2 -2), (none of these ) answer = none of these
  41. 41. Which of these is a factor of (X^3 -5x^2+8x-4) ? (x-1), (x-2)^2, (x+2), (x+1) , (none) answer = (x-1)
  42. 42. What is the remainder when (x^11 +1) is divided by (x+1) ? Answer = zero
  43. 43. (x+1/x) = 3, what is the value of (x^6 +1/x^6) ? Options : 927, 414, 364, 322 let us assume y = 1/x find its cube : x^3+3x^2y+3xy^2+y^3 = 27 =x^3+y^3 + 9 or x^3+y^3 = 18 now square it : x^6+2x^3y^3+y^6 = 324 (we can cancel x^3 and y^3) x^6+y^6 = 324-2 = 322 answer
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  56. 56. ADDITIONAL LINKS http://www.scribd.com/doc/11692763/Advanced-Mathematics-for-GMAT-CAT-MAT http://www.scribd.com/doc/23407929/Advanced-Mathematics-for-GMAT-CAT-MAT http://www.scribd.com/doc/11625819/Basic-Mathematics-for-Cat-GMAT-Mat http://www.scribd.com/doc/23407954/mathematics-for-OPENMAT-MAT-CAT-GMAT-25-april http://www.scribd.com/doc/23407934/Advanced-Mathematics-for-GMAT-CAT-MAT2 http://www.scribd.com/doc/6583520/English-Afterschoool-21-May-2 http://www.scribd.com/doc/23300964/Advanced-Mathematics-for-GMAT-CAT-MAT2 http://www.scribd.com/doc/23407945/MATHEMATICS-FOR-ATMA-CAT-MAT-GMAT-BANK-PO-GRE
  57. 57. http://www.scribd.com/doc/6583303/Reasoning-Afterschoool
  58. 58. http://www.scribd.com/doc/23393680/REASONING-AFTERSCHOOOL http://www.scribd.com/doc/23393719/reasonning-44 http://www.scribd.com/doc/6583347/DI-and-Reasoning http://www.scribd.com/doc/23407636/10-July-reasoning http://www.scribd.com/doc/6583273/Reasoning-Quiz http://www.scribd.com/doc/23393476/10-July-reasoning http://www.scribd.com/doc/23393716/REASONING-QUIZ http://www.scribd.com/doc/14705025/17-Reasoning-II http://www.scribd.com/doc/23393478/10-July-reasoning-II
  59. 59. Free download useful material ... http://www.scribd.com/doc/23393316/general-knowledge http://www.scribd.com/doc/23609752/Group-Discussion-Afterschoool http://www.scribd.com/doc/6583547/General-Knowledge-24-May
  60. 60. THANKS.... GIVE YOUR SUGGESTIONS AND JOIN AFTERSCHOOOL NETWORK / START AFTERSCHOOOL SOCIAL ENTREPRENEURSHIP NETWORK IN YOUR CITY / CONDUCT WORKSHOP ON SOCIAL ENTREPRENEURSHIP IN YOUR COLLEGE / SCHOOL / CITY [email_address] JOIN OUR NETWORK TO PROMOTE SOCIAL ENTREPRENEURSHIP
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