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  • 1. If a two digit positive integer has its digits reversed the resulting integer differs from the original by 27. By how much does the two digits differ?

  • If we say that
    A = the tens digit {দশক স্থানীয় অঙ্ক }
    B = the units digit. {একক স্থানীয় অঙ্ক} 
    then,
    original integer = 10A + B
    and
    original integer with digits reversed = 10B + A
    Now, we can use the fact that the difference between these two two-digit numbers is 27 to write the following equation:
    10A + B - (10B + A) = 27
    We have one equation and two variables. However, this is enough to answer the question, which asks for the difference between the two variables, A - B!
    10A + B - (10B + A) = 27 
    10A + B - 10B - A = 27 
    9A - 9B = 27 
    9(A - B) = 27 
    A - B = 3

  • 2. The sum of prime numbers that are greater than 60 but less than 70 is?
  • 3. If the product of 3 different positive integers is 6, then twice the sum of the integers is?

  • Numbers are: 1,2,3

    Their product= 1×2×3=6

    Their sum=1+2+3=6

    Twice the sum of integers is=6×2

  • 4. How many prime numbers between 56 to 100?

  • 56 to 100 prime numbers:

    59, 61, 67, 71, 73, 79, 83, 89, 97

    Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.

  • 5. How many times 4 comes in 10 to 100?

  • 14, 24, 34, 40, 41, 42, 43, 44 (2 times), 45, 46, 47, 48, 49, 54, 64, 74, 84, 94 =Total 19 Times

  • 6. If n is even, which of the following cannot be odd?
  • 7. The product  of two consecutive negative even integers is 24. What is the larger number?
  • 8. If x and y are positive integers, each greater than 1, and if 13(x-1) =17(y-1),  what is the least possible value of (x+y)?
  • 9. ০.১ এর বর্গমূল কত?

  • সঠিক উত্তর: ০.৩১৬

  • 10. পাঁচ অংকের ক্ষুদ্রতম সংখ্যা ও চার অংকের বৃহত্তম সংখ্যার অন্তর কত?
  • 11. Choose the number pair which is different from others.
  • 12. If a number x is 10% less than another number y and y is 10% more than 125, then x is equal to:
  • 13. The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is:
  • 14. The difference between the local value and the face value of 7 in the numeral 32675149 is

  • (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993

  • 15. The greatest number that exactly divides 105, 1001 and 2436 is:

  • 105 = 3X 5X 7

    1001 = 7X13X11

    2436 = 3X4X7X29

    So, HCF = 7

  • 16. A figure was reached by first multiplying a number by 4 and then dividing the product by 100. The figure can be obtained by diving the original number by
  • 17. Tk. 206 is divided among x, y and z in such a way that y gets Tk. 6 more than x and z gets twice the amount got by x. What amount (in Tk) is received by y?
  • 18. The sum of two numbers is 25 and their difference is 13. Find their product.
  • 19. If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new numbers is:
  • 20. What number should be divided by √0.25 to give the result as 25?
  • 21. A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is the number?
  • 22. The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is:
  • 23. The least number by which 294 must be multiplied to make it a perfect square, is:
  • 24. The number of girls in a class is 5 times the number of boys. Which of the following can not be the total number of children in the class?
  • 25. Find the least number exactly divisible by 12, 15, 20 and 27.
  • 26. Two-thirds of the members of a committee are women, one-fourth of the male members of the committee are married. If there are 9 bachelors in the committee, how many members are there altogether?
  • 27. The sum of 3 consecutive multiple of 3 is 90. What is the largest of these numbers?
  • 28. How many numbers between 1 and 100 are there of the form 7x + 5 where x is a positive integer?
  • 29. একটি চিড়িয়াখানায় মোট ৮০টি ময়ূর ও হরিণ আছে। তাদের পায়ের সংখ্যা ২০০টি হলে কতটি ময়ুর আছে?
  • 30. দুটি ক্রমিক পূর্ণসংখ্যা নির্ণয় করুন, যাদের বর্গের অন্তর ৪৭ ৷
  • 31. এক বিলিয়ন কে সংখ্যায় প্রকাশ করতে হলে ১ এর পর কতটি শুন্য লাগবে?

  • ১ বিলিয়ন=১০০ কোটি

  • 32. তিনটি ক্রমিক সংখ্যার গুণফল ১২০ হলে সংখ্যা তিনটির যোগফল হবে-

  • 4×5×6=120

    সুতরাং 4+5+6=15

  • 33. Moyna has n chocolates, where n is an integer such that 20<n<50. If Moyna divides the chocolates equally among 5 children, she will have 2 chocolates remaining. If she divides the chocolates among 6 children, she will have 1 chocolate remaining. How many chocolates will remain if she divides the chocolates among 7 children?
  • 34. Babu gave 20% of his marbles to Sadeq, and 20% of the rest of the marbles to Tipu. If he now has 320 marbles, how many did he have originally?
  • 35. If x is an even number, what is the difference between the smallest even number greater than (5x +6) and the largest even number less than (3x +9) ?
  • 36. দুই অংকবিশিষ্ট কোন সংখ্যার অংকয়ের সমষ্টি ৯। অংক দুটি স্থান বিনিময় করলে যে সংখ্যা পাওয়া যায়, তা প্রদত্ত সংখ্যা হতে ৪৫ কম। সংখ্যাটি কত হবে?
  • 37. In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
  • 38. If n is an even integer, which of the following must be an odd integer?
  • 39. Find the smallest number by which 5808 should be multiplied so that the product becomes a perfect square.
  • 40. If the number 5*2 is disvisible by 6, then *=?
  • 41. The average of five consecutive odd number is 61. What is the difference between the highest and lowest numbers?
  • 42. Two numbers are such that the ratio between them is 4:7. If each is increased by 4, the radio becomes 3:5. The larger number is:
  • 43. If m and n are whole numbers such that m^n=121, then the value of (m-1)^(n+1) is:
  • 44. The smallest 6-digit number exactly divisible by 111 is:
  • 45. A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:

  • Let the no. is x.
    according to question,x=4a+2.
    a=5b+3.
    b=6c+4
    By solving this, we get
    x=4[5(6c+4)+3]+2 (since a=5b+3,b=6c+4)
    x=120c+94
    Now for checking the answer we put c=1
    x = 214 i.e. ans

  • 46. On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:

  • By hit and trial, we find that

    47619 x 7 = 333333.

  • 47. Which one of the following can't be the square of natural number?

  • The square of a natural number never ends in 7.

    So, 42437 is not the square of a natural number.

  • 48. On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder ? 
  • Number = 269 x 68 + 0 = 18292

 67) 18292 (273
     134
     ----
      489
      469
      ----
       202
       201
       ---
         1
       ---
       
Therefore, Required remainder = 1
  • 49. The sum of first 45 natural numbers is:

  • Middle number of the first natural 45 number is 23.
    So its average is also 23.

    23*45 = 1035.

  • 50. The sum of all two digit numbers divisible by 5 is:

  • Required numbers are 10,15,20,25,...,95
    This is an A.P. in which a=10,d=5 and l=95.
    Let the number of terms in it be n.Then t=95
    So a+(n-1)d=95.
    10+(n-1)*5=95,then n=18.
    Required sum=n/2(a+l)=18/2(10+95)=945.

  • 51. The difference between the place values of two sevens in the numeral 69758472 is

  • Required difference = (700000 - 70) = 699930

  • 52. A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

  • let a number X which is divisible by 4 and 5 respective gives 1 and 4.

    Step 1 :
      
       now, first divide by 4.
       we take Y as dividend.  
        when you divide X by 4 it gives remainder 1.

        4 | X | Y
           ____
             1

       so  X = 4 * Y + 1   ---  eq(1)

    step 2 ;
       
        now,  divide by 5.
        
      we take 1 as dividend because it divides completly.
        when you divide Y by 5 it gives only remainder 4.
       
        5 | Y | 1
           ____
             4

       so 

  • 53. Which one of the following is not a prime number?

  • 91 is divisible by 7.

    So, it is not a prime number.

  • 54. What is the sum of two consecutive even numbers, the difference of whose squares is 84?

  • Let the numbers be x and x + 2.

    Then, (x + 2)2 - x2 = 84

    => 4x + 4 = 84

    => 4x = 80

    => x = 20.

    So, The required sum = x + (x + 2) = 2x + 2 = 42.

  • 55. The sum of two number is 25 and their difference is 13. Find their product.

  • Let the numbers be x and y.

    Then, x + y = 25 and x - y = 13.

    4xy = (x + y)2 - (x- y)2

       = (25)2 - (13)2

       = (625 - 169)

       = 456

    So, xy = 114.

  • 56. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

  • Let the middle digit be x.

    Then, 2x = 10 or x = 5. So, the number is either 253 or 352.

    Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.

    Hence, required number = 253.

  • 57. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

  • Let the numbers be x and y.

    Then, xy = 120 and x2 + y2 = 289.

    So, (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529

    So, x + y = √529 = 23.

  • 58. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

  • Let the numbers be x and y.
    Then, xy = 9375 and x/y =15
    xy/(x/y) = 9375/15
    => y2 = 625
    => y = 25
    => x = 15y = (15×25)=375
    So, Sum of the numbers = x + y = 375 + 25 = 400.
     

  • 59. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

  • Let the number be x.
    Then, x+17=60/x
    => x2+17x-60=0
    => (x+20)(x-3)=0
    => x=3

  • 60. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

  • Let the ten's digit be x.

    Then, unit's digit = x + 2.

    Number = 10x + (x + 2) = 11x + 2.

    Sum of digits = x + (x + 2) = 2x + 2.

    So, (11x + 2)(2x + 2) = 144

    => 22x2 + 26x - 140 = 0

    => 11x2 + 13x - 70 = 0

    => (x - 2)(11x + 35) = 0

    => x = 2.

    Hence, required number = 11x + 2 = 24.

  • 61. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

  • Let the ten's digit be x and unit's digit be y.

    Then, number = 10x + y.

    Number obtained by interchanging the digits = 10y + x.

    (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

  • 62. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

  • Let the numbers be a, b and c.

    Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.

    (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

    => (a + b + c) = √400 = 20.

  • 63. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

  • Let the ten's digit be x and unit's digit be y.

    Then, x + y = 15 and x - y = 3   or   y - x = 3.

    Solving x + y = 15   and   x - y = 3, we get: x = 9, y = 6.

    Solving x + y = 15   and   y - x = 3, we get: x = 6, y = 9.

    So, the number is either 96 or 69.

    Hence, the number cannot be determined.

  • 64. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

  • Let the ten's and unit digit be x and 8/x respectively.
    Then, (10x+8/x)+18=10× 8/x +x
    => 10x2 + 8 + 18x = 80 + x2

    =>  9x2 + 18x - 72 = 0

    => x2 + 2x - 8 = 0

    => (x + 4)(x - 2) = 0

    =>x = 2.

  • 65. The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?  

  • Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

    Let ten's and unit's digits be 2x and x respectively.

    Then, (10 x 2x + x) - (10x + 2x) = 36

    => 9x = 36

    => x = 4.

    So, Required difference = (2x + x) - (2x - x) = 2x = 8.

  • 66. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

  • Let the ten's digit be x and unit's digit be y.

    Then, (10x + y) - (10y + x) = 36

    => 9(x - y) = 36

    => x - y = 4.

  • 67. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

  • Let the three integers be x, x + 2 and x + 4.
    Then, 3x = 2(x + 4) + 3
    => x = 11
    So, Third integer = x + 4 = 15.

     

  • 68. If one-third of one-fourth of a number is 15, then three-tenth of that number is:

  • Let the number be x.

    Then, 1/3 of 1/4 of x = 15

    => x=15×12

    => x=180

    So, required number=(3/10)×180=54 Ans.

  • 69. কাজের দিন ২ টাকা পাওনা এবং অনুপস্থিতির দিন ৫০ পয়সা জরিমানা এই শর্তে সেপ্টেম্বর মাসে ৪০ টাকা পেল। সে কত দিন কাজে উপস্থিত ছিল?

  • সেপ্টেম্বরে দিন সংখ্যা =৩০ দিন

    ধরি,

    উপস্থিত দিন "ক"

    অনুপস্থিত  দিন= ৩০-ক

    প্রশ্নমতে,

    ২ক-.৫(৩০-ক)=৪০

    ২ক-১৫+.৫ক=৪০

    বা,২.৫ক=৪৫

    বা,ক=৪৫/২.৫=২২

     

  • 70. দুটি ক্রমিক সংখ্যার বর্গের অন্তর ২৫১ হলে, বড় সংখ্যাটি কত?

  • ধরি, ছোট সংখ্যাটি = x

          বড় সংখ্যাটি = (x+১)

    প্রশ্নমতে, (x+১)২-x২=২৫১

  • 71. How many ‘8’ will you pass on the way when you count form 1 to 100?

  • 8,18,28,38,48,58,68,78,80,81,82,83,84,85,86,87,88,89,98

  • 72. The average of the two-digit numbers which remain the same when the digits interchange the positions is-

  • 11+22+33+44+55+66+77+88+99=495

    So, 495/9= 55 (Ans.)

  • 73. If 15% of 40 is greater than 25% of a number by 2, then the number is-

  • Let, the number be x

    According to question,

    (15% of 40)-(25% of x)=2

    => 6 – X/4 =2

    => X/4 = 4

    => X=16 (Ans.)

  • 74. If a number decreased by 4 and divided by 6 the result is 8. What would be the result if 2 is subtract from the number and then it is divided by 5?

  • Let, the number be x

    So, (x-4)/6 =8

    => x= 52

     

    Again,

    (52-2)/5

    =50/5

    =10 (Ans.)

  • 75. If the sum of three consecutive integers is less than 75, what is the greatest possible value of the smallest one?

  • If sum were 75 the integers would be 24, 25 and 26
    so the next lowest sum would be 23 + 24 + 25 ie 72.

    The answer is thus 23.

  • 76. Which one of the following is the minimum value of the sum of two integers whose product is 36?

  • 1+ 36 = 37

    2 + 18 = 20

    3 + 12 =15

    4 + 9 = 13

    6 + 6 = 12

  • 77. If n is a positive integer and n2 is divisible by 72. then what is the largest positive integer that must be a factor of n?
  • 78. দুটি সংখ্যার অর্ধেকের যোগফল ৫২। তাদের পার্থক্যের এক-চতুর্থাংশ ১৪ হলে সংখ্যা দুইটি কত?

  • (x+y)/2 = 52

    x+y=104

    (x-y)/4=14

    x-y=56

    2x=160; x=80

    y=24

  • 79. যদি a, b, c এবং d এর গড় একটি বেজোড় পূর্ণসংখ্যা হয়, নিচের কোনটি a+b+c+d এর মান হতে পারে? 

  • যেহেতু সংখ্যা চারটি । সুতরাং সংখ্যাগুলোর মোট যোগফলের সাথে ৪ ভাগ দিলে প্রশ্ন মতে ত্তর বেজোড় সংখ্যা আসবে।

    ২০/৪ = ৫


     

  • 80. তিন অঙ্কের ক্ষুদ্রতম মৌলিক সংখ্যা কোনটি?
  • 81. তিন অঙ্কবিশিষ্ট একটি সংখ্যার অঙ্কত্রয়ের সমষ্টি ১২। প্রতিটি অঙ্ক শুধুমাত্র একবার ব্যবহার করে উক্ত তিন অঙ্কবিশিষ্ট বৃহত্তম সংখ্যা কোনটি?
  • 82. তিনটি ক্রমিক জোড় পূর্ণসংখ্যার ক্ষুদ্রতম সংখ্যাটি বৃহত্তমটির তিনগুন অপেক্ষা ৪০ কম হলে বৃহত্তম সংখ্যাটি কত?

  • x, x+2, x+4

    now,

    (x+4)*3 - 40 = x

    3x + 12 -40 = x

    2x = 40 - 12

    x = 28/2 = 14

    x = 14

    x + 4 = 14 + 4 = 18
     

  • 83. নিচের কোন ক্রমিক পূর্ণ সংখ্যাদ্বয়ের বর্গের অন্তর ৪৩?

  • Option ধরে আগালেই উত্তর বের হয়ে যায় ।

  • 84. যদি ক=৮খ + ২২ হয় এবং খ যদি একটি ধনাত্মক পূর্ণ সংখ্যা হয় তাহলে ক নিচের কোন সংখ্যা দ্বারা বিভাজ্য নয়?
  • 85. পরপর দুটি জোড় সংখ্যার বর্গের পার্থক্য নিচের কোন সংখ্যা দ্বারা বিভাজ্য?
  • 86. কোন সংখ্যার ৫% হবে ২৫৫ ?
  • 87. ১২৫টি কলম ও ১৪৫টি পেন্সিল কতজনের মধ্যে সমানভাবে ভাগ করে দেওয়া যাবে?  
  • 88. .1x.01×.001 /.2X.02X .002  এর মান কত ?
  • 89. কোন সংখ্যাকে ২ দ্বারা গুণ করে গুণফলকে ৩ দ্বারা ভাগ করলে ভাগফল ২ হবে?  
  • 90. If 15% of 40 is greater than 25% of a number by 2, then the number is :
  • 91. A, B, C hired a car for Tk. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were:  
  • 92. The smallest 5-digit number exactly divisible by 41 is.
  • 93. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
  • 94. If a number is decreased by 4 and divided by 6, the results is 8. What would be the result if 2 is subtracted from the number and then it is divided by 5?
  • 95. In a solution of 60 litre of sugar and water,20% is sugar.How much water must be added to make a solution that is 8% sugar?
  • in 60 liter  mixture,
    amount of sugar= 60 X 20/100=12 liter
    suppose,
    after  adding  x  liter quantity of sugar would be 8%
    here,
    (60+x)X8/100 =12
  • 96. Noman is 3 times as old as Abbas is now.Six years from now,he will be twice as old as Abbas will be then.How old is Abbas now?
  • Suppose,
    Abbas’s current age x year
    Noman’s current age 3x year
    after 6 years Abbas’s age=x+6
    after 6 years Noman’s age=3x+6
    here,
    (x+6)2=3x+6
    or,x=6
  • 97. If x and y are negative integers and x-y=1,what is the least possible value for xy?
  • 98. If x and y are integers and x=32y+15,which of the following must be an odd integer?  
  • 99. if x and y are integers and -9<x<9 and 0<y<14. what is the greatest possible value of (y-x)?

  • for -9<x<9 highest value of x = -8
    for 0<y<14 highest value of y =13
    so, y-x=13-(-8)=21

  • 100. if 2x-3 is an odd integer,find the next even integer?
  • 101. শিক্ষা সফরে যাওয়ার জন্য ২৪০০ টাকায় বাস ভাড়া করা হলো এবং প্রত্যেক ছাত্র/ছাত্রী সমান ভাড়া বহন করবে ঠিক হলো ।অতিরিক্ত ১০ জন ছাত্র/ছাত্রী যাওয়ায় প্রতি জনের ভাড়া ৮ টাকা কমে গেলে।বাসে কতজন ছাত্র/ছাত্রী গিয়েছিল?

  • মনেকরি প্রথমে শিক্ষা সফরে যাবার কথা ছিল x জন

    সুতরাং, জনপ্রতি ভাড়া ২৪০০/x টাকা

    সুতরাং, ১০জন অতিরিক্ত যাওয়ায় জনপ্রতি ভাড়া হবে ২৪০০/x+১০ টাকা

    প্রশ্নমতে, (২৪০০/x)-৮ = ২৪০০/x+১০ বা ৩০০/x -১=৩০০/x+১০

    বা, ৩০০-x/x = ৩০০/x+১০ বা, ৩০০x =৩০০x – x2 +৩০০০-১০x

    বা, x2 +১০x-৩০০০ = ০ বা, x2 +৬০x -৫০x-৩০০০=০

    বা, (x+৬০)(x-৫০)=০ হয় x= -৬০ [প্রযোজ্যনহে] অথবা x= ৫০

    সুতরাং,শিক্ষা সফরে মোট গিয়েছিল =(৫০+১০)=৬০ জন। 

  • 102. ৬০ থেকে ৮০-এর মধ্যবর্তী বৃহত্তম ও ক্ষুদ্রতম মৌলিক সংখ্যার অন্তর কত হবে?  

  • ৬০ ও ৮০ এর মধ্যে বৃহত্তম মৌলিক সংখ্যা ৭৯ এবং ক্ষুদ্রতম মৌলিক সংখ্যা

          ৬১ সুতরাং,তাদের মধ্যকার পার্থক্য (৭৯-৬১)=১৮। 

  • 103. ৬০ থেকে ৮০-এর মধ্যবর্তী বৃহত্তম ও ক্ষুদ্রতম মৌলিক সংখ্যার অন্তর কতহবে?

  • ৬০ ও ৮০ এর মধ্যে বৃহত্তম মৌলিক সংখ্যা ৭৯ এবং ক্ষুদ্রতম মৌলিক সংখ্যা ৬১ সুতরাং,তাদের মধ্যকার পার্থক্য (৭৯-৬১)=১৮।

  • 104. দুই অংকবিশিষ্ট কোন সংখ্যার দশকের অংকের সাথে ৩ যোগ করলে এবং    এককের অংক থেকে ২ বিয়োগ করলে প্রাপ্ত সংখ্যাটি মূল সংখ্যার তিনগুন    হয়।সংখ্যাটি কত?

  • ধরি এককের অংক y এবং দশকের অংক x ; তাহলে সংখ্যাটি =10x+y

            প্রশ্নমতে, 10(x+3)+y-2=3 (10x+y)

    = 10x+30+y-2 = 30x+3y = 10x+y+28 =30x+3y

    =20x+2y = 28 =2(10x+y) =28

    =10x+y = 14 ; সুতরাং,সংখ্যাটি ১৪ ।

  • 105. (০.০০৩)২ = কত ?

  • ২২. দেয়া আছে, ১০টি সংখ্যার যোগফল  ৪৬২

       প্রথম  চারটি সংখ্যার গড় ৫২ হলে যোগফল =(৫২X৪)=২০৮

        শেষ পাঁচটি সংখ্যার গড়  ৩৮ হলে যোগফল =(৩৮X৫)=১৯০

        সুতরাং, ৯টিসংখ্যার যোগফল (২০৮+১৯০)=৩৯৮

        সুতরাং, পঞ্চম সংখ্যাটি হবে (৪৬২-৩৯৮)=৬৪।

  • 106. (০.০০৩)২ = কত ?
  • 107. If a man travels p hours at an average rate of q miles per hour, and then r hours at an average rate of s miles per hour, what is his overall average rate of speed?

  • Total miles traveled in p hours = p x q miles and

    Total miles traveled in r hours = r x s miles

    so, average rate of speed = total miles traveled / number of hours

                                         =[{(p x q)+(r x s)} / (p+r)]= (pq+rs)/(p+r)miles per hour

  • 108. All the page numbers from a book are added, beginning at page1. However, one page number was mistakenly added twice. The sum obtained was 1000. which page number was added twice?
  • 109. A red light flasher 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both light start flashing at the same time, how many times do they flash together in each hour ?

  • for red light->flash/min=3
    fro green light->flash/min=10

  • 110.  If X is an integer and Y = 9x + 13, what is the greatest value of x for which Y is less than 100 ?
  • We need to find out the maximum value of x for which (9x + 13) is less than 100 
    --> (9x + 13) < 100 
    --> 9x < (100 - 13) = 87 
    --> x < 87/9 = 9.(something) 
    As x is an integer, maximum possible value of x is 9.
  • 111. The value of (1+ .1+ .01+.001) is
  • 112. A two-digit number becomes five-sixth of itself when its digits its digits are reversed. The two digits differ by one. The number is:
  • 113. The difference between the place value and the face value of 6 in numeral 856974 is 8211

  • (Place value of 6) - (Face value of 6) = (6000 - 6) = 5994

  • 114. A boy was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. The number to be multiplied was:

  •  let number is= x.
     now 52x = 25x + 324
     or, x= 12

  • 115. What mathematical operation should come at the place of ‘?’ in the equation: 2? 6-12÷4 + 2 = 11.  
  • 116. . An athlete runs 200 meters race in 24 seconds. His speed is:

  • speed=distance/time
              = 200/24 m/sec
               =25/3m/sec
               =(25/3 x 18/5)km/hr

  • 117.  The difference between a number and its two-fifth is 510.What is 10 percent of that number?

  • let,
     the number  is  x
    Then,
    x-2/5x=510
    3x/5=510
    x=510 X 5/3=850
    10 % 0f 850 = 85.

  • 118. A number is as much greater than 36 as the less than 86. Find the number.

  • Given,
    x is as much greater than 36 as is less than 86.
    x-36 = 86-x
    x+x = 86+36
    2x = 122
    x = 122/2 = 61
     

  • 119. which of the following is the value of √(0.000064)3
  • 120. In January, the value of a stock increased by 25% and in February, it decreased by 20%. How did the value of the stock at the end of February compare with its value at the beginning of January?

  • The value after 25% increase is tk 125 from tk 100
    At 20% decrease,
    If 100 is the original than the new value is tk 80
    if  1     is the original than the  new value is 80/100
    If 125 is the original than the new value is tk 80 x125/100 =100 tk

  • 121. . If (7a) (7b) = 7c/7d, what is d in terms of a, b and c?

  • (7a) (7b) = 7c/7d
         7a+b=7c-d
    a+b=c-d
    d=c-a-b

  • 122.  If -7 <x <7 and 0<y< 12, what is the greatest possible value of y – x?

  • max value=of y=12
    min value if x=-7
    greatest possible value=max-min=12-(-7)=19

  • 123. কোন ক্ষুদ্রতম সংখ্যাকে ৪,৫, ও ৬ দ্বারা ভাগ করেল প্রতি ক্ষেত্রে  ১ অবিশষ্ট থাকবে?

  • ৪,৫ ও ৬ সঙ্খ্যা ৩ টির  লসাগু=৬০
    প্রতিক্ষেত্রে, যেহেতু ১ অবশিষ্ট থাকে তাহলে সংখ্যাটি = ৬০+১=৬১  

  • 124. The average of two numbers is 62. If 2 is added to the smaller number, the ratio between the numbers becomes 1:2. The smaller number is-

  • suppose,
    small number is x and another one is y
    here,
    x+y/2=62
    or,x+y=124….i
    x+2/y=1/2
    or,2x+4=y
    or,2x-y=-4…….ii
    i+ii ,
    3x=120
    or,x=40

  • 125. The present ratio of student to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teacher were to increase by 5, the ratio of student to teachers would then be 25 to 1. What is the present number of teachers?

  • Suppose,
    number of students 30x
    number of techers x
    here,
    30x+50/x+5=25/1
    or,x=15
    so, number of teacher 15  

  • 126. How many prime numbers are there between 45 and 72?

  • prime numbers are=47, 53, 59, 61, 67, 71

  • 127. Sum of two numbers is 15 and their difference is 13. Identify the smaller number.

  • suppose,
    bigger number=a
    smaller number=b
    here,
    a+b=15
    a-b=13
    so,2a=28
    or,a=14
    so,smaller number is=15-14=1

  • 128. Mr. Karim purchased Tk. 600 worth of traveler’s cheques. If each cheque was worth either Tk. 20 or Tk. 50, which of the following cannot be the number of Tk. 20 cheques purchased?
  • 129. The difference between two numbers is 7 and their product is 60. One of the two numbers must be ----
  • 130. A two-digit number has 6 in its unit digit. The sum of its digits is one fourth of the number itself. What is the number?
  • 131. Of the 45 students in a certain class, 28 are in drama club and 31 are in communication club. If 8 of the students are not in either club, how many of the students are in only one of the two clubs?
  • 132. In the figure, the product of any two numbers in adjacent circles is equal to the product of the two numbers that are opposite those circles. What is the value of h?
  • 133. Which number is appropriate in place of question mark?
  • 134. Fill in the missing number of the series 3, 8, 18, 38, ___, 158

  • 3+5=8 
    8+10=18 
    18+20=38 
    38+40=78 

  • 135. How many ¼’s are there in 47(1/2)?
  • 136. If the mean of numbers 28, x, 42, 78 and 104 is 62, then what is the mean of 128, 255, 511, 1023 and x?          

  • The new mean  =62+{(128+255+511+1023+x)−(28+x+42+78+104)}/5
                             =62+{(1917+x)−(252+x)}/5

  • 137. If n is any negative number, which of the following must be positive?
  • 138. A two digit number has 3 in its unit digit. The sum of its digits is one-seventh of the number itself. What is the number?

  • Let n = tens digit
    Let m = units digit
    Then your whole number is
    N = 10 X n + m……(1)
    here,
     n + m = 1/7 X (10Xn + m)……….(2)

    the units digit is 3 or

    m = 3

    Now to solve, put 3 into (2) and get

    n + 3 = 1/7 X (10 X n + 3)
    or, 7 X n + 21 = 10 X n + 3
    where  simply multiplied both sides by 7.

    Or,3Xn = 18
     or, n = 6

    Therefore your number is from (1)

    N = 10X6 + 3 or
     N = 63

     

  • 139. If an integer y is subtracted from an integer x, and the result is greater than x, then y must be

  • The only way you can subtract from a number and get an answer larger than the number is to subtract a negative quantity

  • 140. Of two groups of tourists, each has 60 people. If three fourth (i.e  75%) of the first group and two-third of the second group board buses to travel to a museum, how many more people of the first group board buses than that of the second group?
  • 141. Barkat bought equal numbers of 2-paisa and 30-paisa stamps. If the total cost of the stamps was Tk. 10.00, what was the total number of stamps bought?
  • 142. If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?

  • Basically any multiple of these number so if you factorize 15 its = 3 x 5 
    therefore 2x3x5 = 30 
    So,
    K + 30 will always be divisible by the given numbers.

  • 143. If  2x+y>10, then 4x + 3y must be
  • 144. If n is an odd integer, which of the following must also be odd?
  • 145. Insert the missing number? 4   11   8   19   12   ?

  • 4:8:12 = 4 differance
    11:19:27= 8 differance

  • 146. If the average of five consecutive even numbers is 8, which of the following is the smallest of the five numbers?

  • here,
    numbers are= n,n+2,n+4,n+6,n+8
    here,
    (n+n+2+n+4+n+6+n+8)/5=8
    or,5n+20=40
    or,5n=20
    or,n=4

     

  • 147. A survey of City A found an average (arithmatic mean) of 3.2 people per household and an average of 1.2 DVD players per household. If 48000 people live in City A, how many DVD players are there in City A?

  • 3.2 people live in 1 house hold
    1 people live in 1/3.2 house hold
    48000 people live in 48000/3.2     house hold=15000 household
    in 1 household the is 1.2 dvd
    in 15000 household 1.2x15000=18000 dvd

  • 148. How many numbers from 1 to 200 inclusive are equal to the cube of an integer?

  • 1^3=1, 2^3 = 8, 3^3=27, 4^3=64, 5^3=125

    So there are 5 integers.

  • 149. 3 + 33 + 333 + 3.33 =?
  • 150. Which one of the following can't be the square of natural number?

  • The square of a natural number nerver ends in 2.

    So, 143642 is not the square of natural number.

  • 151. What is the unit digit in 7105?

  • Unit digit in 7105 = Unit digit in [ (74)26 x 7 ]

    But, unit digit in (74)26 = 1

    So, Unit digit in 7105 = (1 x 7) = 7

  • 152. The sum of all two digit numbers divisible by 5 is:

  • Required numbers are 10, 15, 20, 25, ..., 95

    This is an A.P. in which a = 10, d = 5 and l = 95.

    tn = 95

    => a + (n - 1)d = 95

    => 10 + (n - 1) x 5 = 95

    => (n - 1) x 5 = 85

    => (n - 1) = 17

    => n = 18

    So, Required Sum = (n/2) x (a + l)

    = (18/2) x (10 + 95)

    = (9 x 105) = 945.

  • 153. The sum of first 45 natural numbers is:

  • Let Sn = (1 + 2 + 3 + ... + 45)

    This is an A.P. in which a = 1, d = 1, n = 45 and l = 45

    Sn = (n/2) x (a + l) = (45/2) x (1 + 45) = (45 x 23)   = 1035

    Required sum = 1035.

  • 154. Which one of the following can't be the square of natural number?

  • The square of a natural number never ends in 7.

    So, 42437 is not the square of a natural number.

  • 155. If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y =?

  • 80 = 2 x 5 x 8

    Since 653xy is divisible by 2 and 5 both, so y = 0.

    Now, 653x is divisible by 8, so 13x should be divisible by 8.

    This happens when x = 6.

    So, x + y = (6 + 0) = 6.

  • 156. If 60% of (3/5) of a number is 36, then the number is:

  • Let the number be x. Then

    60% of 3/5 of x = 36

    => 60/100 x 3/5 x x = 36

    => x = (36 x (25/9)) = 100

    Thus, The required number = 100

  • 157. 2 + 22 + 23 + ... + 29 =?

  • 158. The smallest 5 digit number exactly divisible by 41 is: 
  • The smallest 5-digit number = 10000.

 41) 10000 (243
     82
     ---
     180
     164
     ----
      160
      123
      ---
       37
      --- 

 Required number = 10000 + (41 - 37)
                 = 10004.
  • 159. The smallest 6 digit number exactly divisible by 111 is: 
  • The smallest 6-digit number 100000.

 111) 100000 (900
      999
      -----
        100
        ---

 Required number = 100000 + (111 - 100)
                 = 100011.
  • 160. Which one of the following is a prime number?
  • 161. Which one of the following numbers is completely divisible by 99?

  • 99 = 11 x 9, where 11 and 9 are co-prime.

    By hit and trial, we find that 114345 is divisible by 11 as well as 9.

    So, it is divisible by 99.

  • 162. If a and b are odd numbers, then which of the following is even?

  • The sum of two odd number is even. So, a + b is even.

  • 163. The sum all even natural numbers between 1 and 31 is:

  • Required sum = (2 + 4 + 6 + ... + 30)

    This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.

    Let the number of terms be n.

    Then,tn = 30    a + (n - 1)d = 30

    => 2 + (n - 1) x 2 = 30

    => n - 1 = 14

    => n = 15

    Sn = (n/2)(a + l)

    =(15/2) x(2 + 30)

    = 240.

  • 164. The difference of the squares of two consecutive even integers is divisible by which of the following integers?

  • Let the two consecutive even integers be 2n and (2n + 2). Then,

    (2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)

         = 2(4n + 2)

         = 4(2n + 1), which is divisible by 4.

  • 165. (xn - an) is completely divisible by (x - a), when

  • For every natural number n, (xn - an) is completely divisible by (x - a).

  • 166. How many prime numbers are less than 50?

  • Prime numbers less than 50 are:

    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

    Their number is 15

  • 167. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:

  • 987 = 3 x 7 x 47

    So, the required number must be divisible by each one of 3, 7, 47

    553681 –> (Sum of digits = 28, not divisible by 3)

    555181 –>  (Sum of digits = 25, not divisible by 3)

    555681 is divisible by 3, 7, 47.

  • 168. On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:

  • Clearly, (2272 - 875) = 1397, is exactly divisible by N.

    Now, 1397 = 11 x 127

    The required 3-digit number is 127,

    So, The sum of whose digits is 10.

  • 169.

  • 170. If the number 5 * 2 is divisible by 6, then * =?

  • 6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x.

    Then, (5 + x + 2) must be divisible by 3.

    So, x = 2.

  • 171. 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:

  • Let the given number be 476 xy 0.

    Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3.

    And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11.

    x - y - 3 = 0

    =>  y = x - 3

    (17 + x + y) = (17 + x + x - 3) = (2x + 14)

    => x= 2 or x = 8.

    So, x = 8 and y = 5.

  • 172. (12345679 x 72) =?

  • 12345679 x 72 = 12345679 x (70 +2)

                    = 12345679 x 70 + 12345679 x 2

                    = 864197530 + 24691358

                    = 888888888

  • 173. The smallest prime number is:

  • The smallest prime number is 2.

  • 174. 8597 - ? = 7429 - 4358
  • 175. A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) =? 
  •  4 a 3  |
 9 8 4  }  ==> a + 8 = b  ==>  b - a = 8  
13 b 7  |

  • 176. How many 3 digit numbers are divisible by 6 in all?

  • Required numbers are 102, 108, 114, ... , 996

    This is an A.P. in which a = 102, d = 6 and l = 996

    Let the number of terms be n.

    Then, a + (n - 1)d = 996

    => 102 + (n - 1) x 6 = 996

    => 6 x (n - 1) = 894

    => (n - 1) = 149

    => n = 150.

  • 177.
  • 178. How many of the following numbers are divisible by 3 but not by 9? 2133, 2343, 3474, 4131, 5286, 5340, 6336, 7347, 8115, 9276

  • Marking (/) those which are are divisible by 3 by not by 9 and the others by (X), by taking the sum of digits, we get:s

    2133 –> 9 (X)

    2343 –> 12 (/)

    3474 –> 18 (X)

    4131 –> 9 (X)

    5286 –> 21 (/)

    5340 –> 12 (/)

    6336 –> 18 (X)

    7347 –> 21 (/)

    8115 –> 15 (/)

    9276 –> 24 (/)

    Required number of numbers = 6.

  • 179. How many natural numbers are there between 23 and 100 which are exactly divisible by 6?

  • Required numbers are 24, 30, 36, 42, ..., 96

    This is an A.P. in which a = 24, d = 6 and l = 96

    Let the number of terms in it be n.

    Then tn = 96    a + (n - 1)d = 96

    => 24 + (n - 1) x 6 = 96

    => (n - 1) x 6 = 72

    => (n - 1) = 12

    => n = 13

    Required number of numbers = 13.

  • 180. How many 3-digit numbers are completely divisible 6?

  • 3-digit number divisible by 6 are: 102, 108, 114,... , 996

    This is an A.P. in which a = 102, d = 6 and l = 996

    Let the number of terms be n. Then tn = 996.

    So, a + (n - 1)d = 996

    => 102 + (n - 1) x 6 = 996

    => 6 x (n - 1) = 894

    => (n - 1) = 149

    => n = 150

    Number of terms = 150.

  • 181. On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?

  • Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.

    So, x = 5k + 3

    => x2 = (5k + 3)2

    = (25k2 + 30k + 9)

    = 5(5k2 + 6k + 1) + 4

    So, On dividing x2 by 5,

    We get 4 as remainder.

  • 182. What will be remainder when (6767 + 67) is divided by 68?

  • xn + 1) will be divisible by (x + 1) only when n is odd.

    (6767 + 1) will be divisible by (67 + 1)

  • 183. 107 x 107 + 93 x 93 =?

  • 107 x 107 + 93 x 93

    = (107)2 + (93)2

    = (100 + 7)2 + (100 - 7)2

    = 2 x [(100)2 + 72]

    = 20098

  • 184. If n is a natural number, then (6n2 + 6n) is always divisible by:

  • (6n2 + 6n) = 6n(n + 1),

    Which is always divisible by 6 and 12 both,

    since n(n + 1) is always even.

  • 185. On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder?

  • x = 56*y + 29 
    = 7*8*y + 3*8 + 5 
    The remainder is 5

  • 186. The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:

  • Let the required fraction be x.

    Then (1/x) - x = 9/20

    So, (1 - x2)/x = 9/20

    => 20 - 20x2 = 9x

    => 20x2 + 9x - 20 = 0

    => 20x2 + 25x - 16x - 20 = 0

    => 5x(4x + 5) - 4(4x + 5) = 0

    => (4x + 5)(5x - 4) = 0

    So, x = 4/5

  • 187. The difference between the local value and the face value of 7 in the numeral 32675149 is

  • (Local value of 7) - (Face value of 7)

    = (70000 - 7)

    = 69993

  • 188. If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:

  • Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3)

    = (29 + x), which must be divisible by 9.

    So, x = 7.

  • 189. (?) + 3699 + 1985 - 2047 = 31111

  • x + 3699 + 1985 - 2047 = 31111

    => x + 3699 + 1985 = 31111 + 2047

    => x + 5684 = 33158

    => x = 33158 - 5684 = 27474.

  • 190.

  • 191. Which of the following number is divisible by 24?

  • 24 = 3 x8, where 3 and 8 co-prime.

    Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.

    Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.

    Consider option (D),

    Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27,

    Which is divisible by 3.

    Also, 736 is divisible by 8.

    3125736 is divisible by (3 x 8), i.e., 24.

  • 192. The sum of first 45 natural numbers is:

  • n(n + 1)/2

    = 45(45 + 1)/2

    = 1035.

  • 193. (?) - 19657 - 33994 = 9999

  • 194. Which one of the following numbers is exactly divisible by 11?

  • (4 + 5 + 2) - (1 + 6 + 3) = 1, not divisible by 11.

    (2 + 6 + 4) - (4 + 5 + 2) = 1, not divisible by 11.

    (4 + 6 + 1) - (2 + 5 + 3) = 1, not divisible by 11.

    (4 + 6 + 1) - (2 + 5 + 4) = 0,

    So, 415624 is divisible by 11.

  • 195. The smallest 3 digit prime number is:

  • The smallest 3-digit number is 100, which is divisible by 2.

    100 is not a prime number.

    √101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11.

    So, 101 is a prime number.

    Hence 101 is the smallest 3-digit prime number.

  • 196. If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:

  • Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4)

    = (22 + x), which must be divisible by 3.

    So, x = 2.

  • 197. 72519 x 9999 =?

  • 72519 x 9999 = 72519 x (10000 - 1)

                    = 72519 x 10000 - 72519 x 1

                    = 725190000 - 72519

                    = 725117481.

  • 198. (12)3 x 64 ÷ 432 =?

  • Given Exp. = {(12)3 x 64)/432

    = {(12)3 x 64} / (12 x 62)

    = (12)2 x 62

    = (72)2

    = 5184

  • 199. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?

  • Let the smaller number be x. Then larger number = (x + 1365).

    So, x + 1365 = 6x + 15

    => 5x = 1350

    => x = 270

    So, Smaller number = 270.

  • 200. The sum of first five prime numbers is:

  • Required sum = (2 + 3 + 5 + 7 + 11) = 28.

  • 201. 5358 x 51 =?

  • 5358 x 51 = 5358 x (50 + 1)

                    = 5358 x 50 + 5358 x 1

                    = 267900 + 5358

                    = 273258.

  • 202. What is the unit digit in {(6374)1793 x (625)317 x (341491)}?

  • Unit digit in (6374)1793 = Unit digit in (4)1793

        = Unit digit in [(42)896 x 4]

        = Unit digit in (6 x 4) = 4

    Unit digit in (625)317 = Unit digit in (5)317 = 5

    Unit digit in (341)491 = Unit digit in (1)491 = 1

    Required digit = Unit digit in (4 x 5 x 1) = 0.

  • 203. Which of the following is a prime number?

  • Clearly, 97 is a prime number.

  • 204. The largest 4 digit number exactly divisible by 88 is:

  • 205. (935421 x 625) =?

  • 935421 x 625

    = 935421 x 54

    = (935421 x  104)/24

    = (935421 x 104)

    = 9354210000/16

    = 584638125

  • 206. How many of the following numbers are divisible by 132? 264, 396, 462, 792, 968, 2178, 5184, 6336

  • 132 = 4 x 3 x 11

    So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.

    264 –> 11,3,4 (/)

    396 –> 11,3,4 (/)

    462 –> 11,3 (X)

    792 –> 11,3,4 (/)

    968 –> 11,4 (X)

    2178 –> 11,3 (X)

    5184 –> 3,4 (X)

    6336 –> 11,3,4 (/)

    Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.

    Required number of number = 4.

  • 207. 1397 x 1397 = ?

  • 1397 x 1397 = (1397)2

                    = (1400 - 3)2

                    = (1400)2 + (3)2 - (2 x 1400 x 3)

                    = 1960000 + 9 - 8400

                    = 1960009 - 8400

                    = 1951609.

  • 208. What least number must be added to 1056, so that the sum is completely divisible by 23?

  • 209. It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

  • Let 232 = x.

    Then, (232 + 1) = (x + 1).

    Let (x + 1) be completely divisible by the natural number N. Then,

    (296 + 1) = [(232)3 + 1]

    = (x3 + 1)

    = (x + 1)(x2 - x + 1),

    which is completely divisible by N,

    since (x + 1) is divisible by N.

  • 210. (112 x 54) = ?

  • (112 x 54) = 112 x(10/2)4               

    = (112 x 104)/24                

    = 1120000/16

    = 70000

  • 211. Which one of the following is not a prime number?

  • 91 is divisible by 7. So, it is not a prime number.

  • 212. What is the smallest number to be subtracted from 549162 in order to make it a perfect square?  

  •  

  • 213. How many prime numbers are less than 50?

  • 1,2,3,7,11,13,17,19,23,29,31,37,41,43,47

  • 214. Which of the following numbers does not tie between 4/5 and 7/13?
  • 4/5=.8 and 7/13=.53846154
     
    1/2=.5 
    so 1/2  does not tie between 4/5 and 7/13
     

     

  • 215. The sum of two numbers is 15 and the sum of their squares is 113 Find the numbers.
  • The sum of the numbers is 15
    x + y = 15
    or y = (15 - x);
    we can use this for substitution:
    "The sum of the squares is 113"
    x2 + y2 = 113
    Substitute (15-x) for y in the above equation
    x2 + (15-x)2 = 113

    x2 + 225 - 30x + x2 = 113
    Arrange as a quadratic equation:
    x2+ x2 - 30x + 225 - 113 = 0
    2x2 - 30x + 112 = 0
    Simplify, divide by 2
    x2 - 15x+56=0
    => x2 -8x - 7x + 56 =0
    => x(x-8)-7(x-8)=0
    => (x-8)(x-7)=0
    so, x= 8 or 7
    when x = 8, then y=15-8=7
    or, when x = 7, then y=15-7=8
  • 216. By how much is three fifth of 350 greater than four seventh of 210?

  • 3/5 of  350 - 4/7 of 210 = 210 - 120 = 90.

  • 217. The least number which is a perfect is a perfect square and is divisible by each of the numbers 16, 20 and 24, is:

  •  lcm is 4x4x5x6 = 2x2x5x2x3 
    square number is = 2x2x5x5x2x2x3x3 = 3^2x4^2x5^2 = 3600

  • 218. How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 8?

  • A number ending in 8 can never be a perfect square.

  • 219. What is the sum of two consecutive even numbers, the difference of whose squares is 84?

  • Let the numbers be x and x + 2.

    Then, (x + 2)2 - x2 = 84

    => 4x + 4 = 84

    => 4x = 80

    => x = 20.

    Therefore, The required sum = x + (x + 2)

    = 2x + 2 = 42.

  • 220. The sum of two numbers is 25 and their difference is 13. Find their product.

  • Let the numbers be x and y.

    Then, x + y = 25 and x - y = 13.

    4xy = (x + y)2 - (x- y)2

       = (25)2 - (13)2

       = (625 - 169)

       = 456

    So, xy = 114.

  • 221. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is:

  • Let the middle digit be x.

    Then, 2x = 10 or x = 5.

    So, the number is either 253 or 352.

    Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.

    Hence, required number = 253.

  • 222. The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

  • Let the numbers be x and y.

    Then, xy = 120 and x2 + y2= 289.

    So, (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529

    Therefore, x + y = √529 = 23.

  • 223. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

  • Let the numbers be x and y.

    Then, xy = 9375 and        x /y= 15.

    xy/(x/y) = 9375/15

    => y2 = 625

    => y = 25

    => x = 15y = (15 x 25) = 375.

    So, Sum of the numbers = x + y = 375 + 25 = 400.

  • 224. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.

  • Let the number be x.

    Then, x + 17 = 60/x

    =>x2 + 17x - 60 = 0

    =>(x + 20)(x - 3) = 0

    =>x = 3.

  • 225. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

  • Let the ten's digit be x.

    Then, unit's digit = x + 2.

    Number = 10x + (x + 2) = 11x + 2.

    Sum of digits = x + (x + 2) = 2x + 2.

    So, (11x + 2)(2x + 2) = 144

    =>22x2 + 26x - 140 = 0

    =>11x2 + 13x - 70 = 0

    =>(x - 2)(11x + 35) = 0

    =>x = 2.

    Hence, required number = 11x + 2 = 24.

  • 226. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

  • Let the ten's digit be x and unit's digit be y.

    Then, number = 10x + y.

    Number obtained by interchanging the digits = 10y + x.

    So, (10x + y) + (10y + x) = 11(x + y),

    Which is divisible by 11.

  • 227. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

  • Let the numbers be a, b and c.

    Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.

    (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

    => (a + b + c) = √400 = 20.

  • 228. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

  • Let the ten's digit be x and unit's digit be y.

    Then, x + y = 15 and x - y = 3   or   y - x = 3.

    Solving x + y = 15   and   x - y = 3, we get: x = 9, y = 6.

    Solving x + y = 15   and   y - x = 3, we get: x = 6, y = 9.

    So, the number is either 96 or 69.

    Hence, the number cannot be determined.

  • 229. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:

  • Let the ten's and unit digit be x and 8/x respectively.

    Then, (10x + (8/x)) + 18 = 10 x (8/x) + x

    => 10x2 + 8 + 18x = 80 + x2

    => 9x2 + 18x - 72 = 0

    => x2 + 2x - 8 = 0

    => (x + 4)(x - 2) = 0

    => x = 2.

  • 230. The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2?

  • Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.

    Let ten's and unit's digits be 2x and x respectively.

    Then, (10 x 2x + x) - (10x + 2x) = 36

    => 9x = 36

    => x = 4.

    So, Required difference = (2x + x) - (2x - x) = 2x = 8.

  • 231. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

  • Let the ten's digit be x and unit's digit be y.

    Then, (10x + y) - (10y + x) = 36

    => 9(x - y) = 36

    => x - y = 4.

  • 232. Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

  • Let the three integers be x, x + 2 and x + 4.

    Then, 3x = 2(x + 4) + 3

    =>  x = 11.

    So, Third integer = x + 4 = 15.

  • 233. If one-third of one-fourth of a number is 15, then three-tenth of that number is:

  • Let the number be x.

    Then, 1/3 of ¼ of x = 15

    => x = 15 x 12 = 180

    So, required number = (3/10) x 180 =54

  • 234. If n and p are both odd numbers, which of the following must be an even number?

  • An odd number is always = An Even number + 1

    Thus, n = Even number +1

    p = Even number + 1

    Thus,

    n + p = Even Number + Even Number + 1 + 1

    or, n + p = Even Number + 2 [ As Even + Even = Even Number]

    or, n + p = Even Number [As Even + 2 = Even Number]

  • 235. If 18 is 15 percent of 30 percent of a certain number, what is the number?

  • Lets assume that number is a 
    30% of number = a x 30/100 = 3a/10 
    15% of 3a/10 = 3a/10 x 15/100 = 45a/1000 
    Given
    45a/1000 = 18 

  • 236. A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

  • Let the number of horses = x
    Then the number of pigeons = 80 – x.
    Each pigeon has 2 legs and each horse has 4 legs.
    Therefore, total number of legs  = 4 x + 2 ( 80 − x ) = 260

    ⇒ 4 x + 160 – 2 x = 260
    ⇒ 2 x = 100
    ⇒ x =  50

  • 237. If the sum of the 3 consecutive integers 240, then the sum of the two larger integers is:

  • suppose,
    integers are=x,x+1,x+2
    here,
    x+x+1+x+2=240
    or,x=79
    so, the largest number is 80,81
    x+x+1+x+2=240
    or,3x+3=240
    or,x=79

     

  • 238. In a group of 15, 7 have studied Latin, 8 have studied Greek, and 3 have not studied either. How many of these studied both Latin and Greek?

  • In the group of 12 who have studied at least one, 7 have studied Latin and 8 have studied Greek. 
    7+8=15, which is 3 larger than 12. 
    Therefore, 3 students studied both. 

  • 239. There are 200 questions on a 3-hour examination. Among these questions 50 are mathematics problems. It is suggested that twice as much time be spent on each math problem as for each other question. How many minutes should be spent on mathematics problems?

  • First, since we're talking about minutes, convert 3 hr into minutes:
    3X60 = 180 minutes
    Let x = minutes spent on a non-math problem
    then,
    2x = minutes spent on a math problem
    Here,
    x(200-50) + 2x(50) = 180
    x(150) + 2x(50) = 180
    150x + 100x = 180
    250x = 180
    x = 0.72 minutes
    Time to spend on math problems:
    2x(50)=100x = 100(0.72) = 72 minutes

     

  • 240. What is the maximum number of half pint bottles of cream that can be filled with a 4-gallon can of cream?

  • From ques
    1 gallon = 4 qt.
    => 4 gallon = 16 qt.
    Now
    since 1 qt can fil up 2 pt bottles
    so, 1 qt can fil up 4 half pt bottles
    so, 4*16 = 64 half pint bottles can be filled up using 4 gallon cream
  • 241. Divide 60 by half and deduct twenty. What do you get?

  • 60/0.5 - 20 = 120-20 = 100

  • 242. If 6 and X have the same mean as 2, 4 and 24, what is the value of X?

  • Average:\\\\\frac{2+4+24}{3}=\frac{30}{3}=10\\\\\frac{6+x}{2}=10\\\\6+x=20\\\\x=20-6=14

  • 243. If p is an even integer and q is an odd integer, which of the following must be an odd integer?

  • Whenever you add an odd number to an even number, the result will be odd.

    A&E are out because with division, you can't be sure to get an integer.
    B is out because the product of an even number and an odd number is always even.
    D is out because any integer times two is even.

  • 244. There are 8 more men than women on board of directors of a company. If there are 20 members on the board, how many are men?

  • If, number of women = x

    then, number of men = x +8

    Now,

    x + x + 8 = 20

    or, 2x + 8 = 20

    or, 2x = 12

    or, x = 6

    So,

    number of men = 6 + 8 = 14

  • 245. The sum of 3 consecutive odd numbers is 57. The middle one is-

  •  x + (x+2) + (x+4) = 57 
    3x + 6 = 57 
    3x = 51 
    x = 17 
    so, the middle one is=17+2=19

  • 246. 25/?=?/81. What is the missing number?

  • Go through the options and calculationg by placing the number in their respective place.

    While doing 45,

    25/45 = 45/81

    is seen.

  • 247. Consider the following series: 3, 4, 6, 9, 13,----, what comes next?

  • 3+1=4; 4+2=6; 6+3=9; 9+4=13; 13+5=18

  • 248. What is the sum of 0.15, 0.10 and 0.65?

  •    0.65

    + 0.15

    + 0.10

    ---------------

    = 0.90

    = 90 /100

    = 9 / 10

  • 249. If 4 times an integer x is increased by 10, the result is always greater than 18 and less than 34. What is the least value of x?

  • You have to go through the options here to find out the answer.

    Option 1:

    2*4 + 10 = 18

    This is not greater than 18.

    Option 2:

    3*4 + 10 = 22

    This is greater than 18 and less than 34.

    Plus, this is the lowest integer that follows the given conditions.

  • 250. When 4 is added to one half of a number, the result is 14. What is the number?

  • The number is x.

    One half of the number is x /2

    So, (x / 2) + 4 = 14

    or, (x / 2) = 14 - 4 = 10

    or, x = 10 * 2 = 20

  • 251. 108+? Of 1/3+2/5×33/4=101/2

  • Correct answer নেই।

  • 252. Find the least number of six digits which is exactly divisible by 15, 21 and 28.

  • In this case, reverse process is much more faster.

    Go through the options. Divide each option with the following numbers: 15, 21 and 28.
    Here, all the option meets the condition of being six digit number.

    If only one option meets the condition, that will be the answer.
    If more than one option meets the divisibility condition. Then, as asked in the question, find out which option is the least in the numerical order.

  • 253. You can rent a bungalow on daily basis at Taka 500 per day or on monthly basis at Taka 10,000 per month. How much can you save annually by renting on monthly basis?

  • On Daily Basis,
    Annual cost will be = (500 * 365) taka

                                   = 182500 taka

    On monthly basis,

    Annual cost will be = (10000 * 12) taka

                                   = 120000 taka

    Total save = (182500 - 120000) taka

                     = 62,500 taka

  • 254. To fill a number of vacancies, a company must hire 3 officers from 6 applicants, and 2 managers from 4 applicants. What is the total number of ways in which the company can make its selection?    
  • 255. In a class of 40 students, the number of students who passed the math exam is equal to half the number of students who passed the science exam. Each student in the class passed at least one of the two exams. If 5 students passed both exams, then how many students passed the math exam?

  • Let the number of those passed in math be m

    and those who passed in science be s.

    Thus, m = s/2.

    Now, m + s – 5 = 40.

    Thus, s/2 + s -5 =40.

    or, s = 30 and m = 15
     

  • 256. If the sum of three consecutive integers is odd, then   the   first and   the   last   integers must be-
  • 257. Robi has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?

  • "individual" just means 1.
    It doesn't mean that we are selecting exactly 1 sock from each pair. It just means that we are removing 7 socks.

     

    John has 10 pairs of socks. Convert to actual socks. 20 actual socks. He loses 7. He only has 13 socks left. He needs two/pair. 13/2 is 6.5 pairs. He can only, at most have 6 pair.

  • 258. Three consecutive even numbers are such that if the first is divided by 6, the second by 4 and the third by 7, the sum of the quotients is 38. Find the numbers,
  • 259. An amount of money was distributed among some people in such a way that it there had been 4 more people, everyone would have got Tk. 16 less. But if there had been 4 less people everyone would have got Tk. 24 more. How many people were there in the group?
  • 260. In a class, 50% of the male students and 2/3 of the female students speak French. If there are 3/4 as many girls' as boys, What fraction of the entire class speaks French?

  • Let themale student be 100. Then french speaking males are 50.

    Therefore the girls students would be (3/4)*100 = 75 and French speaking girls student would be 75 * (2/3) = 50

    Now, Total students = 175

    Total french spoken student = 100

    so fraction of entire class who speaks french is 100/175 = 4/7

  • 261. A student's marks were wrongly entered as 83 instead of 63. Due to this mistake, the average marks of the class got increased by half(0.5). What is the number of students in the class?
  • 262. A school's honor society has 100 members: 40 boys and 60 girls' of whom 30 are juniors and 70 are seniors. What is the smallest possible number of senior boys in the society?

  • Total girls = 60,

    Total seniors = 70

    So smallest possible of senior boys in the society is (70-60) = 10

  • 263. If the sum of all the positive even integers less than 1000 is S, what is the sum of all the positive odd integers less than 1000?
  • 264. A garrison of 500 men had provisions for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?

  • days=(27-3)=24 days
    people=(500+300)days=800 days
    500 man can  eat 24 days
    1   man   can  eat (24x500)days
    800 man can eat 500x24/800=15 days
     

  • 265. A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the original number?

  • here,

    if 10% decreased,
    then ,number is =900
    again,if increase 10 %
    number=990
    (1000-990) =10 less from original number
     

  • 266. 3-3 এর মান নিচের কোনটি? 

  • পাওয়ারে (-) থাকলে লবে ১ রেখে পুরো সংখ্যাটি নিচে নিতে হবে; 

    3-3 = 1/33 =1/27

  • 267. Marium has n chocolates, where n is an integer such that 20<n<50. If Marium divides the chocolates equally among 5 children, she will have 2 chocolates remaining. If she divides the chocolates among 6 children, she will have 1 chocolate remaining. How many chocolates will remain if she divides the chocolate among 7 children? 

  • here,
    here,
    value of n is lesser  than 50 and greater than 20. And if the number is divided by 5 remains 2.
    so,the number could be 22,27,32,37,42,47
    again,
    after distributing among 6 children remains 1
    so the number could be 25,31,36,43,49
    here, 37 fills both the conditions.
    so,n=37
    so,after distributing seven children remains=2

  • 268. Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.

  • 7x - 15 = 2x + 10

    => 5x = 25

    x=5

  • 269. The least perfect square number divisible by 3, 4, 5, 6 and 8 is : 

  • 8 = 2^3
    12 = 2^2 * 3
    15 = 3 * 5
    20 = 2^2 * 5

  • 270. A sum of Tk. 312 was divided among 100 boys and girls in such a way that each boy gets  Tk. 3.60 and each girl Tk. 2.40, the number of girls is : 

  • Let x be the number of boys and y be the number of girls. 
    Given total number of boys and girls = 100
    x+y=100           -------------- (i)

    A boy gets Taka 3.60 and a girl gets Taka 2.40
    The amount given to 100 boys and girls = Taka 312
    3.60x+2.40y=312 -------------- (ii)


    Solving (i) and (ii)
    3.60x+3.60y=360       ------- Multiply (i) by 3.60
    ⇒ 3.60x+2.40y=312 --------- (ii)
    1.20y=48

    y = 40
     

  • 271. Two-fifth of one-fourth of three-seventh of a number is 15. What is half of that number? 

  • 2/5 of 1/4 of 3/7 of x = 15

    => 6/140 x =15

    => x = 15X140/6 = 350

    => half of x = 175

  • 272. The greatest number that exactly divides 105, 1001 and 2436 is: 

  • 105 = 3X 5X 7

    1001 = 7*13*11

    2436 = 3*4*7*29

    HCF = 7

  • 273. If a and b are odd numbers, then which of the following is even?

  • odd + odd = even

    3+ 7 = 10

  • 274. What percentage of numbers from 1 to 70 have squares that end in the digit 1?

  • Only 12= 1

    92 = 81 but it is greater than 70.

    So 1/70 * 100% = 1.42% 

  • 275. A number, when 35 is subtracted from it, reduces to its 80 percent. What is four-fifth of that number?

  • let,
    the number is x
    here,
    x-35=x-xX80/100
    or,x=35 x 100/80
    so ,four -fifth of the number is =35x100/80x4/5=140
     

  • 276. A collection of books want on sale and two third of them was sold for tk. 2.30 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?

  • Here,
    1/3 of the unsold book= 36
    so,
    2 X  1/3 or 2/3 of total book  = 36 x 2 =72
    Total mount = (72 X 2.30)= 165.6 tk

  • 277. If a is an even integer and b is an odd integer, which of the following expression could be an even integer?

  • solve eaach eqn by putting a=2 and b=3

  • 278. Dividing by 3/8 and then multiplying by 5/6 is the same as dividing by what number?

  • suppose,
    the number is x
    here,
     x/3/8 X 5/6=8/3 X 5/6
    or,x=20/9

  • 279. The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?

  • suppose,
    the small number is x
    the bigger number is x+2+2
    here,
    3(x+4)-x=40
    or,3x+12-x=40
    or, x= 14

    so,bigger number is  (14+4)=18
          smaller number is 14

  • 280. The Lions’ Club has a target of raising at least Tk. 500 thousand. It has already raised Tk. 100 thousand. The club is sponsoring a 'Pitha' festival and charging Tk. 5000 per ticket. Which equation represents the number of tickets (t) that the club must sell to meet its target?

  • Remaining Tk. (500-100)= Tk. 400 thaousand

    Here, 400 thousand = (5t) thousand

    So, The required equation is 5t+100=500

  • 281. If the following number pattern continues, what numbers will come next? 50, 30, 40, 20, 30….

  • 50, 30, 40, 20, 30, ...10, 20

  • 282. Aida divides a number greater than 100 by a number greater than 10. Which statement about Aida’s quotient is always true?
  • 283. In a class of 50 students, 18 take music, 26 take art, and 2 take both art and music. How many students in the class are not enrolled in either music or art?

  • Students only take music=18-2=16

    Students only take art = 26-2=24

    Take both art and music=2

    So, in the class students who do not take either music or art=50-(16+24+2)=8 (Ans.)

  • 284. If the product of two numbers is 10 and the sum of the two numbers is 7, then the larger of the numbers is

  • Let, larger number = x

    and small number = y

    So, xy=10 and, x+y=7--------(i)

    We know, (x-y)2=(x+y)2 - 4xy

                           =(7)2 - 4×10

                           =49 - 40

                           =9

                 so, x-y=3--------(ii)

    Now, (i)+(ii)

    2x=10

    => x=10/2

    => x=5

    So, larger number = 5 (Ans.)

  • 285. Which of the following is the next number in the series: 2,4,3,9,4,16,5,25, 6,…….?
  • 286. If the sum of three consecutive integers is odd, then the first and last integers must be
  • 287. The sum of three consecutive positive integers must be divisible by which of the following?
  • 288. The sum of prime numbers that are greater than 60 but less than 70 is
  • 289. How many times does the digit ’4′ come to write numbers from 1 to 100?
  • 290. Which of the following terms does not describe the number 9?
  • 291. A man has Tk. 480 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each-denomination is equal. What is the total number of notes that he has?

  • x*1 + x*5 + x*10 = 480

    x + 5x + 10x = 480

    16x = 480

    x = 480/16 = 30

    Each denomination of notes is = 30

    Total number of notes is = 3*30 = 90

  • 292. At a dinner party every two guests shared a bowl of rice between them, every three guests shared a bowl of vegetable between them and every four shared a-bowl of meat between them. There were altogether 65 bowls. How many guests were present at the party?
  • 293. A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) =? 
  • 4 a 3 
    9 8 4
    13 b 7

    so, the second digit a+8 = b

      ==>  b -a = 8

  • 294. The difference of two numbers is 1365.0n dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?

  • Let the smaller number be x. Then larger number = (x + 1365).

     x + 1365 = 6x + 15

  • 295. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

  • Let the ten's digit be x and unit's digit be y.

    Then, (10x + y) - (10y + 

  • 296. When 5 is added to 1/3 of a number, the result is 8. What is the number?

  • Number is = x

    Now,

    x/3 + 5 = 8

    or, (x + 15) = 8*3

    or, x + 15 = 24

    or, x = 24 - 15 = 9

  • 297. The sum of prime numbers that are greater than 60 but less than 70 is-
  • 298. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. What is the number?

  • Let the ten's and unit digit be x and

    8

    respectively.

    x

     

    Then,

    Description: http://boibd.com/question_img/1-sym-oparen-h1.gif

    10x +

    8

    Description: http://boibd.com/question_img/1-sym-cparen-h1.gif
  • 299. Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons will be increased by -
    • 300. There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. What is the number of students in room A?

    • Let the number of students in rooms A and B be x and y respectively.

      Then, x - 10 = y + 10      x - y = 20 .... (i)

           and x + 20 = 2(y - 20)      x - 2y = -60 .... (ii)

      Solving (i) and (ii) we get: x = 100 , y = 80.

      The required answer A = 100.

    • 301. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. What is the number?

    • Let the middle digit be x.
      Then, 2x = 10 or x = 5.
      So, the number is either 253 or 352,

      Since the number increases on reversing the digits, so the hundred's digit is smaller

      than the unit's digit.
      Hence, required number = 253.

    • 302. Mr. Jamal employed 50 workers to finish a work within 30 days. After 20 days he found out that only 50% of the work had been completed. How many additional workers will Mr. Jamal need to finish the work in time?

    • 50 workers in 20 days can do 1/2 of the job

      1 worker in 1 day can do 1/(2*50*20) of the job

                                         = 0.0005 of the job

      Now,

      0.0005 job can be done in 1 day by 1 worker

      1/2 job can be done in 10 day by 1*0.50/(10*0.0005) worker

                                                    = 100 workers

      So, additional worker needed = (100 - 50) workers = 50 workers

    • 303. A two-digit number has 6 in its unit digit. The sum of its digits is one-fourth of the number itself. What is the number?
    • 304. The largest number from among √2,3√3 and 4√4 is:

    • √2=1.414214

      3√3=1.4425

      4√4=1.414214

      so 3√3 is largest

    • 305. If the sum of two numbers is 33 and their difference is 15, the smaller number is:

    • x + y = 33{sum of two numbers is 33} ..........(1)

      x - y = 15 {difference of two numbers is 15}..........(2)

      eqn (1-2)

      x+y-x+y=33-15

      y=9

    • 306. The greatest number that exactly divides 105, 1001 and 2436 is:

    • 105=3×5×7

      1001=7×11×13

      2436=2×2×3×7×29

      so, H.C.F=7

    • 307. Sixty-five percent of a number is 21 less than four-fifth of that number. What is the number?

    • Let the number be x.

      Then, 4 × x/5 –(65% of x) = 21

      4x/5 –65x/100 = 21

    • 308. The difference of two numbers is 11 and one-fifth of their sum is 9. Find the numbers.

    • According to ques,

      x-y=11..................(1)

      again

      (x+y)/5=9

      x+y=45.......................(2)

      we get equation (1)+(2)

      x=28

      y=(28-11)=17

    • 309. The average of the two- digit numbers, which remain the same when the digits interchange their positions, is:

    • The average of two-digit numbers, which remain the same when the digits interchange their positions, is .. 11,22,33,44,55,66,77,88,99

      average is=(11+22+33+44+55+66+77+88+99)/9

    • 310. The value of  √(10+√(25+√(108+√(154+√225))))

    • √(10+√(25+√(108+√(154+√225))))

      =√(10+√(25+√(108+√(154+15))))

      =√(10+√(25+√(108+√169)))

      =√(10+√(25+√(108+13)))

      =√(10+√(25+√121))

      =√(10+√(25+11))

      =√(10+√36

    • 311. If the number 91876*2 is completely divisible by 8, then the smallest whole number in place of* will be:

    • আমরা জানি, একটি সংখ্যা ৮ দ্বারা বিভাজ্য হয় যদি সংখ্যাটির শেষ তিনটি digit দ্বারা গঠিত সংখ্যা ৮ দ্বারা বিভাজ্য হয়।এখন * এর মান  ৩ হলে অর্থাৎ শেষ তিনটি digit  ৬৩২ হলে এটি  ৮ দ্বারা বিভাজ্য । * এর মান  ৩ 

    • 312. A school has 10 classes with the same number of students in each class. One day, the weather was bad and many students were absent. 5 classes were half full, 3 classes were 3/4 full and 2 classes were 1/8 empty. A total of 70 students were absent. What is the total number students in this school?

    • Let x=number of students in each class
      Then 10x=total number of students in school
      If 5 classes are half full then we have 5x/2 students absent
      If 3 classes are 3/4 full that means that (1/4)*3x students are absent
      If 2 classes are 1/8 empty that means that (1/8)*2x students are absent
      Now we are told that:
      (5x/2)+(1/4)*3x+(1/8)*2x=70 simplify
      (5x/2)+(3x/4)+(x/4)=70 multiply each term by 4 and we get:
      10x+3x+x=280
      14x=280
      x=20----------------------number of students in each class
      10x=10*20=200--------------number of student in this school

    • 313. The sum of three consecutive even numbers is 42 and the sum of three consecutive odd numbers is 51. Find the ratio of the lowest ever and odd numbers.
    • 314. The average of 7 consecutive numbers is 33. The largest of these numbers is:
    • 315. What is the sum of 0.15,0.10 and 0.65?

    • sum of 0.15,0.10 and 0.65 = .90 = 9/10

    • 316. Jesmin spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had Tk. 500 left over. How much money did she start with?
    • 317. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a school sale, an additional 15% is taken off the discounted price. Rahim, a student at the local high school, purchases a flute for Tk. 306. What was its original cost before discount?

    • Let original price be X

      10% discount = 0.9X taka

      15% discount on 0.9X taka = 85*0.9X/100 = 0.765X

       

      0.765X = 306

      X = 306/0.765 = 400 taka

    • 318. What is the sum of 134.679, – 45.548 and – 67.8807 rounded to the nearest tenths place?
    • 319. The electric company charges Tk. 0.30 per kilowatt-hour (KWH). Rahim used 2800 KWH in April, 3200 KWH in May, and 3600 KWH in June. What was his average cost of electricity for the 3 months?
    • 320. Which of the following is a true statement?
    • 321. The ratio of the number of red balls, to yellow balls, to green balls in an urn is 2 : 3 : 4. What is the probability that a ball chosen at random from the urn is a red ball?

    • Probability=2/(2+3+4)=2/9

    • 322. The sum of two numbers is 5, and their product is 4. Then what is the difference between the numbers?

    • x+y=5

      xy=4

      x-y=√{(x+y)2-4xy}

           =3

    • 323. Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of the elements of the set S?

    • The average of set S=(0+2+4+5+9)/5=20/5=4

      Without changing the average of the elements of the set S we deduct 4 from 20

      If one number removed from set S =(20-4)/4=16/4=4

       

    • 324. The product of two numbers x and y is twice the sum of the numbers. What is the sum of the reciprocals of x and y?

    • xy=2(x+y)

      (x+y)/xy=2

      1/x+1/y=1/2

    • 325. One third the sum of 13 and a certain number is the same as one more than twice the number. Find out the number

    • Number=x

      a.t.q,

      (x+13)/3=2x+1

      x+13=6x+3

      x=2

       

    • 326. What is the probability’ that the product of two integers (not necessarily different integers) randomly selected from the numbers 1 through 20, inclusive, is odd?

    • Only possible if both numbers chosen are odd (since even*anything=even), and you're picking with replacement (since numbers can be the same).

      The odd numbers between 1 and 20, inclusive, are {1,3,5,7,9,11,13,15,17,19}, 10 in all, and there is a total of 20 numbers to choose from (20-1+1).

    • 327. Difference between two numbers is 2 and their sum is 4. Then what is the difference of their square?

    • x+y=4

      x-y=2

      x=3;y=1

      x2-y2=8

    • 328. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36.What is the difference between the two digits of that number?

    • The number=10y+x

      10y+x-10x0y=36

      y-x=4

    • 329. Find the smallest number of oranges that can be distributed completely among 4,6,10 or 18 children-
    • 330. 5 percent of a number is 1, then what is the number?

    • 5% of a number is 1

      100% of a number is 1*100%/5%

                                  = 1*100/5

                                  = 20

    • 331. Sum of a number and its inverse is double of the number. Then what is the number?
    • 332. If 4 were subtracted from one- fourth of a number, the result is 20. The number is -

    • x/4 - 4 = 20

      or, x/4 = 20 + 4

      or, x/4 = 24

      or, x = 24*4

      or, x = 96

    • 333. If n and p are both odd numbers, which of the following must be an even number?
    • 334. One third of the sum of 13 and a certain number is the same as one more than twice the number, find out the number?

    • (13 + x)/3 = 2x + 1

      13 + x = 6x + 3

      or, 13 - 3 = 6x - x

      or, 5x = 10

      or, x = 2

    • 335. Sum of the two numbers is 21 and their difference is 7.what is the half of the greater number?
    • 336. What is the greatest integer that will always evenly divide the sum of the three consecutive even integers?
    • 337. How many even integers are between 10/3 and 62/3?

    • 10/3 = 3.34

      62/3 = 20.67

      Even integers = 4, 6, 8, 10, 12, 14, 16, 18, 20

    • 338. There are 12 more apples than oranges in a basket of 36 apples and oranges, how many apples are in the basket?

    • O + (O+12) = 36

      or, 2(O) = 36 - 12 = 24

      or, O = 24/2 = 12

    • 339. Describe the following sequence in mathematical terms-144, 72, 36, 18, 9 
    • 340. The average of three numbers is v. If two numbers are x and y, which is the third number?
    • 341. If m and p are positive integers and (m + p)m is even, which of the following must be true?
    • 342. If both x and y are prime numbers, which of the following CANNOT be the product of x and y?
    • 343. At the beginning of a class period, half-of the students in a class go to the library. Later in the period, half of the remaining students go to the computer lab. If there are 8 students remaining in the class, how many students were originally in the class?
    • 344. If 10% of x is equal to 25% of y, and y = 16, what is the value of x?
    • 345. The difference of two numbers is 7 and their product is 60, then one of the two numbers must be
    • 346. Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
    • 347. If 15 is the fifth number in a series of 5 consecutive odd numbers, what is the third number in the series?
    • 348. What is the number of integers between “101 and 199 which divisible by 5 or 7?
    • 349. There are 12 more apples than oranges in a basket of 36 apples and oranges. How many apples are in the basket?
    • 350. What least number must be added to 1056, so that the sum is completely divisible by 23?
    • 351.     If product of 3 consecutive integers is 120, then the sum of the integers is

    • Let, The consecutive numbers be 4,5,6

      .:. sum of 4,5,6 = 15 (Ans.)

    • 352. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36.What is the difference between the two digits of that number?

    • (x*10)+y - [y*10+x] = 36

      or, 10x+y - 10y - x = 36

      or, 9x - 9y = 36

      or, 9(x-y) = 36

      or, x - y = 36/9 = 4

    • 353. If n and p are both odd number, which of the following must be an even number?
    • 354. Sum of the two numbers is 21 and their difference is 7.What is the half of the greater number?

    • x + y = 21 .................. (1)

      x - y = 7 .................. (2)

      Now,

      From, (1) + (2), we get,

      2x = 28

      or, x = 14

      And, the other number is,

      14 + y = 21

      or, y = 21 - 14

      or, y = 7

      Thus,

      The greater number is = 14

      Half of the greater number is= 14/2 = 7

    • 355. Divide 60 by half and deduct twenty. What do you get?

    • The twist is that, the question specifically asks you to divide the number by half (1/2), not by two (2).

      Thus, dividing 60 by half means,

      60 / (1/2) = 60*2/1 = 120

      And deducting 20 from the derived value = 120 - 20 = 100

    • 356. The product of two numbers x and y is twice the sum of the members. what is the sum of the reciprocals of x and y ?
    • 357. The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member? 

    • Let the members be Old Having age O + other 9 having ages x and New one having age Y
      Sum of their ages = (Y + 9 × x) and average = (Y + 9 × x)/10
      Before 4 years sum was (O + 9 x – 10 × 4) and average = (O + 9 x – 10 × 4) /10
      equating, Y + 9 x = O + 9x – 40
      Y = O – 40
      Younger is 40 years younger than Old one.

    • 358. A toy store regularly sells all stock at a discount of 20% to 40%. If an additional 20% were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing tk. 16 before any discount?
    • 359. What is the least integer that is a sum of three different primes each greater than 20?

    • greater than 20 prime no.=23+29+31=83

    • 360. Out of total profit, A gets 40%, B 25%, C 20%, D 10%, E 5%. A’s profit is what percentage of that of B? 
    • 361. 3.003/2.002 =?
    • 362. If k is an integer and .0010101 x 1k is greater than 1000,what is the least possible value of k ?
    • 363. The sum of two numbers is 22. Five times of number is equal to six times the other. The bigger is of the two numbers is:

    • let the first number=x
      :.2nd number=22-x
      according to question,
      6x=5(22-x)
      or,x=10
      so, bigger number is=12
       

    • 364. The average 5 consecutive odd numbers is 61. What is the difference between the highest and the lowest number?

    • suppose, the number are
      x,x+2,x+4,x+6,x+8
      according to question,
      x+x+2+x+4+x+6+x+8=61x5
      or,x=57
      so,lowest number=57
        highest numbe=65

      difference=(65-57)=8

    • 365. The least perfect square, which is divisible by each of 21, 36 and 66 is:

    • LCM of 21,36,66=2772
      but, 2772 x 77=213444=(462)2
       

    • 366. A boy multiplied 423 by a number and obtained 65589 as his answer. If both the fives in the answer are wrong and all other figures are correct, the correct answer is:

    • the sum of the divider 423 is = 4+3+3=9
      which meaans ,423 is divisible by 3

    • 367. The least number of 5 digits which is exactly divisible by 12, 15 and 18, is 

    • Go through by the options.

    • 368. The sum of the two numbers is 12 and their product is 35. What Is the sum of the reciprocals of these numbers? 

    • x + y = 12

      xy = 35

      1/x + 1/y = (y+x)/xy = 12/35

    • 369. When number 6 is added to 1/3 of a number, the result is 28. What is that number?

    • Let the number be= x

      Then, 6+ x/3 = 28

      or, (18+x)/3 = 28

      or, 18+x = 84

      or, x = 84 - 18

      or, x = 66

    • 370. What number divided by 250 gives 15%? 

    • Let the number be x.

      x/250 = 15x/100

      or, 100x= 3750

      or, x = 3750/100 = 37.50

    • 371. ছয়টি ক্রমিক বিজোড় সংখ্যার যোগফল সবচেয়ে বড় সংখ্যাটির দ্বিগুন অপেক্ষা ৩৮ বেশি । বিজোড় সংখ্যাগুলোর যোগফল কত?

    • প্রথম সংখ্যা ধরি ক।

      তবে,

      ক + ক+২ + ক+৪ + ক+৬ + ক+৮ + ক+১০ = ২(ক+১০) + ৩৮

      বা, ৬ক + ৩০ = ২ক + ২০ + ৩৮

      বা, ৬ক - ২ক = ৫৮ - ৩০

      বা, ৪ক = ২৮

      বা, ক = ৭

      সুতরাং যোগফল,

      ২(ক+১০) + ৩৮

      = ২ক + ২০ + ৩৮

      = ২*৭ + ২০ + ৩৮ [ক এর মান বসিয়ে]

      = ১৪ + ২০ + ৩৮

      = ৭২

    • 372. The ratio of three numbers is 3:4:5 and the sum of their squares is 1250. The sum of the numbers is:

    • Let the numbers be 3x, 4x and 5x Then,

      9x2 + 16x2 + 25x2 = 1250

      <=> 50x2 = 1250

      <=> x2 = 25

      <=> x = 5.

       

      ∴

      Sum of numbers = (3x + 4x + 5x) = 12x = (12 * 5) = 60.

       

    • 373. If 35% of a number is 12 less than 50% of that number, then the number is:

    • 35% of a number is = 35*X/100

      50% of the number is = 50*X/100

      Now,

      A.Q

      50*X/100 - 35*X/100 = 12

      or, (50*X - 35*X)/100 = 12

      or, 15*X / 100 = 12

      or, X = 12* 100/ 15

      or, X = 80

    • 374. The sum of two positive integers multiplied by the bigger number is 204, and their difference multiplied by the smaller number is 35. The numbers are:

    • If numbers are 12 & 5

      .:. (12+5) X 12 = 204

      (12-5) X 5 = 35

      Ans. 12, 5

    • 375. If one-third of one fourth of a number is 15, then three-tenth of that number is:

    • let the number be X

      now,

      1/3 * 1/4 * X = 15

      or, 1/12*X = 15

      or, X = 15*12 = 180

      Thus,

      (3/10) * X = (3/10) * 180 = 3 * 18 = 54

    • 376. A third of Karim’s marks in Mathematics exceeds a half of his marks in social studies by 30, if Karim got 240 marks in the two subjects  together, how many marks did he get in Social Studies?

    • Let marks of Karim's Mathematics be = m

      And, marks of Karim's Social Studies be = s

      Then, A/Q,

      m/3 - s/2 = 30

      (2m - 3s)/6 = 30

      2m - 3s = 180 .................. (1)

      And, we know that, m+s = 240 ............... (2)

      multipying (2) with 2, we get,

      2m + 2s = 480 ................. (3)

      From (3) - (1), we get,

      2m + 2s - 2m +3s = 480 + 180

      5s = 660

      s = 660/5 = 132

    • 377. If product of two sequential positive odd numbers is 255, what are those numbers?

    • Go through the options. That is the fastest way

    • 378. How many of the integers between 110 and 120 are prime numbers?

    •  prime number between 110 and 120 is 113. 

    • 379. If one-third of one-fourth of a number is 15, then three-tenth of that number is-

    • 1/3 of 1/4 of x = 15

      x/12 = 15

      3/10 x = 15X 3/10 X 12 = 54

    • 380. How many 3-digit numbers can be formed the digits 2, 3, 4, 5, 6,7 and 9, which are divisible by 5 and none of the digits is repeated?

    • As the 3 digit number must be a multiple of 5, it must have 5 in its units place

      Ex: xy5. X and Y can be any of the remaining 5 digits(2,3,6,7,9).

      These remaining 5 digits can have 5p2 permutations ( P- because the arrangement is important). 5p2 =20.

      That gives 20 possible arrangements of the 5 digits. 

    • 381. Square of a number plus two times the number equal 63. What is the number?

    • x2+2x=63

      =x2+2x-63=0

      x=-9,x=7

       

    • 382. How many “8” will you pass on the way when you count from 1 to 100?

    • 1 to 100   '8' will come- 8,18,28,38,48,58,68,78,80,81,82,83,84,85,86,87,88,89,98= 20 

    • 383. In the two consecutive numbers one-fourth of the smaller one exceeds one-fifth of the larger one by 3. The numbers are:

    • Let, two number x,x+1

      x/4=(x+1)/5+3

      x=64

      x+1=64+1=65

    • 384. If x and y are consecutive positive integers, which of the following must be an even integer?

    • we know that, odd × even = even

      As x and y are consecutive positive integers 

      let x=1 and y = 2

      so, xy=1 ×2 =2

    • 385. The present ratio of students to teacher at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

    • Here's what I did

      s/t = 30/1 => s=30T

      S+50/t+5 = 25/1

      Substitute S=30T in the above equation

      30t+50 = 25t+125

      5t = 75
      t=15

    • 386. Of 30 applicants for a job, 14 had at least 4 years experience. 18 had degrees, 3 had less than 4 years experience and did not have a degree. How many of the applicants had at least 4 years experience and a degree?

    • Step 1: assign variables to each of the data points provided in the question so that they correspond to the OVERLAPPING SETS formula:

      30 = Total Applicants = T
      14 = Applicants with 4 yrs exp = G1
      18 = Applicants with degrees = G2
      3 = Applicants with NEITHER 4yrs exp nor degrees = NONE
      ?? = Applicants with BOTH 4yrs exp AND degrees = BOTH

      Step 2: recall the formula for overlapping sets with 2 groups: Total = G1 + G2 - BOTH + NONE

      Step 3: Plug and chug the variables that we just assigned to solve for BOTH:
      T = G1 + G2 - BOTH + NONE
      30 = 14 + 18 - BOTH + 3
      30 = 35 - BOTH
      -5 = -BOTH
      5 = BOTH

    • 387. Four of the following five are alike in a certain way and so form a group. Which one of the following does not belong to that group?
    • 388. Mithu is ranked twenty first in a class of sixty five students,what will be his rank if the lowest candidate is assigned rank 1 ?

    • Mithu is (21-1) or, 20 Person away from Rank 1.

      If, He must be 20 person away from 65th person, he would be (65-20)th or 45th person.

    • 389. Product of two numbers is 162. if the greater number is 2 times the smaller number. What is the greater number?

    • solution:

      Let, Small number= x

      then, Greater number=2x

      According to the questions,

      2x × x=162

      =>2x2=162

      => x2=81

      => x=9

      Therefore, The greater number is (2×9)=18 Ans:

    • 390. A number when multiplied by 21 is increased by 420. find the number ?
    • 391. On subtracting 5 from one fifth of a number the result is 10.what is the number?
    • 392. What is the number of integers between 101 and 199 which exactly divisible by 5 or 7?

    • The number of integers between 101 and 199 which exactly divisible by 5 or 7 is  3 (105,140,175)

    • 393. if A and B are positive and A>B, which of the following is true?
    • 394. One third the sum of 13 and a certain number is the same as one more than twice the number find out the number ?

    • 1/3 (13 + x) = 1 + 2x

      => 13 + x = 3 + 6x

      => 5x = 10

      x = 2

    • 395. Sum of the two numbers is 21 and their difference is 7. what is the half of the greater number ?

    • Let greater number is x

      smaller number is y

      x+y=21.........(1)

      x-y=7............(2)

      from 1 and 2

      we got,x=14

      half of the greater number is 14/2=7

    • 396. If n and p are both odd numbers which of the following must be an even number?    

    • If n 1 and p=3

      the n+p=(1+3)=4=even number

    • 397. Pick the odd one out-331,482,551,263,382,242,111

    • 1st no× last no.=middle no ৩৮২=৩×২=৬ সুতরাং,৩৬২ হওয়ার কথা

      ২৬৩=২×৩=৬ 

    • 398. If the sum of the 3 consecutive integers is 240 then the sum of the two larger integers is :

    • Let 3 consecutive integers is x,x+1,x+2

      according to ques,3x+3=240

      x=79

      x+1=80

      x+2=81

      the sum of the two larger integers is 80+81=161

    • 399. A number is multiplied by 4 and then the product is divided by 100.This same result can be obtained if the original number is divided by-

    • Let, The number be x

      So, (x × 4)/100

      = x/25

      Ans. 25

    • 400. In a class of 30 students 18 play football 14 play circket and 5 do not play any game,how many students play both the games ?

    • T=A+B-AB+N

      Here, T=Total = 30

      A = Play football = 18

      B = Play cricket = 14

      AB = play both the game = ?

      N = Not play any game = 5

      So, 30 =18 + 14 - AB + 5

      => AB = 37-30

      => AB = 7

      Ans. 7

    • 401. Which of the following is the lowest positive integer devisible by 2,3,4,5,6,7,8 and 9?

    • LCM = 2×2×3×5×7×2×3 = 2520 (Ans.)

    • 402. The product to two numbers is 900 and their sum exceeds their difference by 30. The greater of these two numbers is :
    • 403. If the product of 20% of 85 and 40% of 45 is divided by 4 the result would be-

    • [{85×(20/100}×{45×(40/100)}]/4

      = (17×18)/4

      = 76.5 Ans.

    • 404.  Which one of the following is the largest?    

    • Here,

      1/2 = 0.5

      7/15 = 0.504

      and 1999/4000 = 0.499

      So, 0.504>0.5>0.499>0.49>0.47

      Ans. 126/250 = 0.504

    • 405. Find the value of (0.1 x 0.01 x 0.001)+(0.2 x 0.02) x 0.002    

    • (0.1×0.01×0.001)/(0.2×0.02×0.002)

      = 1/8

      = 0.125 (Ans.)

    • 406. ¼ of Ahsan’s money is equal to 1/6 of Babu’s money. If both together have tk 600, what is the difference between their amounts?  
    • 407. The sum of two numbers is 146 and difference between them is 18. What are the numbers?
    • 408. If 4 is subtracted from 1/4th of a number the result is 20.what is that number ?
    • 409. Find the missing number in the series 3,6,18,72,360-

    • 3 X 2 = 6

      6 X 3 = 18

      18 X 4 = 72

      72 X 5 = 360

      360 X6 = 2160

    • 410. 0.1 is how many times greater than 0.001?
    • 411. If the product of three consecutive integers is 210,then the sum of the two smaller integers is-
    • 412. How many 3-digit integers can be chosen such that none of the digits appear more than twice, none of the digits equal 0?
    • 413. The value of -3 -(-10) is how much greater than the value of -10 - (-3)?
    • 414. Average of 6 numbers is 8.5. When one number is discarded, the avenge of the remaining numbers , becomes 7.2. What is the discarded number?
    • 415. One third of a number is four times of eleven. What is the half of that number?
    • 416. If n is an even integer, which of the followings must be an odd integer,
    • 417. the product of two consecutive negative even integers is 24. what is the larger number?  

    • The product of two (two numbers multiplied together) 
      consecutive (the numbers are right after each other in a given sequence ie- 1,2 in the sequence 12,3,4 or 20,30 in 10,20,30) 
      negative ( the numbers must be from the scale below zero ie “-3” is a negative number- which happens to be the temperature here today) 
      even integers (the numbers are multiples of 2 ie from this sequence .(..-8,-6,-4,-2,0,2,4,6,8....) is 24. 

      And, (-6) x (-4) = 24

    • 418. the sum of k consecutive integers is 41. if the least integer is -40, then k =?  
    • 419. how many odd, positive divisors does 540 have?    
    • 420. the average (arithmetic mean) of 4 different integers is 75.. if the largest integer is 90, what is the least possible value of the smallest integer?  

    • the sum of the four different numbers is 75 * 4 =  300, the largest one is 90, so the sum of the rest three numbers is 300-90 = 210, the average of them is 210/3 = 70. Since the 4 numbers are different, the second largest and third largest should be 89,88. Hence, the least number is 70- ( (89-70) + (88 - 70 )) = 70 - 37 = 33. 

    • 421. if A, B, C and D are positive integers such that 4A = 9B, 17C = 11D, and 5C = 12A, then the arrangement of the four numbers from greatest to least is -  

    • 4A = 9B => B = 4/9 A 

      5C = 12A => C = 12/5 A 

      17C = 11D => D = 17/11 C = 17/11 (12/5 A) = 204/55 A 

      So the order from greatest to least is, 
      204/55 A, 12/5 A, A, 4/9 A 

      Nothing but, DCAB

    • 422. dividing by 3/8 and then multiplying by 56 is the same as dividing by what number?  
    • 423. the smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?  

    • let the three numbers be a,b and c..
      now,

      The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..
      3c-a=40..
      2c+c-a=40..
      c-a=4, as a,b,and c are consecutive even integers..
      2c+4=40..
      2c=36 or c=18.

    • 424. in a division sum, the remainder is zero. A student mistook the divisor as 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?  

    • we all know the formula.

      Divisor = Dividend-Remainder/Quotient. 

      Now we have given Remainder=0, Quotient=35 and having two divisor one is true and other is by mistake taken by him.

      So true divisor = 21 and by mistake divisor is 12 and we have to find the correct quotient. So, as he has taken false divisor so it is obvious that quotient is also false.

      Now our formula become like this:

      False divisor = True dividend - Remainder/False quotient.

      Now put the value in this:

      12 = True dividend - 0/35.
      12*35 = True dividend - 0.
      420 + 0 = True dividend.

      So our true dividend = 420.

      True Divisor is already given in question that is = 21.

      Now, Dividend / Divisor => 420/21.

      That is 20 Answer.

    • 425. Which of the following cannot be a sum of two prime integers?  
    • 426. how many positive integers less than 100 have a remainder of 2 when divided by 13?  

    • Number closest to 100 but less than 100 and divisible by 13 = 91.
      91 = 13 * 7.
      91+2 < 100.

      Satisfies all the conditions. 

    • 427. 49 pumps can empty a reservoir n 6.5 days, working 8 hours a day . If 196 pumps are used for 5 hours each day ,then the same work will be completed in-  

    •  Let,
        the required number of days be x.
       Then,

      More pumps, Less days (Indirect Proportion)
       Less working hrs / day, More days (Indirect Proportion)
       Pumps =196 : 49
       Working Hrs / Day =5 : 8 :: 13/2 : x 96 x 5 x x = 49 x 8 x 13/2 x = 49 x 8 x 13/2 x 1 / (196 x 5) x = 13/5

    • 428. √(176 + √2401)  is equal to-

    • √2401 = 49

      49+176=225

    • 429. the smallest prime number is-  
    • 430. The sum of a number and its reciprocal is 1/8  of 34. what is the product of the number and its square root?  

    • Explanation:
       Let the number be x. Then,
      x + 1/x = 34/8
      8x2 - 34x + 8 = 0
      4x2 - 17x + 4 = 0
      (4x - 1)(x - 4) = 0
      x = 4
      required number = 4 * √4 = 4 * 2 = 8.

    • 431. How many times in a day are the hands of a clock in straight line but opposite in direction?  

    • The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only). So, in a day, the hands point in the opposite directions 22 times.

    • 432. 7.0.04 X ? = 0.000016  
    • 433. (0.04)-1.5 =  
    • 434. The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is:  

    • Let x and y denote the two numbers and, without a loss of generality, let x > y. 

      Since the sum of the numbers is x + y

      and

      the difference is x - y,

      we see that we have the system: 
      x + y = 40 and

      x - y = 4. 

      By adding these two equations: 
      (x + y) + (x - y) = 40 + 4 
      ==> 2x = 44 
      ==> x = 22. 

      Then, since x + y = 40 implies y = 40 - x: 
      y = 40 - x = 40 - 22 = 18. 

      Therefore, the two numbers are 22 and 18. so the ratio =22:18=11:9

    • 435. The average of the first 50 natural number is:  

    • Sum of first n non-zero positive integers n(n + 1)/2

      So,

      average of first n non-zero positive integers n(n + 1)/2n = (n + 1)/2 => (50 + 1)/2 = 25.5

    • 436. The square root of (7 + 3√5)(7 - 3√5) is  
    • 437. 138.009+341.981-146.305=123.6+?  
    • 438. Find the greatest number that will divide 43,91 and 183 so as to leave the same remainder in each case?  

    • Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)

           = H.C.F. of 48, 92 and 140 = 4.

    • 439. Which one of the following is not a prime number?  
    • 440. What is the unit digit in the product (684*759*413*676)?  
    • 441. (87*87+61*61*2*87*61) = ?  
    • 442. If root 2^n = 64 , then the value of n is :  
    • 443. There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The largest of the two is :  

    • Let,

      the numbers be x and y.

      Then,

      2x + 3y = 39...(i)

      and

      3x + 2y = 30 ...(ii)
      On solving (i) and (ii), we get :  x = 6 and y = 9.
      larger number = 9

    • 444. What is the following is equal to 3.14× 10^6?  
    • 445. The sum of first five prime number is :  
    • 446. The sum of two numbers is equal to thrice their difference. If the smaller of the number is 10.find the other number  

    • Let,

      two numbers are X and Y. Y is the smaller number.
      Given,
      Y = 10
      And,
      According to question,
      (X +Y) =3*(X - Y)
      (X +10) = 3* (X -10)
      X - 3X = -30 - 10
      -2X = -40
      X = 20.
      So, the required number is 20.

    • 447. How many integers from 1 to 1000 are divisible by 30 but not by 16 ?
    • 448. If * is defined for all positive real numbers a and b by a*b=ab/(a+b), then 10*2=?
    • 449. If first thousand natural numbers, how many integers exist such that they leave a reminder 4 when divided by 7 and remaineder 9 divided by 11?
    • 450. কোন ক্ষুদ্রত্তম সংখ্যাকে ৪,৫ ও ৬ দ্বারা ভাগ করলে প্রতি ক্ষেত্রে ৩ অবশিষ্ট থাকবে?
    • 451. .০০১/(০.১*০.১) = কত ?
    • 452. কোন সংখ্যা হতে ১৭৫ বিয়োগ করলে ১৩০ যোগ করলে যোগফল যোগফল হবে ২৯৭?
    • 453. ২৪৫০ সংখ্যাটিকে কত দ্বারা গুণ করলে সংখ্যাটি পূর্ণবর্গ সংখ্যা হবে?
    • 454. একটি সংখ্যা ৫৬০ থেকে যত কম ৩৮০ থেকে তার সাড়ে তিনগুণ বেশী। সংখ্যাটি কত?
    • 455. ৪৩ থেকে ৬০ এর মধ্যে মৌলিক সংখ্যা মোট কতটি?
    • 456. দুই অঙ্কবিশিষ্ট কোন সংখ্যার অঙ্কদ্বয়ের সমষ্টি ১৫ এবং গুণফল ৫৬; সংখ্যাটি নির্নয় কর?
    • 457. The difference between the place value and the face value of 6 in the numeral 856973 is --
    • 458. 4500 *? =3375
    • 459. Which one of the following numbers is exactly divisible by 11?
    • 460. 0.002*0.5=?
    • 461. (8/88)*8888088=?
    • 462. 49*49*49*49=7?
    • 463. Which of the number below is now equivalent to 4% ?
    • 464. How many integers from 1 to 1000 are divisible by 30 but not by 16 ?
    • 465. If m And p are positive integers and ( m + p ) m is even , which of the following must be true ?
    • 466. যদি একটি সংখ্যার ৫/১৫ অংশ ১০ এর সঙ্গে যোগ করলে হয় ২৮। সংখ্যাটি কত?
    • 467. নিচের কোনটি সবচেয়ে বড়?
    • 468. In a sequence of 8 consecutive integers, how much greater is the sum of the last four integers than the sum of the first four integers ?
    • 469. How many integers from 1 to 1000 are divisible by 30 but not by 16 ?
    • 470. How many integers from 1 to 1000 are divisible by 30 but not by 16?
    • 471. The average of the remaining two numbers is-
    • 472. What is 200% of 0.010?
    • 473. Find the average of all the numbers between 6 and 34 which are divisible by 5.
    • 474. The difference between a number and its three-fifth is 50. What is the number?
    • 475. If 120 is 20% of a number, then 120% of that number will be:
    • 476. If n is even, which of the  following cannot be odd?
    • 477. The product of two numbers x and y is twice the sum of the numbers. What is the sum of the reciprocals of x and y?
    • 478. What number when multiplied by 4/7 yields 6/7 as the result? 
    • 479. The least number by which 294 must be multiplied to make it a perfect square is: 
    • 480. (০.০০৩৬)(২.৮)/(০.০৪)(০.১)(০.০০৩) =
    • 481. 0.1 + (0.1)2 + (0.1)3 =? 
    • 482. The difference between two numbers is 5 and the difference between their squares is 65. What is the larger number?
    • 483. The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is  

    • The 6th number is = (50×9) – (5×54 + 3×52) = 450 – 426 = 24.

    • 484. How many numbers are there from 1 to 100 which are completely divisible by 7?
    • 485. Divide 60 by half and deduct twenty. What do you get?

    • (60/0.5) – 20 = 120 – 20 = 100

    • 486.  If the sum of two number is 33 and their difference is 15, the smaller number is-- 

    • Let,
      Smaller number = x
      So, larger number = x+15

      Now,
      x+x+15 = 33
      Or, 2x = 33-15
      Or, x = 9

    • 487. If n and p are both odd numbers, which of the following must be an even number?
    • Let,
      n=3, p=5
      a) np + 2 = 3×5+2=17
      b) n + p = 3+5 = 8 (Sum of two odd numbers makes an even number.)
      c) n + p + 1 = 3+5+1 = 9
    • 488. 0.01 is what percent of 0.1?
    • is x% of 0.1
      Or, 0.01 = (x/100) ×0.1
      Or, x=(0.01×100)/0.1=10
    • 489. (৩√৩)৩ = কত?
    • 490. দুই অঙ্কবিশিষ্ট একটি সংখ্যার অংকদ্বয়ের সমষ্টি ৭। অংকদ্বয় স্থান বিনিময় করলে যে সংখ্যা পাওয়া যায় তা প্রদত্ত সংখ্যা থেকে ৯ বেশী। সংখ্যাটি কত? 
    • 491. ১ থেকে ১০ পর্যন্ত সংখ্যার মধ্যে মৌলিক সংখ্যা কয়টি? 
    • 492. (০.২)২ / (০.১)৩ = কত? 
    • 493. ০.৩৫ কে ভগাংশে প্রকাশ করলে কত হবে? 
    • 494. Two-fifth of one-fourth of three seventh of a  number is 15. What is the half of the number?

    • Let,

      The number = x

      ATQ,

      2/5 × ¼ × 3/7 × x =15

      Or, 16x/ 140 = 15

      Or, x = 350

      ½ of 350 =175

    • 495. If (89)2 is added to the square of a number, the answer so obtained is 16202. What is the 1/26 of that number

    • (89)2 + x2 = 16202

      Or, x2 = 16202 – (89)2= 16202 – 7921 = 8281

      .::x=√(8281) = ±91

      Now, 1/26 of 91 = 3.50

    • 496. The pair of co-prime numbers is ___?
    • 497. {(১/৫)√৯} × (৫√৯) =?
    • 498. 72 × 75 × 33 × 43 × 28 কে ন্যূনতম কত দ্বারা গুণ করলে গুণফল একটি পূর্ণ সংখ্যা হবে?

    • 72 × 75 × 33 × 43 × 28

      =23 × 32 × 3 × 52 × 33 × 26 × 28

      = 23+6+8 ×32+1+3 × 52

      = 217 × 36 × 52

      দেখা যাচ্ছে যে, 3 ও 5 এর পাওয়ার জোড় সংখ্যায় আছে কিন্তু 2 এর পাওয়ার বিজোড় সংখ্যায় আছে। অর্থাৎ কমপক্ষে 1টি 2 গুন করলে সংখ্যাটি পূর্ণবর্গ হবে।

    • 499. If n is an even integer, which of the following must be an odd integer
    • Let, n=2 then, 3n-1 =3×2-1=6-1=5
    • 500. If m and n are whole numbers such that mn =121, the value of (m-1)n is-

    • We know that 112 = 121.

      Putting m = 11 and n = 2,

      we get:

      (m – 1)n + 1 = (11 – 1)(2 + 1) = 103 = 1000.

    • 501. The sum of the digits of two-digit numbers is 10 while when the digits are reversed, the number decrease by 54. Find the changed number.

    • Let number be (10x+y).
      According to question,
      (10x+y)-(10y+x) = 54;
      10x-10y+y-x = 54;
      Or, 9x-9y = 54;
      Or, x-y = 6 ————(i)
      Sum of digits,
      (x+y) = 10; —— (ii)
      (i)-(ii);
      So, x-y-x-y = 6-10;
      Or, -2y = -4;
      Or, y = 2; and, x = 8.
      Then, the required number is
      (10y+x) = 10×2+8 = 28.

       

    • 502. There are two numbers. 1st number is 12 more than the 2nd number. The average of the two numbers is 19. If 2 is added in both numbers, find the ratio of the numbers.
    • 503. If for integer x, 5<x<10 and y=x+5, what is the greatest possible value of x+y?

    • Given,

      5 < x < 10 and y =x+5

      Possible value of x = 6, 7, 8, 9

      When x =9,

      y =9+5 = 14

      Now, x + y = 9 + 14 = 23


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