Problems on Numbers(Aptitude) Questions asked in Various Campus Placements

Number:

               A Number is a group of digits.

Various types of Numbers:

1) Natural Numbers:

      1, 2, 3, 4, 5, 6, 7, 8, 9, 10................

These are called as Natural Numbers

2) Whole Numbers:

      0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10............

These are called as Whole Numbers

3) Integers:

............,-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...............

These are called as Integers

Positive Integers(Natural Numbers): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.........

Negative Integers: -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, ..............

Non-Negative Integers(Whole Numbers): 0, 1, 2, 3, 4, 5, 6, ...............

Even Numbers:  Numbers which are divisible by 2 are called as Even Numbers

Odd Numbers:  Numbers which are not divisible by 2 are called as Odd Numbers

Prime Numbers: If a number has exactly two factors called as prime number

Divisibility:

1)Divisible by 2: last digit is Even or not
       
         Eg: 1234 is divisible by 2
                1235 is not divisible by 2

2) Divisible by 3 and 9: Sum of digits

         Eg: 246591 = 2+4+6+5+9+1 = 27 which is divisible by 3 & 9
                1234 = 1+2+3+4 = 10 which is not divisible by 3 & 9

3) Divisible by 4: last two digits

         Eg: 5932  last two digits are 32, it is divisible by 4
                1435 last two digits are 35, it is not divisible by 4

4) Divisible by 8: last 3 digits

         Eg: 54352 last three digits are 352, it is divisible by 8
                576484 last three digits are 484, it is not divisible by 8

5) Divisible by 10: unit digit (or) last digit is 0
       
         Eg: 7849320, unit digit is 0, it is divisible by 10
                678405, unit digit is 5, it is not divisible by 10

6) Divisible by 11:

            (Sum of its digits at odd places) - (Sum of digits at Even Places)



Problems on Numbers:

1) What is the unit design in 7¹⁰⁵?
  a) 1
  b) 2
  c) 3
  d) 7

Show Answer

   7¹⁰⁵ = (7⁴)²⁶ x 7
   The Unit Digit of (7⁴)²⁶ is 1
   So, 7¹⁰⁵ = 1 x 7 = 7
   The Unit Digit of 7¹⁰⁵ is 7

2) 7589 - ? = 3434
  a) 4426
  b) 4706
  c) 4526
  d) 4155

Show Answer

   7589 - 3434 = ?
   4155=?
   So, Answer is 4155

3) 8988  ÷ 8 ÷ 4 = ?
  a) 280.75
  b) 280.50
  c) 280.20
  d) 280

Show Answer

4) How many of the following numbers is divisible by 132?

    264, 396, 462, 792, 968, 2178, 5184, 6336

  a) 4
  b) 5
  c) 6
  d) 7

Show Answer

   The factors of the 132 are 11, 3, 4
   264, 396, 792 and 6336 are divisible by 11, 3, 4
   So, Answer is 4.

5) Which one of the following number is exactly divisible by 11
  a) 235641
  b) 245642
  c) 315624
  d) 415624

Show Answer

   The Divisible condition for 11 is as follows
   (sum of digits at odd places) - (Sum of digits at even places)
   (4 + 5 + 2) - (1 + 6 + 4) = 11 - 11 = 0
   415624 is only divisible by 11.
   So, Answer is 415624

6) The difference of the squares of two consecutive odd integers is divisible by which of the following integers?
  a) 3
  b) 6
  c) 7
  d) 8

Show Answer

   Answer is 8

7) A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be?
  a) 3
  b) 1
  c) 5
  d) 8

Show Answer

   Answer is 1

8) How many natural numbers between 17 and 80 are divisible by 6?
  a) 5
  b) 6
  c) 7
  d) 11

Show Answer

   The Numbers which are divisible by 6 are as follows(from 18 to 78)
   18, 24, 30, 36,........ 79
   Let a=18, d=(24-18)=6, l=78=t_n
   t_n = a+(n-1)d
   78 = 18+(n-1)6
   (n-1)6 = 60
   n=11
   So, Answer is 11

9) What is the sum of (2+2²+2³+2⁴+...........+ 2¹⁰)?
  a) 2046
  b) 2048
  c) 1023
  d) 512

Show Answer

   Let a=2, r=2²/2=2, n=10
   sum = a(rⁿ-1)/(r-1)
   2(2¹⁰-1)/(2-1) = 2(1024 - 1) = 2046
   So, Answer is 2046

10)  What is the sum of whole numbers upto 100?
  a) 2050
  b) 5000
  c) 5050
  d) none

Show Answer

   So, Answer is 5050

11) which of the following numbers si divisible by 6?
  a) 4322
  b) 3142
  c) 2256
  d) 1640

12) Which number should be subtracted from 321 so that it becomes prime?
  a) 2
  b) 4
  c) 6
  d) 9

13) What is the value of (3³ * 81² * 2⁰)/(9⁵)?
  a) 0
  b) 3
  c) 1/3
  d) None of the above

14) Write 4.004 as a fraction of the lowest form
  a) 500/125
  b) 2002/500
  c) 1001/250
  d) 500/225

15) Find the number to be multiplied by (-6)^(-1). so as to get (-8)^(-1) as the product?
  a) 3/4
  b) -(3/4)
  c) 4/3
  d) -(4/3)

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