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61. Find the average of these consecutive odd numbers: 81,83,85,87,89,91,93,95
  A.  88
  B.  82
  C.  93
  D.  91
     
   
View Answer

Shortcut:
The average of n (where n is an even number) consecutive numbers (even/odd/natural numbers) is always the averae of the middle two number.
Case 1. Let consecutive natural numbers are 1,2,3,4,5 and 6
Here n = 6, middle two numbers are 3 & 4
∴ Average =
3+4 / 2
= 3.5

Case 2. Let consecutive odd numbers are 1,3,5,7,9 and 11
Here n = 6, middle two numbers are 5 & 7
∴ Average =
5+7 / 2
=
12 / 2
= 6

Case 3. Let consecutive even numbers are 2,4,6,8,10 and 12
Here n = 6, middle two numbers are 6 & 8
∴ Average =
6+8 / 2
=
14 / 2
= 7

Using these shortcut method, we can conclude that average of 6 consecutive odd numbers 81,83,85,87,89,91,93 and 95 is
87+89 / 2
=
176 / 2
= 88

Hence, average is 88

62. Find the average of the consecutive even numbers: 82,84,86,88,90,92
  A.  89
  B.  87
  C.  91
  D.  85
     
   
View Answer

Shortcut:
The average of n (where n is an even number) consecutive numbers (even/odd/natural numbers) is always the averae of the middle two number.
Case 1. Let consecutive natural numbers are 1,2,3,4,5 and 6
Here n = 6, middle two numbers are 3 & 4
∴ Average =
3+4 / 2
= 3.5

Case 2. Let consecutive odd numbers are 1,3,5,7,9 and 11
Here n = 6, middle two numbers are 5 & 7
∴ Average =
5+7 / 2
=
12 / 2
= 6

Case 3. Let consecutive even numbers are 2,4,6,8,10 and 12
Here n = 6, middle two numbers are 6 & 8
∴ Average =
6+8 / 2
=
14 / 2
= 7

Using these shortcut method, we can conclude that average of 6 consecutive even numbers 82,84,86,88,90 and 92 is
86+88 / 2
=
174 / 2
= 87

Hence, average is 87

63. Find the average of the consecutive even numbers: 50,52,54,56,58,60,62,64
  A.  60
  B.  55
  C.  57
  D.  63
     
   
View Answer

Shortcut:
The average of n (where n is an even number) consecutive numbers (even/odd/natural numbers) is always the averae of the middle two number.
Case 1. Let consecutive natural numbers are 1,2,3,4,5 and 6
Here n = 6, middle two numbers are 3 & 4
∴ Average =
3+4 / 2
= 3.5

Case 2. Let consecutive odd numbers are 1,3,5,7,9 and 11
Here n = 6, middle two numbers are 5 & 7
∴ Average =
5+7 / 2
=
12 / 2
= 6

Case 3. Let consecutive even numbers are 2,4,6,8,10 and 12
Here n = 6, middle two numbers are 6 & 8
∴ Average =
6+8 / 2
=
14 / 2
= 7

Using these shortcut method, we can conclude that average of 8 consecutive even numbers 50,52,54,56,58,60,62 and 64 is
56+58 / 2
=
114 / 2
= 57

Hence, average is 57

64. What is the average of odd numbers from 1 to 35?
  A.  21
  B.  16
  C.  18
  D.  20
     
   
View Answer

Shortcut:
The average of odd numbers from 1 to n (n = odd number) is given by
last odd number + 1 / 2

Here last odd number = 35
Using the shortcut method, we get:
Average =
35+1 / 2
=
36 / 2
= 18

Hence, average is 18

65. What is the average of even numbers from 1 to 50?
  A.  26
  B.  24
  C.  27
  D.  30
     
   
View Answer

Shortcut:
The average of even numbers from 1 to n (n = even number) is given by
last even number + 2 / 2

Here last even number = 50
Using the shortcut method, we get:
Average =
50+2 / 2
=
52 / 2
= 26

Hence, average is 26

66. Find the average of squares of natural numbers till 7.
  A.  19
  B.  23
  C.  17
  D.  20
     
   
View Answer

Shortcut:
The average of square of natural numbers till n is given by
(n + 1)(2n + 1) / 6

Here n = 7
Using the shortcut method, we get:
Average =
(7+1)(2x7 + 1) / 2
=
(8)(14+1) / 2
=
(8)(15) / 2
= 60

Hence, average is 60

67. Find the average of cubes of natural numbers till 7.
  A.  112
  B.  108
  C.  114
  D.  116
     
   
View Answer

Shortcut:
The average of cubes of natural numbers till n is given by
n(n + 1)2 / 4

Here n = 7
Using the shortcut method, we get:
Average =
7(7+1)2 / 4
=
(7)(8)(8) / 4
= 112

Hence, average is 112

68. Find the average of first 50 consecutive even numbers.
  A.  51
  B.  53
  C.  48
  D.  50
     
   
View Answer

Shortcut:
The average of first n natural numbers is given by (n + 1)
Here n = 50
Using the shortcut method, we get:
Average = (50 + 1)
Hence, average is 51

69. Find the average of first 16 consecutive odd numbers.
  A.  19
  B.  16
  C.  13
  D.  15
     
   
View Answer

Shortcut:
The average of first 'n' natural numbers is given by 'n'
Here n = 16
Using the shortcut method, we get:
Average = 16
Hence, average is 16

70. Find the average of squares of first 10 consecutive even numbers.
  A.  160
  B.  155
  C.  152
  D.  154
     
   
View Answer

Shortcut:
The average of squares of first n consecutive even numbers till n is given by
2(n + 1)(2n + 1) / 3

Here n = 10
Using the shortcut method, we get:
Average =
2(10+1)(2x10 + 1) / 3
=
(2)(11)(21) / 3
= 154

Hence, average is 154

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