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71. Find the average of squares of consecutive even numbers till 10.
  A.  47
  B.  42
  C.  44
  D.  50
     
   
View Answer

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

Here n = 10
Using the shortcut method, we get:
Average =
(10+1)(10 + 2) / 3
=
(11)(12) / 3
= 44

Hence, average is 44

72. Find the average of squares of consecutive odd numbers till 15.
  A.  89
  B.  87
  C.  82
  D.  85
     
   
View Answer

Shortcut:
The average of squares of consecutive odd numbers till 'n' is given by
n(n + 2) / 3

Here n = 15
Using the shortcut method, we get:
Average =
15(15 + 2) / 3
=
(15)(17) / 3
= 85

Hence, average is 85.

73. In a calculation Madan found that the average of 4 numbers is 25 and on rechecking Sam noticed that a number 15 is wrongly taken as 51. Find the correct average.
  A.  16
  B.  15
  C.  20
  D.  18
     
   
View Answer

Shortcut:
If the average of n members is 'Z' and on rechecking it is noticed that some of the numbers (i.e a1,a2,a3..........an) are wrongly taken as (b1,b2,b3....................bn), then their correct average is given by
Z +
a1,a2,a3..........an) − (b1,b2,b3....................bn) / 3

Here n = 4, Z=25, a=15, b=51
Using these values in shortcut, we get:
Correct Average = 25 +
15 − 51 / 4
= 25 +
(−36) / 4
= 25 − 9 = 16

Hence, correct average is 16.

74. Find the geometric mean of 4, 8, 16
  A.  14
  B.  8
  C.  6
  D.  9
     
   
View Answer

Shortcut:
Geometric mean of x1, x2, x3.............................xn is given by n√(x1, x2, x3.............................xn)
Here n = 3, x1 = 4, x2 = 8, x3 = 16
Using these values in shortcut, we get:
Geometric Mean = 3√(4 x 8 x 16) = 3√(512) = 8
Hence, GM is 8.

75. Find the harmonic mean of 2,3,4 and 5
  A.  
237 / 75
  B.  
220 / 77
  C.  
245 / 77
  D.  
240 / 77
     
   
View Answer

Shortcut:
Harmonic mean of x1, x2, x3.............................xn is given by
1 / 1/n [1/x1 + 1/x2 + 1/x3] + .......+ 1/xn
n√(x1, x2, x3.............................xn)
Here n = 4, x1 = 2, x2 = 3, x3 = 4, x4 = 5
Using these values in shortcut, we get:
Harmonic Mean =
1 / 1/4 [1/2 + 1/3 + 1/4 + 1/5]
=
1 / (30+20+15+12)/60]
=
4x60 / 77
=
240 / 77

76. Find the average of the given series: 25,27,29,31,33
  A.  29
  B.  27
  C.  31
  D.  33
     
   
View Answer

Shortcut:
Average of a series having common difference 2 is given by
first term + last term / 2

first term = 25, last term = 33
Using these values in shortcut, we get:
Average =
25+33 / 2
=
58 / 2
= 29

77. The average of the first and the second of three numbers is 10 more than the average of the second and the third of these numbers. What is the difference between the first and the third of these three numbers?
  A.  22
  B.  18
  C.  20
  D.  25
     
   
View Answer

Shortcut:
If the average of the first and the second of three numbers is 'a' more or less than the average of the second and the third of these numbers, then the difference between the first and the third of these three numbers is given by '2a'.
Here, a = 10
Using it in the shortcut, we get:
The difference between first & Third number = 2 x 10 = 20 Detailed solution: Average of 1st & 2nd numbers =
1st + 2nd / 2
and
Average of 2nd & 3rd numbers =
2nd + 3rd / 2

78. The average of Santosh marks in English and History is 55. His average of marks in English and Science is 65. What is the difference between the marks which he obtained in History and Science?
  A.  24
  B.  20
  C.  17
  D.  19
     
   
View Answer

Shortcut:
If the average of the first and the second of three numbers is 'a' more or less than the average of the second and the third of these numbers, then the difference between the first and the third of these three numbers is given by '2a'.
Here, Santosh's average in English & History is 10 less than the average marks in English & Science = 10 ( 65 − 55)
Using it in the shortcut, we get:
The difference between marks between History & Science = 2 x 10 = 20

79. The average marks scored by Geeta in English, Science, Maths and History is less than 15 from that scored by her in English, History, Geography and Maths. What is the difference of marks in Science and Geography scored by her?
  A.  64
  B.  61
  C.  56
  D.  60
     
   
View Answer

Shortcut:
If the average of the first and the second of three numbers is 'a' more or less than the average of the second and the third of these numbers, then the difference between the first and the third of these three numbers is given by '2a'.
Here, 4 subjects i.e (English, Science, Mathematics and History) in 1st group and (English, History, Geography and Mathematics) in 2nd group. We see that English, Mathematics and History are common in both group. Hence, the difference of marks in in Science and Geography is 4 x 15 = 60

80. The average temperature for Monday, Tuesday and Wednesday was 40 ° C. The average for Tuesday, Wednesday and Thursday was 41° C. That for Thursday being 42° C. What was the temperature on Monday?
  A.  44° C
  B.  40° C
  C.  42° C
  D.  43° C
     
   
View Answer

Shortcut:
If the average of the first and the second of three numbers is 'a' more or less than the average of the second and the third of these numbers, then the difference between the first and the third of these three numbers is given by '2a'.
Here, Monday to Wednesday means Monday, Tuesday & Wednesday
Similarly, Tuesday to Thursday means Tuesday, Wednesday & Thursday
∴ Difference of temperature between Monday and Thursday = 3 x (37 − 34) = 9° C
According to the question: a -
4a / 5
= 9
∴ a = 45
∴ Temperature of Monday = 45° C
and temperature of Thursday =
4 / 5
x 45 = 36° C

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