Average, General Mathematics

Question: The average of first five prime numbers is:
A
4.5

B
5

C
5.6

D
7.5

Note: Average = `((2+3+5+7+11)/5) = 28/5 = 5.6`
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Question: The average of first five multiples of 3 is:
A
3

B
9

C
12

D
15

Note: Average = `((3(1+2+3+4+5))/5)=45/5=9`
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Question: The average of first `50` natural numbers is :
A
`12.25`

B
`21.25`

C
`25`

D
`25.5`

Note: Sum of first n natural numbers `= (n(n + 1))/(2n)` `= (n + 1)/2` :. Average `= ((50 + 1)/2)` `= 51/2` `= 25 .5`
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Question: The mean of `1^2,2^2,3^2,4^2,5^2,6^2,7^2` is:
A
`40`

B
`20`

C
`30`

D
`10`

Note: `1^2 + 2^2 + 3^2 +....+n^2` `= (n(n + 1)(2n + 1))/(6)` `:. 1^2 + 2^2 +3^2 +......+7^2` `= ((7 xx 8 xx 15)/6)` `= 140`. :. Required average `= (140/7)` `= 20`
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Question: The average of all odd numbers upto `100`is:
A
`51`

B
`50`

C
`49.5`

D
`49`

Note: Sum of odd numbers upto `100` `= 1 + 3 + 5 + 7 +......+ 95 + 97 + 99` `= (1 + 99) + (3 + 97) + (5 + 95) +...upto `25`pairs. `= 100 + 100 + 100+....(25 times)` `= 2500` :. Average `= (2500/50)` `= 50`
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Question: If a,b,c,d,e are five consecutive odd numbers ,thier average
A
`5(a + 4)`

B
`(abcde)/5`

C
`5 (a + b + c + d + e)

D
None of these

Note: ckearly ,`b = a + 2,c = a + 4, d = a + 6 and e = a + 8`. :. Average `= (a + (a + 2) + (a + 4) + (a + 6) + (a + 8))/5` `= ((5a + 20)/5)` `= (a + 4)`
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Question: The average of `7`consecutive numbers is `33`.The largest of these numbers is :
A
`36`

B
`32`

C
`30`

D
`28`

Note: Let the numbers be `x,x + 2,x + 4 and `x + 6`.Then `(x + x + 2 + x + 4 + x + 6)/4` `= 27⇒ (4x + 12)/4` `= 27 ⇒ x + 3` `= 27⇒ x = 24` :. Largest number `= (24 + 6)` `= 30`
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Question: The average height of `30`boys out of a class of `50`,is `160`cm.If the average hieght of the remaining boys is `165`cm, the average height of the whole class (in cm) is :
A
`161`

B
`162`

C
`163`

D
`164`

Note: Required average `= ((30 xx 160 + 20 xx 165)/50)` `= 162 cm`.
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Question: The average of three numbers is `20`.If two numbers are `16` and `22`, the third is :
A
`22`

B
`20`

C
`19`

D
`18`

Note: Total sum of three numbers `= (20 xx 3)` `= 60` Third number `= 60 - (16 + 22)` `= 22`
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Question: The average of two numbers is M.If one number is N,then the other number is :
A
`2 N`

B
`2 M`

C
`M - N`

D
`2 M - N`

Note: Total sum of two numbers `= 2 M`. :. Other number `= (2 M - N)`.
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Question: The average of first five prime numbers is:

Question: The average of first five multiples of 3 is:

Question: The average of first `50` natural numbers is :

Question: The mean of `1^2,2^2,3^2,4^2,5^2,6^2,7^2` is:

Question: The average of all odd numbers upto `100`is:

Question: If a,b,c,d,e are five consecutive odd numbers ,thier average

Question: The average of `7`consecutive numbers is `33`.The largest of these numbers is :

Question: The average height of `30`boys out of a class of `50`,is `160`cm.If the average hieght of the remaining boys is `165`cm, the average height of the whole class (in cm) is :

Question: The average of three numbers is `20`.If two numbers are `16` and `22`, the third is :

Question: The average of two numbers is M.If one number is N,then the other number is :