If the average of six consecutive odd natural numbers is 24, then what is the average of the four smaller numbers out of the six numbers?
- A24
- B20
- C21
- D22
Solution & Step-by-step Explanation
Let the six consecutive odd natural numbers be x−5,x−3,x−1,x+1,x+3,x+5.
The average of these six numbers is the middle term, which is the average of x−1 and x+1, equal to x.
Given that the average is 24:
x=24
The six consecutive odd numbers are:
24−5,24−3,24−1,24+1,24+3,24+5⟹19,21,23,25,27,29
The four smaller numbers out of these six are: 19,21,23,25.
The average of these four numbers is:
Average=
4
19+21+23+25
=
4
88
=22
The average of these six numbers is the middle term, which is the average of x−1 and x+1, equal to x.
Given that the average is 24:
x=24
The six consecutive odd numbers are:
24−5,24−3,24−1,24+1,24+3,24+5⟹19,21,23,25,27,29
The four smaller numbers out of these six are: 19,21,23,25.
The average of these four numbers is:
Average=
4
19+21+23+25
=
4
88
=22