The average of a set of 20 consecutive integers is 21.5. What is the smallest integer in the set?
- A11
- B33
- C31
- D12
Solution & Step-by-step Explanation
For an even number of consecutive integers (n=20), the average is the mean of the two middle terms (10
th
and 11
th
terms).
Given average =21.5, the two consecutive integers enclosing 21.5 must be 21 and 22.
10
th
term=21
11
th
term=22
To find the smallest (1
st
) integer:
Smallest integer=10
th
term−(10−1)=21−9=12
th
and 11
th
terms).
Given average =21.5, the two consecutive integers enclosing 21.5 must be 21 and 22.
10
th
term=21
11
th
term=22
To find the smallest (1
st
) integer:
Smallest integer=10
th
term−(10−1)=21−9=12