Correct option is A
Given:
- The average of 13 consecutive integers is 36.
- Two times the smallest integer is added to the largest integer.
Concept Used:
Let the 13 consecutive integers be x, x+1, x+2, ..., x+12.
The average of these integers is given by:
Average =
Solution:
The sum of 13 consecutive integers is 13 times the average:
Sum = 13 × 36 = 468
The sum of 13 consecutive integers can also be written as:
13x + (0 + 1 + 2 + ... + 12)
The sum of the numbers 0 to 12 is
So, the sum of these integers is:
13x + 78 = 468
13x = 468 - 78 = 390
x = 390 / 13 = 30
Two times the smallest integer = 2 × 30 = 60
The largest integer = 42
Sum = 60 + 42 = 102
The sum obtained is 102.
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