Question : The average of 6 consecutive even numbers is 35. What will be the sum of the smallest and largest even number among these 6 numbers?
Option 1: 68
Option 2: 72
Option 3: 70
Option 4: 66
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Correct Answer: 70
Solution :
The average of 6 consecutive even numbers is 35.
Let the 6 consecutive even numbers be n, (n + 2), (n + 4), (n + 6), (n + 8), (n + 10).
The Sum of 6 consecutive numbers = n + (n + 2) + (n + 4) + (n + 6) + (n + 8) + (n + 10) = 210
Average= $\frac{\text{Sum of values}}{\text{Number of values}}$
⇒ 6n + 30 = 6 $\times$ 35
⇒ 6n + 30 = 210
$\therefore$ n = 30
So, the smallest number = 30 and the largest number = 30 + 10 = 40
The sum is 30 + 40 = 70
Hence, the correct answer is 70.
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