Question : The average of seven consecutive even numbers is 12. What will be the new average if the next even number is also considered?
Option 1: 16
Option 2: 13
Option 3: 14
Option 4: 15
Correct Answer: 13
Solution :
The average of seven consecutive even numbers = 12
The sum of seven consecutive even numbers = 12 × 7 = 84
Let $x$ be the first number
So, $x + (x+2) + (x+4) + (x+6) +(x+8) + (x+10) + (x+12)$ = 84
⇒ $7x+ 42 = 84$
⇒ $x = \frac{84-42}{7} = 6$
New number added = $x+14 = 6+14 = 20$
When 20 is added,
Sum = 84 + 20 = 104
So, the average = $\frac{104}{8}$ = 13
Hence, the correct answer is 13.
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