The sum of 3 consecutive even numbers is 312 . What is the largest of these 3 numbers?
(A) 54
(B) 106
(C) 86
(D) 108
(E) 102

Part B: Each correct answer is worth 6.
The smallest of 3 consecutive even numbers is 2 less than the middle number.

The largest of 3 consecutive even numbers is 2 more than the middle number.

Therefore, the sum of 3 consecutive even numbers is three times the middle number.

To see this, consider subtracting 2 from the largest of the 3 numbers, and adding 2 to the smallest of the 3 numbers.

Since we have subtracted 2 and also added 2 , then the sum of these 3 numbers is equal to the sum of the original 3 numbers.

However, if we subtract 2 from the largest number, the result is equal to the middle number, and if we add 2 to the smallest number, the result is equal to the middle number.

Therefore, the sum of any 3 consecutive even numbers is equal to three times the middle number.

Since the sum of the 3 consecutive even numbers is 312 , then the middle number is equal to $312 \div 3=104$.

If the middle number is 104, then the largest of the 3 consecutive even numbers is $104+2=106$. (We may check that $102+104+106$ is indeed equal to 312 .)

ANSWER: (B)