The sum of three consecutive even numbers is 78. What is the smallest possible value of the sum?

SOLUTION:

Let us take three consecutive even numbers as x, x+4 and x+8 .

Then, their sum is (x+4) + (x+8) = 2*x + 12 = 2(x+2) .

Therefore, x+2 must be a multiple of 3. But we know that this number is not divisible by 4 or 8 as it would then be an odd number. Hence, we conclude that 2 is a multiple of 3.

Hence, x can be any number between 0 and 29 inclusive.

So the largest possible sum of three consecutive even numbers with maximum value 78 is 29 + 30 + 31 = 92.

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Last modified: October 4, 2022