Question

On adding any three consecutive even numbers, the summation result would always be divisible by which of the following?

• A. \(5\)
• B. \(7\)
• C. \(6\)
• D. \(11\)

Hint:

The sum of any three consecutive even numbers is always divisible by \(6\).

Answer 1

The Correct Option is C

Concept:
Consecutive even numbers differ by \(2\). We can represent any three consecutive even numbers algebraically.

Step 1: Let the three consecutive even numbers be: \[ 2n,\quad 2n+2,\quad 2n+4 \]

Step 2: Add the three numbers. \[ S=2n+(2n+2)+(2n+4) \] \[ S=6n+6 \] \[ S=6(n+1) \]

Step 3: Interpret the result.
Since the sum is: \[ 6(n+1) \] it is always divisible by \(6\). \[ \therefore \text{Correct Answer is (C)} \]