Question

Find three consecutive even integers such that the sum of first two integers is same as the sum of third integer and $6$.

• A. $4,6,8$
• B. $6,8,10$
• C. $8,10,12$
• D. $10,12,14$

Answer 1

The correct option is C $8,10,12$

Let us say the first even integer be $x$. The second consecutive even integer would be $x+2$ (zit would not be $x+1$ because that would result in an odd integer. The sum of two even integers is even). The third consecutive even integer would be $(x+2)+2$ or $x+4$.

Now, it is given that the sum of first two integers is same as the sum of the third integer and $6$ which means:

$x+(x+2)=(x+4)+6\Rightarrow 2x+2=x+10\Rightarrow 2x-x=10-2\Rightarrow x=8$

Therefore, the first even integer is $8$ then the second integer is $x+2=8+2=10$ and the third integer is $x+4=8+4=12$

Hence, the three consecutive even integers are $8,10,12$.