Question

$M$ is a set of six consecutive even integers. When the least three integers of set $M$ are summed, the result is $x$. When the greatest three integers of set $M$ are summed, the result is $y$. Mark the true equation.

• A. $y=x-18$
• B. $y=x+18$
• C. $y=2x$
• D. $y=2x+4$
• E. $y=2x+6$

Answer 1

The correct option is B $y=x+18$

Suppose that $n$ is the first even integer.
Then the remaining integers are $n+2$, $n+4$, $n+6$, $n+8$ and $n+10$.
The sum of the least three of these integers is $x$ $=n+n+2+n+4=3n+6$
and the sum of the greatest three of these integers is $y$ $=n+6+n+8+n+10=3n+24$
$y-x=3n+24-(3n+6)=0+24-6=18$
So, $y=x+18$
Hence, option B is correct.