contestada

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. Which of the following is true?
(A) y = x − 18
(B) y = x + 18
(C) y = 2x
(D) y = 2x + 4
(E) y = 2x + 6

Respuesta :

Answer:

The correct option is (B) y = x + 18.

Step-by-step explanation:

Consider the provided information.

Let n is the first even integer. Now 5 consecutive even integers are: n+2, n+4, n+6, n+8, n+10

Now the sum of first 3 integers are:

x = [tex]n+n+2+n+4=3n+6[/tex]

Similarly the sum of last 3 integers are:

y = [tex]n+6+n+8+n+10=3n+24[/tex]

Now subtract x from y.

[tex]y-x=3n-24-3n-6[/tex]

[tex]y-x=18[/tex]

[tex]y=x+18[/tex]

Hence, the correct option is (B) y = x + 18.