Question

The sum of four consecutive even integers is 1284. The greatest of them is:
(a) 320
(b) 322
(c) 324
(d) 326

Answer 1

Hint: We solve this problem by assuming the consecutive even integers as variables. The general representation of consecutive even numbers is
\[2n,2n+2,2n+4,2n+6\]
We use the given condition that the sum of these four numbers is 1284 to find the value of \['n'\] then the greatest of them will be \[2n+6\]

Complete step-by-step solution
We are given that the sum of four consecutive even integers is 1284.
We know that the general representation of consecutive even numbers is
\[2n,2n+2,2n+4,2n+6\]
Let us assume that the required four even integers as
\[2n,2n+2,2n+4,2n+6\]
By using the given condition that is the sum of numbers is 1284 to this general representation of numbers we get
\[\begin{align}
  & \Rightarrow 2n+2n+2+2n+4+2n+6=1284 \\
 & \Rightarrow 8n=1284-12 \\
 & \Rightarrow n=\dfrac{1272}{8} \\
 & \Rightarrow n=159 \\
\end{align}\]
Therefore the value of \['n'\] is 159.
We assumed that the four consecutive even numbers as
\[2n,2n+2,2n+4,2n+6\]
Here, we can see that the greatest number is \[2n+6\]
Let us assume that the greatest number of four consecutive numbers as \[N\]
So, we can write the greatest number as
\[\Rightarrow N=2n+6\]
Now, by substituting the value of \['n'\] in above equation we get
\[\begin{align}
  & \Rightarrow N=2\left( 159 \right)+6 \\
 & \Rightarrow N=324 \\
\end{align}\]
Therefore, the greatest number such that the sum of four consecutive even integers is 1284 is 324.
So, option (c) is the correct answer.

Note: Students may make mistakes in the consideration of four consecutive even integers.
We know that the general representation of consecutive even numbers is
\[2n,2n+2,2n+4,2n+6\]
But students may do mistake in this consideration and take the numbers as
\[2n,2n+1,2n+2,2n+3\]
In this representation, the second and fourth numbers are not even numbers.