Question

The average of four consecutive even numbers is 27. Find the largest of these numbers.
(a) 50
(b) 40
(c) 20
(d) 30

Answer 1

Hint: Assume the four consecutive even numbers as: - ‘x’, ‘x + 2’, ‘x + 4’ and ‘x + 6’. Take the sum of
these four numbers. Now find the average by using the formula: - Average = (sum of observations) /
(number of observations). Equate this average with 27 to form a linear equation in one variable, which is
‘x’. Solve this equation to get the value of ‘x’ and substitute it in ‘x + 6’ to get the correct answer.

Complete step by step answer:
We have been given that the average of four consecutive even numbers is 27, and we have to find the
largest number.
Let us assume the four consecutive even numbers as: -
‘x’, ‘x + 2’, ‘x + 4’ and ‘x + 6’.
Adding these four numbers, we get,
Sum = \[x+\left( x+2 \right)+\left( x+4 \right)+\left( x+6 \right)\]
Sum = 4x + 12
Sum = 4 (x + 3)
Now, let us find the average. We know that,
Average = (sum of observations) / (number of observations)
Therefore, applying the above formula, we have,
Average = \[\dfrac{4\left( x+3 \right)}{4}\]
\[\Rightarrow 27=\dfrac{4\left( x+3 \right)}{4}\]
By cross multiplication, we get,

\[\Rightarrow 27\times 4=4\left( x+3 \right)\]
Cancelling the common factors, we have,
\[\begin{align}
& \Rightarrow 27\times 1=\left( x+3 \right) \\
& \Rightarrow 27=x+3 \\
& \Rightarrow x=27-3 \\
& \Rightarrow x=24 \\
\end{align}\]
Therefore, substituting the value of ‘x’ in all the assumed even numbers, we get,
\[\begin{align}
& \Rightarrow x=24 \\
& \Rightarrow x+2=26 \\
& \Rightarrow x+4=28 \\
& \Rightarrow x+6=30 \\
\end{align}\]
Clearly, we can see that the largest of these numbers is ‘x + 6’ or 30.

So, the correct answer is “Option D”.

Note: You may note after assuming ‘x’ as the first even number we have assumed the second even
number as ‘x + 2’ and not ‘x + 1’. This is because, as ‘x’ is even, therefore ‘x + 1’ will be odd and so it
cannot be considered as the next even number. Also, note that after getting the values of ‘x’ we have to
check the greatest or smallest number by substituting the values of ‘x’ in the assumed numbers.