Question

The sum of five consecutive whole numbers is less than $25$. One of the numbers is $6$. Which of the following is the greatest of the consecutive numbers?
$\begin{gathered}
  A - 6 \\
  B - 7 \\
  C - 8 \\
  D - 9 \\
\end{gathered} $

Answer 1

Hint: This problem is from the chapter Numbers. There is no need to think of any formula for solving such a type of sum. It can be solved on the basis of common sense. The student has to assume the smallest whole number as $x$ and then for consecutive numbers keep on adding $1$. After that the student has to take the sum of the numbers and equate it to $25$ as given. Last step is finding all the numbers and then out of those numbers find which is the greatest.

Complete step-by-step answer:
Let us assume that the smallest whole number is $x$.
Next consecutive whole number would be $x + 1$
Similarly all the five consecutive numbers can be written as
 $x,x + 1,x + 2,x + 3,x + 4............(1)$
It is given that the sum of 5 consecutive numbers is $25$.
Thus adding all the five consecutive numbers from equation 1 and equating it to $25$.We get the following equation
\[x + x + 1 + x + 2 + x + 3 + x + 4 = 25............(2)\]
Simplifying the equation we get
\[5x + 10 = 25............(3)\]
$\therefore $Value of $x$ is $3$.
It is given that one of the consecutive numbers is $6$. Since the value of $x$ is $3$, we can say that the consecutive number representing it is \[x + 3\]. Thus the greatest whole number is $x + 4$ which is $7$.

Thus the answer to this question is Option $B - 7$.

Note: In order to solve a much more complex sum the student should use the method as used above. This is because the student can find the answer with this method even if it consists of big numbers. A structured approach in such a type of numerical with the proper method would help the student to solve any typical sum of this category Only thing the student should know while solving these types of sums is the difference between Whole Numbers, Real Numbers & Natural Numbers.