Question

If $x$ is an odd number, the largest odd number preceding $x$ is.

A. $x-1$
B. $x-2$
C. $x-3$
D. $x-4$

Answer 1

Hint: We will look over the basic definition of even numbers. Then we will try to find the series of odd numbers to find the largest odd number preceding $x$.

Complete step by step answer:
It is given in the question that $x$ is an odd number then we have to find the odd number preceding $x$. Odd numbers are those which are not directly divisible by $2$. Whenever we divide any odd number we get $1$ as remainder. For example, $1,3,5,7,9,11,13,.......$ etc.

Generally we can represent an odd number with $(2n+1)$, where $n$ is any whole number. Whereas, even numbers are those which are directly divisible by $2$.Whenever we divide any even number with $0$ as remainder. For example, $2,4,6,8,10,12,.....$ etc. Generally we can represent an even number with $(2n)$, where $n$ is any whole number.

Now, if you look at the series of odd numbers and even numbers the difference between any two consecutive odd numbers or even numbers is $2$. Also, it is given in question that $x$ is an odd number and we have to find the largest odd number preceding $x$.

Let us assume that $x$ is in any place. Then, its preceding number is given by $(x-2)$, this is because the difference between any two consecutive odd numbers or even numbers is $2$. So, the preceding odd number of $x$ is given by $(x-2)$ and option (B) is the correct answer.


Note: Both even numbers and odd numbers are in arithmetic progression (AP) series and the common difference between any two consecutive numbers in series is $2$. We can use (AP) formula to find the preceding terms in a series of odd numbers and even numbers directly by using the formula \[{{a}_{n-1}}=a+(n-2)d\]. To find the exact number preceding $x$ in series.