Question

What is the difference between a two-digit even and odd number?
A. $20$
B. $25$
C. $40$
D. $45$

Answer 1

Hint: We can take two variables one as an odd number and the other one as an even number. We should also know that the difference between an even number and an odd number is always odd. We can make a two-digit even or odd number using these variables.

Complete step by step answer:
Let a be an even digit and b be an odd digit.
Therefore, two-digit even number $ = \,10b + a$
Two-digit odd number $ = \,10a + b$
Now, the difference between two-digit even number and two-digit odd number $ = \,10b + a\, - \,\left( {10a + b} \right)$
On simplification, we get
$ \Rightarrow 10b + a - 10a - b$
On further calculation, we get
$ \Rightarrow 9b - 9a$
Taking common, we get
$ \Rightarrow 9\left( {b - a} \right)$
Here, $b$ is an odd number and a is an even number and the difference between these two is odd. So, if we multiply $9$ with an odd number we will get an odd number. Therefore, from this conclusion we can eliminate the $\left( A \right)$ and $\left( C \right)$ option. Now, as we can see, the final answer is a multiple of $9$. So on that basis we can also eliminate the option $\left( B \right)$ which is $20$. Therefore, the answer to our given question is $45$.

Hence, the correct option is $\left( D \right).$

Note: Here in this question, we can also find the difference between the two variables, that is a and b. We just have to equate the product of $9$ and $\left( {b - a} \right)$ with $45$. Therefore, we will get the desired result as $5\,.$There can be other methods to solve this question but this is the easiest one in which we just eliminate the options one by one.