Question

Find the sum of the smallest three digits even number and the greatest three digits odd number using the digits $6$, $2$ and $3$.
(A) $859$
(B) $958$
(C) $598$
(D) $985$

Answer 1

Hint: We have to write the smallest three digits even number and the greatest three digits odd number using the digits $6$, $2$ and $3$. A number is an even number if its unit digit is either $0$, $2,4,6$ or $8$. The number formed using the given digits is the smallest if the digit at hundred place is the smallest. Similarly, a number is an odd number if its unit digit is either $1,3,5,7$ or $9$. And the number is the largest number if the digits at hundred place is the largest. After writing the largest and the smallest number we have to add them to get the required result.

Complete step-by-step answer:
Given digits are $6$, $2$ and $3$.
Firstly, we have to write the smallest even number formed using these digits.
For the number to be even either $6$ or $2$ is on unit place and for the number to be the smallest number, the smallest digit that is $2$ at hundred place. So, the smallest even number formed using these digits is $236$.
Now, we have to write the greatest odd number formed using these digits.
For the number to be an odd number $3$ must be at unit place and for the number to be greatest number, the largest digit that is $6$ at hundred place. So, the greatest odd number formed using these digits is $623$.
Now, we have to find the summation of these numbers.
Summation $ = 623 + 236 = 859$.

Thus, the required result is $859$.

Note:
Similarly, we can write the smallest and largest natural number using these digits. For the smallest number put the largest digit at unit place and the smallest digit at the hundred place. And for the greatest number put the largest digit at hundred place and the smallest digit at the unit place.