Question

Form the greatest and smallest numbers using the digits 5,2,9,7(each digit used only once). What is the difference between the two numbers formed?
A. 6853
B. 7173
C. 7359
D. 8659

Answer 1

Hint: To obtain the greatest number, arrange the given digits in descending order. To obtain the smallest number, arrange the given digits in ascending order.

Complete step-by-step solution -
The greatest number is obtained by arranging the digits 5,2,9,7 in descending order as shown below.
\[{\text{Greatest number}} = 9752\]
The smallest number is obtained by arranging the digits 5,2,9,7 in ascending order as shown below.
\[{\text{Smallest number}} = 2579\]
The difference of the greatest number and smallest number is obtained as shown below.
\[\begin{gathered}
  {\text{Difference}} = 9752 - 2579 \\
  {\text{Difference}} = 7173 \\
\end{gathered}\]
Thus, the difference of the greatest number and smallest number is 7173, hence, option (B) is the correct answer.

Note: If we have the leftmost digit greatest out of the given digits, then the number formed would be greatest. If we have the leftmost digit smallest out of the given digits, then the number formed would be smallest.