Question

A three-digit number $XYZ$ is formed of three different non-zero digits $X,Y$ and $Z$. A new number is formed by rearranging the same three digits. What is the greatest possible difference between the two numbers? (For example, $345$ could be rearranged into $435$, for a difference of $435-345=90$.)

• A. $792$
• B. $293$
• C. $564$
• D. $984$
• E. $456$

Answer 1

Answer: (A)

$792$

To get the greatest difference, we want to subtract a small number from a large one, so we will need the digit $9$ and 1,to make numbers in $100$s and the number $900$s.
Let $m$ be the digit from $2$ to $8$.
The larger three digit number will look like $9m1$, while the smaller three digit number will look like $1m9$.
Assume a three digits number lets say $189$.
Then the largest possible three digit number after rearranging above number is $981$.
$\Rightarrow$$981-189=792$
Again assume a three digits number lets say $149$.
Then the largest possible three digit number after rearranging above number is $941$.
$\Rightarrow$$941-149=792$
As you see no matter what is the value you are plugging for m their difference is constant i.e:$792$, which is the highest possible difference.
Hence, option A is correct.