Find the sum of the smallest and the largest 4-digit number that can be formed by using the digits 2, 0, and 9 by repeating any one digit twice.

The correct option is A 11,929
To form the smallest 4-digit number by using the given set of numbers, provided only one number can be used twice, we repeat the smallest number twice and arrange the given numbers in ascending order.

$\begin{array}{cccc}\text{Thousands}& \text{Hundreds}& \text{Tens}& \text{Ones}\\ 2& 0& 0& 9\end{array}$

∴ $2,009$ is the smallest 4-digit number formed.

In similar way,
To form the largest 4-digit number by using the given set of numbers, provided only one number can be used twice, we repeat the largest number twice and arrange the given numbers in descending order.

$\begin{array}{cccc}\text{Thousands}& \text{Hundreds}& \text{Tens}& \text{Ones}\\ 9& 9& 2& 0\end{array}$

∴ $9,920$ is the largest 4-digit number formed.
Hence, the sum of the largest and the smallest numbers $=9920+2009$
$=11,929$