Question

Find out $(A+B+C+D)$ such that $AB\times CB=DDD$, where $AB$ and $CB$ are two-digit numbers and $DDD$ is a three-digit number.

• A. $21$
• B. $19$
• C. $17$
• D. $18$

Answer 1

The correct option is A $21$

Given $DDD$ is a $3-$digit number with all $3-$digits same, then it has to be any number in $\{111,222,333,...,999\}$.

$111$ can be written as $37\times 3$.

$222$ can be written as $37\times 6$.

.

.

$999$ can be written as $37\times 27$.

So, if $37$ is $AB$, then $CB$ must be $27$ such that $37\times 27$ is $999$ which is the only possible combination.
Hence, $A$ is $3,B$ is $7,C$ is $2$ and $D$ is $9$.
Their sum is $21$.

Hence, option A.