Question

If $A,B,C,D$ are distinct decimal digits, then which of the following option is correct?
$A4BC$
$\times C$
-----------------------
$1$ $A$ $1$ $D$ $C$

• A. $A=3;B=7;C=5;D=9$
• B. $A=2;B=3;C=6;D=5$
• C. $A=3;B=8;C=6;D=5$
• D. $A=2;B=3;C=5;D=7$

Answer 1

The correct option is D $A=2;B=3;C=5;D=7$

$A4BC$
$\times C$
--------------------------------------
$1$ $A$ $1$ $D$ $C$
-----------------------------------------
$C$ can be $1$ or $5$ or $6$.Because square of $1,5,6$ ends with the same number.

But $C$ cannot be $1$ because we get $5$ digits in answser
$C$ is $5$ or $6$
By looking into the solution:

When $C=5$
$A=2;B=3;C=5;D=7$

$2$ $1$ $2$
$2$ $4$ $3$ $5$
$\times 5$
-----------------------
$1$ $2$ $1$ $7$ $5$