Question

Let $0<a<b<c$ be $3$ distinct digits. The sum of all 3-digit numbers formed by using all the $3$ digits once each is $1554$. The value of $c$ is:

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

The possible combination with these digits are,

$abc,acb,bac,bca,cab,cba.$

Now $abc=100a+10b+c.$

Finding sum of all we get $222(a+b+c)=1554$

Or $a+b+c=7$

$\because a,b,c$ are district and greater than $0$ but $c$ can be equal to $4.$

Hence, the answer is $4.$