Question

The three-digit number whose hundred's digit is the cube of its unit's digit and the ten's digit is the sum of unit's and hundred's digit is

• A. 121
• B. 144
• C. 169

Answer 1

The correct option is A 121

Any three digit number can not have its hundred's digit more than 9. If the unit's digit is 'x', then the hundred's digit is $x^3$.
$\Rightarrow x^3<9$
$\Rightarrow x=1or2$
When x=1, the ten's digit is $1+1=2$
When x=2, the ten's digit is $8+2=10$ which is greater than 9 and hence $x\ne 2$.
Therefore, the number is 121.