NMTC 2002 Kaprekar Contest

Number Theory Level 2

Let $a*b\space =\space a+b+ab$ . For example,

$6*2\space =\space 6+2+(6\times2)\space =\space 20$

If $a*x\space =\space 0$ , then $x$ is

(A) $\dfrac{a}{a+1}$

(B) $\dfrac{a}{a-1}$

(D) $\dfrac{-a}{a+1}$

C B D A

1 solution

Aaryan Maheshwari
Jun 11, 2017

$a*x\space =\space 0$ $\Rightarrow\space a+x+ax=0$

$\Rightarrow\space x(1+a)\space =\space -a\space or$ $x\space =$ $\frac{-a}{1+a}$