BTGmoderatorDC wrote:What is the value of integer x?
(1) |1 - x| - |x + 1| = 0
(2) |7 - x| + |3 + x| = 10
Source: Veritas Prep
$$? = x\,\,\left( {{\mathop{\rm int}} } \right)$$
$$\left( 1 \right)\,\,\,\,\left| {x - 1} \right| = \left| {x + 1} \right|\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,dist\left( {x,1} \right) = dist\left( {x, - 1} \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,x = 0\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}$$
$$\left( 2 \right)\,\,\,\,\left| {x - 7} \right| + \left| {x + 3} \right| = 10\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{inspection}}!} \,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,x = 7\,\,\, \hfill \cr
\,{\rm{Take}}\,\,x = - 3\,\, \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
