piyush2694 wrote:Are the integers z and f to the right of 0 on the number line?
(1) The product of z and f is positive.
(2) The sum of z and f is positive.
$$z,f\,\,\mathop > \limits^? \,\,0\,\,\,\,\,\left[ {{\rm{ints}}} \right]$$
$$\left( 1 \right)\,\,zf > 0\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {z,f} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {z,f} \right) = \left( { - 1, - 1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$
$$\left( 2 \right)\,\,z + f > 0\,\,\,\left\{ \matrix{
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {z,f} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,\left( {z,f} \right) = \left( { - 1,2} \right)\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,\left( 1 \right)\,\,\,\, \Rightarrow \,\,\,\,z,f\,\, > 0\,\,\,{\rm{or}}\,\,\,\,z,f < 0 \hfill \cr
\,\left( 2 \right)\,\,\,\,z,f < 0\,\,\,{\rm{impossible}} \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
