AAPL wrote:Magoosh
If a child is randomly selected from Columbus Elementary School, what is the probability that the child will be a boy?
1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75.
2) There are 35 more boys than there are girls.
$$? = {b \over {b + {\rm{g}}}}$$
$$\left( 1 \right)\,\,{{b - 25} \over {\left( {b - 25} \right) + g}} = {3 \over 4}\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {28,1} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{28} \over {29}} \hfill \cr
\,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {31,2} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{31} \over {33}} \ne {{28} \over {29}} \hfill \cr} \right.$$
$$\left( 2 \right)\,\,b = g + 35\,\,\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {36,1} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{36} \over {37}} \hfill \cr
\,{\rm{Take}}\,\,\left( {b,g} \right) = \left( {37,2} \right)\,\,\,\, \Rightarrow \,\,\,\,? = {{37} \over {39}} \ne {{36} \over {37}} \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,\,{{\left( {g + 35} \right) - 25} \over {\left[ {\left( {g + 35} \right) - 25} \right] + g}} = {3 \over 4}\,\,\,\,\mathop \Rightarrow \limits^{{1^{{\rm{st}}}}\,\,{\rm{degree}}} \,\,\,\,g\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,b\,\,{\rm{unique}}\,\,\,\, \Rightarrow \,\,\,\,{\rm{SUFF}}.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
