AAPL wrote:Veritas Prep
If the remainder when positive integer x is divided by 7 is 4, what is the value of x?
1) x is less than 50
2) x is prime
$$x \ge 1\,\,{\mathop{\rm int}} \,\,\,\left( * \right)$$
$$x = 7M + 4\,\,\,,\,\,M\mathop \ge \limits^{\left( * \right)} 0\,\,\,{\mathop{\rm int}} $$
$$? = x$$
$$\left( 1 \right)\,\,x < 50\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,x = 4\,\,\,\,\, \hfill \cr
\,{\rm{Take}}\,\,x = 4 + 7 = 11 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.$$
$$\left( 2 \right)\,\,x\,\,{\rm{prime}}\,\,\,\left\{ \matrix{
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,x = 11\,\,\,\,\, \hfill \cr
\,{\rm{Take}}\,\,x = 11 + 6 \cdot 7 = 53 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}{\rm{.}}$$
$$\left( {1 + 2} \right)\,\,\,\,? = 11\,\,\,\,\,\,\left( {{\rm{11}}\,{\rm{and}}\,\,{\rm{53}}\,\,{\rm{are}}\,\,{\rm{the}}\,\,{\rm{smallest}}\,\,{\rm{possibilities}}\,\,{\rm{for}}\,\,{\rm{the}}\;{\rm{bifurcation}}\,\,{\rm{of}}\,\,\left( {\rm{2}} \right)} \right)$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
