Nirenjan
If A and B are positive is A greater than B ?
1) A = 5
2) 2A = 5B
\(A,B\,\,\, > 0\)
\(A\,\,\mathop > \limits^? \,B\)
\(\left( 1 \right)\,\,A = 5\,\,\,\left\{ \begin{gathered}\\
\,{\text{If}}\,\,\,\,B = 1\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\\\
\,{\text{If}}\,\,\,\,B = 5\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \\
\end{gathered} \right.\)
\(\left( 2 \right)\,\,2A = 5B\,\,\,\, \Rightarrow \,\,\,\,A = \frac{5}{2}B\,\,\mathop > \limits^{\left( * \right)} \,\,B\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle\)
\(\left( * \right)\,\,\,\frac{5}{2} > 1\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,B\,\,\left( {B\, > \,0} \right)} \,\,\,\frac{5}{2}\left( B \right) > 1 \cdot B\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{5}{2}B > B\,\)
Conclusion: the right answer is (B).
The above follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.