Nirenjan wrote:

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.

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)

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