swerve wrote:Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. How many apples did she buy?
1) She spent more than $6 on buying oranges.
2) She spent less than $10 on buying oranges.
Source: e-GMAT
\[\left\{ \begin{gathered}
\,{\text{apples}}\,:\,\,A \geqslant 1\,\,{\text{int}}\,\,{\text{,}}\,\,{\text{\$ 2}}\,\,{\text{each}} \hfill \\
\,{\text{orangs}}\,:\,\,R \geqslant 1\,\,{\text{int}}\,\,{\text{,}}\,\,{\text{\$ 1}}\,\,{\text{each}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,{\text{with}}\,\,\,2 \cdot A + 1 \cdot R = 10\,\,\,\left[ \$ \right]\,\,\,\,\left( * \right)\]
\[? = A\]
\[\left( 1 \right)\,\,\,R \cdot 1 > 6\,\,\,\left[ \$ \right]\,\,\,\mathop \Rightarrow \limits^{R\,\,\operatorname{int} } \,\,\,R \geqslant 7\,\,\,\,\left[ \$ \right]\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,2A \leqslant 3\,\,\,\, \Rightarrow \,\,\,\,A = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}{\text{.}}\]
\[\left( 2 \right)\,\,\,R \cdot 1 < 10\,\,\,\left[ \$ \right]\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {A,R} \right) = \left( {1,8} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 1 \hfill \\
\,{\text{Take}}\,\,\left( {A,R} \right) = \left( {2,6} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 2 \hfill \\
\end{gathered} \right.\]
The correct answer is therefore (A).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
