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.
The OA is A
Source: e-GMAT
Joan spent $10 to buy at least one piece each of apples and
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\[\left\{ \begin{gathered}swerve wrote:Joan spent $10 to buy at least one piece each of apples and oranges at a store where each apple cost $2 and each orange cost $1. How many apples did she buy?
1) She spent more than $6 on buying oranges.
2) She spent less than $10 on buying oranges.
Source: e-GMAT
\,{\text{apples}}\,:\,\,A \geqslant 1\,\,{\text{int}}\,\,{\text{,}}\,\,{\text{\$ 2}}\,\,{\text{each}} \hfill \\
\,{\text{orangs}}\,:\,\,R \geqslant 1\,\,{\text{int}}\,\,{\text{,}}\,\,{\text{\$ 1}}\,\,{\text{each}} \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,{\text{with}}\,\,\,2 \cdot A + 1 \cdot R = 10\,\,\,\left[ \$ \right]\,\,\,\,\left( * \right)\]
\[? = A\]
\[\left( 1 \right)\,\,\,R \cdot 1 > 6\,\,\,\left[ \$ \right]\,\,\,\mathop \Rightarrow \limits^{R\,\,\operatorname{int} } \,\,\,R \geqslant 7\,\,\,\,\left[ \$ \right]\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,2A \leqslant 3\,\,\,\, \Rightarrow \,\,\,\,A = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}{\text{.}}\]
\[\left( 2 \right)\,\,\,R \cdot 1 < 10\,\,\,\left[ \$ \right]\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {A,R} \right) = \left( {1,8} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 1 \hfill \\
\,{\text{Take}}\,\,\left( {A,R} \right) = \left( {2,6} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 2 \hfill \\
\end{gathered} \right.\]
The correct answer is therefore (A).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Target question: How many apples did Joan buy?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.
Given: 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.
Since there are only a handful of possible outcomes, we might benefit from quickly listing them:
i) Joan buys 1 apple (for $2) and 8 oranges (for $8)
ii) Joan buys 2 apples (for $4) and 6 oranges (for $6)
iii) Joan buys 3 apples (for $6) and 4 oranges (for $4)
iv) Joan buys 4 apple (for $8) and 2 oranges (for $2)
Statement 1: She spent more than $6 on buying oranges
When we check our list of possible outcomes, we see that only one outcome (case iv) satisfies statement 1.
So, it MUST be the case that Joan bought 4 apples
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: She spent less than $10 on buying oranges
When we check our list of possible outcomes, we see that ALL 4 outcomes satisfy statement 2.
So, it's possible that Joan bought 1 apple, 2 apples, 3 apples OR 4 apples
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent