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The figure above represents a rectangular garden bordered by

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by AAPL » Mon Oct 29, 2018 4:03 am

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The figure above represents a rectangular garden bordered by a walkway that has a uniform width of 3 feet. What's the perimeter of the garden?

1) The outer perimeter of the walkway is 124 feet.
2) The area of the garden is 600 feet.

OA A.
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by fskilnik@GMATH » Mon Oct 29, 2018 7:53 am
AAPL wrote:GMAT Prep

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The figure above represents a rectangular garden bordered by a walkway that has a uniform width of 3 feet. What's the perimeter of the garden?

1) The outer perimeter of the walkway is 124 feet.
2) The area of the garden is 600 feet squared.
All lengths are considered in feet.
\[? = 2\left[ {\left( {a - 6} \right) + \left( {b - 6} \right)} \right]\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,\,? = a + b\,\,}\]
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\[\left( 1 \right)\,\,\,2\left( {a + b} \right) = 124\,\,\,\, \Rightarrow \,\,\,\,? = a + b\,\,\,{\text{unique}}\]
\[\left( 2 \right)\,\,\left( {a - 6} \right)\left( {b - 6} \right) = 600\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {a,b} \right) = \left( {16,66} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{16 + 66}}\,\, \hfill \\
\,{\text{Take}}\,\,\left( {a,b} \right) = \left( {26,36} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{26 + 36}} \ne {\text{16 + 66}}\,\, \hfill \\
\end{gathered} \right.\]

This solution follows the notations and rationale taught in the GMATH method.

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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by [email protected] » Mon Oct 29, 2018 9:17 am
Hi All,

We're told that the figure above represents a rectangular garden bordered by a walkway that has a uniform width of 3 feet. We're asked for the PERIMETER of the garden. This question can be solved with a mix of Arithmetic and TESTing VALUES.

1) The outer perimeter of the walkway is 124 feet.

Fact 1 tells us that the OUTER perimeter is 124 feet. We know from the prompt that the walkway has a uniform width of 3 feet, meaning that to find the 'inner length' of the walkway (which is the length of the garden), we subtract (2)(3) feet from the 'outer length.' To find the 'inner width' of the walkway (which is the width of the garden), we subtract (2)(3) feet from the 'outer width.'

Those inner sides represent the 4 sides of the garden, so we can calculate the perimeter of the garden: 124 feet - 6 feet - 6 feet = 112 feet.
Fact 1 is SUFFICIENT

2) The area of the garden is 600 ft^2.

With an area of 600 ft^2, the perimeter could be a variety of different totals. For example:
IF....
the garden is 20 feet x 30 feet, then the perimeter is 20+20+30+30 = 100 feet
the garden is 10 feet x 60 feet, then the perimeter is 10+10+60+60 = 140 feet
Fact 2 is INSUFFICIENT

Final Answer: A

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