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NoHalfMeasures
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Posts: 219
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The figure above represents a rectangular garden bordered by a walkaway that has a uniform width of 3 feet. What's the perimeter of the garden?
(1) The outer perimeter of the walkaway is 124 feet
(2) The area of the garden is 600 feet.
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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MensaNumber
the statement says the uniform width of the walkway is 3 feet. Nothing more info on that. Lets check the answer.
1. We know the outer perimeter as 124 ft. So we can find the length and width. And if we subtract the 3 feet(Uniform) from both length and breath we find the perimeter of the garden- Sufficient.
2. we know the area, but we do not know whether the area includes the walkway or not. . Also in either case, we may have multiple values of length and breath which can give the area of 600 feet. So In-sufficient
The answer is A.
NoHalfMeasures
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Let x and y be two sides of the garden. So what is 2(x+y)?
St1) If outer perimeter of a walkaway is 124, 2*{(x+6)+(y+6)} = 124. We can calculate x+y from it. SUFF
St2) x*y=600. INSUFF
St1) If outer perimeter of a walkaway is 124, 2*{(x+6)+(y+6)} = 124. We can calculate x+y from it. SUFF
St2) x*y=600. INSUFF
NoHalfMeasures
Retired Moderator
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Posts: 219
2*{(x+6)+(y+6)} = 124
{(x+6)+(y+6)} = 62
X+Y+12=62
X+Y=50
But its imp to realize we must resist doing these sorts of calculations on DS as its enough to know if we have sufficient information to answer the question
{(x+6)+(y+6)} = 62
X+Y+12=62
X+Y=50
But its imp to realize we must resist doing these sorts of calculations on DS as its enough to know if we have sufficient information to answer the question
what does "outer perimeter" mean exactly though? they didn't give any info about garden just walkway so how is 1 sufficient?
GMAT 1: 760 Q51 V42
Posts: 10,057
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
The figure above represents a rectangular garden bordered by a walkaway that has a uniform width of 3 feet. What's the perimeter of the garden?
1) The outer perimeter of the walkaway is 124 feet
2) The area of the garden is 600 feet.
Modify the original condition and the question. Suppose the width and the length of the garden ‘a’ and ‘b’ respectively. Then you can come up with an equation 2(a+b)=?. In 1), you can get a+b=50 from 2(a+b)+24=124, which is sufficient and therefore the answer is A.
-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
The figure above represents a rectangular garden bordered by a walkaway that has a uniform width of 3 feet. What's the perimeter of the garden?
1) The outer perimeter of the walkaway is 124 feet
2) The area of the garden is 600 feet.
Modify the original condition and the question. Suppose the width and the length of the garden ‘a’ and ‘b’ respectively. Then you can come up with an equation 2(a+b)=?. In 1), you can get a+b=50 from 2(a+b)+24=124, which is sufficient and therefore the answer is A.
-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
LakerFan24
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Last visit: 03 Apr 2018
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Location: United States (CA)
Concentration: Finance, Strategy
WE:Investment Banking (Finance: Venture Capital)
Posts: 162
NoHalfMeasures
i understand St2) but am lost on St1).
Where do you get (x+6)(y+6)?
I understand Perimeter = 2(x+y). if outer perimeter is 124, isn't the equation: 124 = 2(x+y)? I understand the walkway (3') borders the garden so there needs to be a little more to the "x+y" but i can't understand why you put "x+6 and y"+6" here...
Bunuel - What do we mean here by outer perimeter?
If the garden is surrounded by a walkway and the perimeter of that is 124 feet, then ideally the perimeter should be calculated as the perimeter of the bigger box - Perimeter of the garden.
Which i tried to solve but the variables get cancelled out 2(X+6+y+6)<------Perimeter of bigger box MINUS 2(X+Y)<------ Perimeter of the Garden(Smaller box)=124
Please correct me.
If the garden is surrounded by a walkway and the perimeter of that is 124 feet, then ideally the perimeter should be calculated as the perimeter of the bigger box - Perimeter of the garden.
Which i tried to solve but the variables get cancelled out 2(X+6+y+6)<------Perimeter of bigger box MINUS 2(X+Y)<------ Perimeter of the Garden(Smaller box)=124
Please correct me.
siddyj94
The outer perimeter of the walkaway is the perimeter of the larger rectangle.
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NoHalfMeasures
All lengths are considered in feet.
\(? = 2\left[ {\left( {a - 6} \right) + \left( {b - 6} \right)} \right]\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,\,? = a + b\,\,}\)
\(\left( 1 \right)\,\,\,2\left( {a + b} \right) = 124\,\,\,\, \Rightarrow \,\,\,\,? = a + b\,\,\,{\text{unique}}\)
\(\left( 2 \right)\,\,\left( {a - 6} \right)\left( {b - 6} \right) = 600\,\,\,\,\left\{ \begin{gathered}\\
\,{\text{Take}}\,\,\left( {a,b} \right) = \left( {16,66} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{16 + 66}}\,\, \hfill \\\\
\,{\text{Take}}\,\,\left( {a,b} \right) = \left( {26,36} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\,{\text{ = }}\,\,{\text{26 + 36}} \ne {\text{16 + 66}}\,\, \hfill \\ \\
\end{gathered} \right.\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
ankitnoida2018
Joined: 08 Jul 2017
Last visit: 05 Aug 2019
Posts: 38
Schools: Fisher '19 Boston U '20 Duke '20
GMAT 1: 740 Q51 V38
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The figure above represents a rectangular garden bordered by a walkaway that has a uniform width of 3 feet. What's the perimeter of the garden?
(1) The outer perimeter of the walkaway is 124 feet
(2) The area of the garden is 600 feet.
Let the smaller reactangle be of dimension lxb. We need the value of 2(l+b). The outher rectangle is of the dimension l+6, b+6.
1. 2l + 2b + 24 = 124; l+b =100. Insufficient.
2. lb = 600. Insufficient.
Combining, we have two variables and two equations. Solvable.
Sufficient.
C.
(1) The outer perimeter of the walkaway is 124 feet
(2) The area of the garden is 600 feet.
Let the smaller reactangle be of dimension lxb. We need the value of 2(l+b). The outher rectangle is of the dimension l+6, b+6.
1. 2l + 2b + 24 = 124; l+b =100. Insufficient.
2. lb = 600. Insufficient.
Combining, we have two variables and two equations. Solvable.
Sufficient.
C.
A rectangular garden is bordered by a walkway that has uniform width of 3 feet. What is the perimeter?
Let \(x + 6 \)= walkway width
let \(y + 5\) = walkway length
What is \(x + y\)?
(1) If the outer perimeter is 124 feet, then
\(2(x+y+12) = 124\)
\(x+y+12 = 62\)
\(x+y = 50\)
SUFFICIENT
(2) We can't determine x or y from the area. INSUFFICIENT.
Answer is A.
Let \(x + 6 \)= walkway width
let \(y + 5\) = walkway length
What is \(x + y\)?
(1) If the outer perimeter is 124 feet, then
\(2(x+y+12) = 124\)
\(x+y+12 = 62\)
\(x+y = 50\)
SUFFICIENT
(2) We can't determine x or y from the area. INSUFFICIENT.
Answer is A.
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