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Math Expert V
Joined: 02 Sep 2009
Posts: 58311
The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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Difficulty:   5% (low)

Question Stats: 88% (00:47) correct 12% (01:00) wrong based on 487 sessions

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The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

(1) The length of the garden is twice the width.
(2) The difference between the length and width of the garden is 60 feet.

Data Sufficiency
Question: 60
Category: Geometry; Algebra Perimeter; Simultaneous Equations
Page: 157
Difficulty: 600

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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Math Expert V
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Posts: 58311
Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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SOLUTION

The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

The perimeter of a rectangular garden is 360 feet: 2(L + W) = 360.

(1) The length of the garden is twice the width. L = 2W. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

(2) The difference between the length and width of the garden is 60 feet. L - W = 60. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

(1) The length of the garden is twice the width.
(2) The difference between the length and width of the garden is 60 feet.

If Length = L and Breadth = B
Then 2(L + B) = 360
=> L+B = 180

Statement 1) L = 2B
Substituting in the above equation, 3B = 180. I can determine B and subsequently A. Hence Sufficient.

Statement 2) L-B = 60
Solving with the premise equation, we can determine the length. Hence Sufficient.

Hence Option D)
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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1
Perimeter=2(l+b)=360
l+b=180 (1)
From S1:l=2b=>Replacing b in (1),we can calculate length of rect.Sufficient

From S2:l-b=60.We get 2 equations which can be solved ot get length.
This is also sufficient.

Ans.D
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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1
Let l be the length and w be the width.
From the question stem, we derive the foll equation: 2l+2w=360

Going to the statements:
(1) from this statement, we can deduce that l=2w. by substitution, we can solve the equation for l and w above (statement 1 is sufficient)
(2) from this statement, we can deduce the foll equation, l-w=60. by substitution, we can solve the equation in the question stem. (statement 2 is sufficient)

Answer is therefore D
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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2
Let the rectancle sides be X (the short one) and Y (the longer one).

After reading the information we can say that 2X+2Y = 360. Hence we already have one equation and we only need another one to solve the problem.

1) Y = 2X We have enough equations to solve the system and find the incognites.

2) Y-X = 60 We have enough equations to solve the system and find the incognites.

Hence answer is C.
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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1
Bunuel wrote:
SOLUTION

The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

The perimeter of a rectangular garden is 360 feet: 2(L + W) = 360.

(1) The length of the garden is twice the width. L = 2W. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

(2) The difference between the length and width of the garden is 60 feet. L - W = 60. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

Hi Bunuel,

I have a query.

According to me the answer should be A. given below is my reasoning.

Statement 1 is sufficient there is no doubt in that.

In statement 2, its given that difference between length and width is 60 feet.

Which means : |L-W| = 60. (Thats where my query is. Why we are assuming that length is greater that width)

So statement 2 is insufficient , hence my answer A.

Please let me know where did i go wrong.

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 58311
Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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1
prabhakarsharma wrote:
Bunuel wrote:
SOLUTION

The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

The perimeter of a rectangular garden is 360 feet: 2(L + W) = 360.

(1) The length of the garden is twice the width. L = 2W. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

(2) The difference between the length and width of the garden is 60 feet. L - W = 60. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

Hi Bunuel,

I have a query.

According to me the answer should be A. given below is my reasoning.

Statement 1 is sufficient there is no doubt in that.

In statement 2, its given that difference between length and width is 60 feet.

Which means : |L-W| = 60. (Thats where my query is. Why we are assuming that length is greater that width)

So statement 2 is insufficient , hence my answer A.

Please let me know where did i go wrong.

Thanks

The point is that the length of a rectangle is the measure of its longest side. So, the length is never smaller than the width.
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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Bunuel wrote:
prabhakarsharma wrote:
Bunuel wrote:
SOLUTION

The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

The perimeter of a rectangular garden is 360 feet: 2(L + W) = 360.

(1) The length of the garden is twice the width. L = 2W. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

(2) The difference between the length and width of the garden is 60 feet. L - W = 60. We have two distinct linear equations with two unknowns. We can solve for both. Sufficient.

Hi Bunuel,

I have a query.

According to me the answer should be A. given below is my reasoning.

Statement 1 is sufficient there is no doubt in that.

In statement 2, its given that difference between length and width is 60 feet.

Which means : |L-W| = 60. (Thats where my query is. Why we are assuming that length is greater that width)

So statement 2 is insufficient , hence my answer A.

Please let me know where did i go wrong.

Thanks

The point is that the length of a rectangle is the measure of its longest side. So, the length is never smaller than the width.

Thanks B,

but can you please let me know your reference for this assumption.

AFAIK no such property is associated with rectangle. I have also not seen any mention of such property in any of my reference books.

Thanks again.
Math Expert V
Joined: 02 Sep 2009
Posts: 58311
Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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prabhakarsharma wrote:
Bunuel wrote:
prabhakarsharma wrote:

Hi Bunuel,

I have a query.

According to me the answer should be A. given below is my reasoning.

Statement 1 is sufficient there is no doubt in that.

In statement 2, its given that difference between length and width is 60 feet.

Which means : |L-W| = 60. (Thats where my query is. Why we are assuming that length is greater that width)

So statement 2 is insufficient , hence my answer A.

Please let me know where did i go wrong.

Thanks

The point is that the length of a rectangle is the measure of its longest side. So, the length is never smaller than the width.

Thanks B,

but can you please let me know your reference for this assumption.

AFAIK no such property is associated with rectangle. I have also not seen any mention of such property in any of my reference books.

Thanks again.

Check here: http://mathworld.wolfram.com/Length.html
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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I'm contesting the answer given by the Official Guide to GMAT Quantitative Review 2015, specifically, #60 (pg. 157) in the Data Sufficiency section. For those of you who do not have this book, here is the question:

60. The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

(1) The length of the garden is twice the width.

(2) The difference between the length and width of the garden is 60 feet.

Easy enough of a question, right?

The book says that both (1) and (2) is sufficient, so the multiple choice answer is D, but I argue that only (1) is sufficient so the answer should be A.

I know exactly how to get the answer for both 1 and 2, but 2 is ambiguous. The difference between the length and width of the garden isn't necessarily saying l - w = 60 feet. If the width of the garden is longer, colloquially speaking, you can still state that the difference between the length and width is 60 feet - you wouldn't say the difference is negative 60 feet. So, you wouldn't actually know if the length is longer than the width.

Is there a GMAT rule where you literally translate the order of a sentence into its math sequence, always?

Math Expert V
Joined: 02 Sep 2009
Posts: 58311
Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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iPen wrote:
I'm contesting the answer given by the Official Guide to GMAT Quantitative Review 2015, specifically, #60 (pg. 157) in the Data Sufficiency section. For those of you who do not have this book, here is the question:

60. The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

(1) The length of the garden is twice the width.

(2) The difference between the length and width of the garden is 60 feet.

Easy enough of a question, right?

The book says that both (1) and (2) is sufficient, so the multiple choice answer is D, but I argue that only (1) is sufficient so the answer should be A.

I know exactly how to get the answer for both 1 and 2, but 2 is ambiguous. The difference between the length and width of the garden isn't necessarily saying l - w = 60 feet. If the width of the garden is longer, colloquially speaking, you can still state that the difference between the length and width is 60 feet - you wouldn't say the difference is negative 60 feet. So, you wouldn't actually know if the length is longer than the width.

Is there a GMAT rule where you literally translate the order of a sentence into its math sequence, always?

Check here: the-perimeter-of-a-rectangular-garden-is-360-feet-what-is-t-166669.html#p1405337
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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I can understand the convention of taking the length to be longer than a width for non-square rectangles. However, one example I found on the 'net...

If you were to buy a blind for a window, the length of the blind would correspond to the drop from top to bottom of the window, and the width of the blind would correspond to the distance from side to side. If the window was a short, wide window the width of the blind would be longer than its length!

With that example above, you shouldn't order a blind where it's wider than it is tall, and expect the blind supplier to send you a wide blind without specifying the dimensions further (e.g. using height instead, but the point still remains). The supplier will probably send you a tall, skinny blind to go with your wide, short window.

Conversely, if someone said that the difference between the width and the length is 60 feet, would you assume w - l = 60, or that the absolute value is 60?
Anyway, for all intents and purposes, the GMAT seems to accept the definition that length is greater than width for all non-square rectangles, so I'll stick to that.
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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iPen wrote:
I'm contesting the answer given by the Official Guide to GMAT Quantitative Review 2015, specifically, #60 (pg. 157) in the Data Sufficiency section. For those of you who do not have this book, here is the question:

60. The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

(1) The length of the garden is twice the width.

(2) The difference between the length and width of the garden is 60 feet.

Easy enough of a question, right?

The book says that both (1) and (2) is sufficient, so the multiple choice answer is D, but I argue that only (1) is sufficient so the answer should be A.

I know exactly how to get the answer for both 1 and 2, but 2 is ambiguous. The difference between the length and width of the garden isn't necessarily saying l - w = 60 feet. If the width of the garden is longer, colloquially speaking, you can still state that the difference between the length and width is 60 feet - you wouldn't say the difference is negative 60 feet. So, you wouldn't actually know if the length is longer than the width.

Is there a GMAT rule where you literally translate the order of a sentence into its math sequence, always?

per merriam webster: length: the longer or longest dimension of an object So technically L>W and thus statement 2 is sufficient. Also, note that GMAT is GMAC's playground and so you will have to play by their rules!

http://www.merriam-webster.com/dictionary/length
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Re: The perimeter of a rectangular garden is 360 feet. What is the length  [#permalink]

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niheil wrote:
The perimeter of a rectangular garden is 360 feet. What is the length of the garden?

(1) The length of the garden is twice the width.
(2) The difference between the length and width of the garden is 60 feet.

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.

Let l and w be the length and the width of the rectangular garden, respectively.
From the original condition of the question, we have $$2(l+w) = 360$$ or $$l + w = 180$$.
There are 2 variables and 1 equation. Thus D is the answer most likely.

Condition 1) $$l = 2w$$
$$l + w = 2w + w = 3w = 180$$ or $$w = 60$$.
Thus $$l = 120$$.
It is sufficient.

Condition 2) $$l - w = 60$$, since the length is the longest side of a rectangle.
When we add two equations, $$l + w = 180$$ and $$l - w = 60$$, we have $$2l = 240$$ or $$l = 120$$.
It is sufficient.

Therefore the answer is D.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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