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# The perimeter of a rectangular garden is 360 feet. What is

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The perimeter of a rectangular garden is 360 feet. What is [#permalink]

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09 Nov 2010, 13:09
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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.

[Reveal] Spoiler:
I agree that (1) is sufficient, but I don't think (2) is sufficient. (2) can be interpreted as l - w = 60 or w - l = 60. Solving the two equations (one of these two equations and 2w + 2l = 360) will yield different answers for the value of w and l.
[Reveal] Spoiler: OA
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09 Nov 2010, 13:15
niheil wrote:
I think the official answer is wrong. What do you think?

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.

[Reveal] Spoiler:
I agree that (1) is sufficient, but I don't think (2) is sufficient. (2) can be interpreted as l - w = 60 or w - l = 60. Solving the two equations (one of these two equations and 2w + 2l = 360) will yield different answers for the value of w and l.

l - w = 60 is not the same as w - l = 60.

l - w = 60 is the same as w - l = -60
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09 Nov 2010, 13:34
I guess my question is does the phrase, "the difference between the length and width of the garden is 60 feet", only mean that l - w = 60 or can it also be interpreted to mean that w - l = 60?
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09 Nov 2010, 13:47
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I usually assume length is greater than width. But, I guess width can be greater than the length unless stated otherwise. But in GMAT I am pretty sure that statement 1 and 2 can't lead to contradicting answers so l - w = 60 is what needs to be used.

Also the phrase difference between "a" and "b"
usually translates into "a" - "b".

Can someone else confirm this?
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09 Nov 2010, 13:51
chaoswithin, I think that statements (1) and (2) of a Data Sufficiency question could lead to contradicting answers. I've never read anything that led me to believe otherwise.

My question is the same as chaoswithin's. Could someone please confirm?
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09 Nov 2010, 15:10
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The question is slightly badly worded.

Length & width are inter changable terms, there is no reason to believe that length is always greater than width. This is why the question seems to have a bit of ambiguity around it. You will not find such ambiguity on real GMAT questions
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09 Nov 2010, 21:38
Thanks for your input, shrouded1 and chaoswithin. However, this question was in the GMAT Quantitative Review book, which is composed of past GMAT questions.
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11 Nov 2010, 12:43
niheil wrote:
Thanks for your input, shrouded1 and chaoswithin. However, this question was in the GMAT Quantitative Review book, which is composed of past GMAT questions.

A couple of things -
1. Difference between two numbers means absolute value of negation. Difference is always positive. If difference between a and b is 20, we cannot say which one of them is greater.
2. Length need not be greater than Width. Either side can be called the length.

It is rather unfortunate that the said question appears in an Official GMAT book. Official books have retired questions of GMAT. If it was active at some time, it must have been a long time back. The experimental questions and continual monitoring of statistics on correct/incorrect by user ability level get rid of a problem such as that quickly. The purpose of these questions is to separate candidates based on ability level, and if a problem includes an arbitrary definition then the statistical analysis will throw it out – GMAC watches those stats religiously.

Finally, don't worry about the solution of that question. Difference is always absolute value. In case there are different views on that, GMAC will not test you on it.
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14 Nov 2010, 20:20
There's nothing wrong with the wording of the question. The 'length' of a rectangle is the measure of its longest side:

http://mathworld.wolfram.com/Length.html

The length is never smaller than the width.
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15 Nov 2010, 19:53
chaoswithin wrote:
I usually assume length is greater than width. But, I guess width can be greater than the length unless stated otherwise. But in GMAT I am pretty sure that statement 1 and 2 can't lead to contradicting answers so l - w = 60 is what needs to be used.

Also the phrase difference between "a" and "b"
usually translates into "a" - "b".

Can someone else confirm this?

It is wrong to awesome that length is always larger than width. Also for me the wording "the difference between the length and the width" translates to L-W=60. I didn't find the wording to be ambiguous.
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16 Nov 2010, 06:10
the 2nd statement is straight forward for me too... l-b= 60.
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08 Nov 2012, 01:30
gettinit wrote:
chaoswithin wrote:
I usually assume length is greater than width. But, I guess width can be greater than the length unless stated otherwise. But in GMAT I am pretty sure that statement 1 and 2 can't lead to contradicting answers so l - w = 60 is what needs to be used.

Also the phrase difference between "a" and "b"
usually translates into "a" - "b".

Can someone else confirm this?

It is wrong to awesome that length is always larger than width. Also for me the wording "the difference between the length and the width" translates to L-W=60. I didn't find the wording to be ambiguous.

I too got wrong answer on this one because I always use |l - w| to be the difference between length and width. In GMAT, you CANNOT assume anything unless stated. I agree that this question is very badly worded, just like the Q55 in OG Quant Review 2nd edition (machine filled order BY 10:30 - full discussion here on-monday-morning-a-certain-machine-ran-continuously-at-a-57810.html)

Now if you don't see any ambiguity, consider this: this difference between 4 and 6 is 2, and the difference between 6 and 4 is 2 too. So, it's |6 - 4| = |4 - 6| = 2. On the number line, 4 is 2 units away from 6, and 6 is 2 units away from 4.

Therefore this question should be understood that |l - w| = 60. When considering statement 2, I don't (and shouldn't) care about statement 1.
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Re: The perimeter of a rectangular garden is 360 feet. What is [#permalink]

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11 Feb 2016, 07:14
A perimeter can be defined by $$l + l + w + w$$ ---> $$2(l + w)$$
The perimeter of the rectangular garden is 30 feet. Therefore, $$2(l + w) = 360$$

(1) The length of the garden is twice the width.
$$l = 2w$$. ---> $$2(2w + w) = 360$$. Sufficient.

(2) The difference between the length and width of the garden is 60 feet.
$$l - w = 60$$ ---> $$l = 60 + w$$ ---> $$2(60 + w + w) = 360$$. Sufficient

Both statements are sufficient.
Re: The perimeter of a rectangular garden is 360 feet. What is   [#permalink] 11 Feb 2016, 07:14
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