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# The length of a rectangular floor is twice its width. The

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The length of a rectangular floor is twice its width. The [#permalink]

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02 Nov 2013, 14:09
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The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor?

A. 8
B. 16
C. 20
D. 24
E. 32

Got this wrong on a practice test and think I've come up with the correct answer, but cant check it since the damn software erased my test; throwing it up here on the forum, hoping someone on here can confirm or disprove what I came up with on the second shot...
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Nov 2013, 11:51, edited 1 time in total.
Edited the question and added the OA
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The length of a rectangular floor is twice its width. The [#permalink]

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02 Nov 2013, 16:02
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Jem2905 wrote:
The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor?

a) 8

b) 16

c) 20

d) 24

e) 32

Should be C

Dimensions of Rectangular floor
Width = w
Length = 2w

Dimensions of Carpet
Width = w-2
Length = 2w
Area = 160 sq.ft.

Area = 160 = 2w(w-2) ---------> $$160 = 2w^2 - 4w$$ ---------> $$2w^2 - 4w - 160 = 0$$ ---------> $$w^2 - 2w - 80 = 0$$ --------> $$(w-10)(w+8)=0$$

So, w=10 Hence L=20
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Re: The length of a rectangular floor is twice its width. The [#permalink]

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19 Jan 2015, 14:51
Ah nice this is much quicker than my method. I did it like this:

L=2w area = L*w

area is here 160 = L*w but because the carpet is 2 feet less w = w-2
160=
w-2 * 2w this can be:
1 * 160 or
2 * 80 or
4 * 40 or
5 * 32 or
8 * 20 or
10 * 16

Now you see that 8 * 20 is the only option. But it takes much more time..
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Re: The length of a rectangular floor is twice its width. The [#permalink]

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19 Jan 2015, 14:53
Ah nice this is much quicker than my method. I did it like this:

L=2w area = L*w

area is here 160 = L*w but because the carpet is 2 feet less w = w-2
160=
w-2 * 2w this can be:
1 * 160 or
2 * 80 or
4 * 40 or
5 * 32 or
8 * 20 or
10 * 16

Now you see that 8 * 20 is the only option.
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Re: The length of a rectangular floor is twice its width. The [#permalink]

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19 Jan 2015, 19:54
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Expert's post
Hi All,

This question can obviously be solved with a bit of Algebra and Geometry. You can also take those basic ideas, along with the answer choices (which are numbers) and TEST THE ANSWERS....

We're given a lot of information about a floor and a carpet on top of it:

1) The Floor's length is TWICE it's width.
2) The Carpet has the SAME length as the floor, but it's width is 2 feet less than the width of the floor
3) The area of the carpet is 160 ft^2.

We're asked to find the length of the floor (which is the same as the length of the carpet).

Since the area of the carpet is a "round number", it's likely that it's dimensions are probably round numbers.

Area of carpet is 160
If length = 16, then width = 10
Since the carpet width is 2 less than the floor width, the dimensions of the floor would be...
Length = 16, width = 12.
This does NOT match (the length is supposed to be TWICE the width. Eliminate B (and A, since a length of 8 would be way too small).

Area of carpet is 160
If length = 20, then width = 8
Since the carpet width is 2 less than the floor width....
Length = 20, width = 10.
This DOES match (the length IS TWICE the width), so this MUST be the answer.

[Reveal] Spoiler:
C

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Re: The length of a rectangular floor is twice its width. The [#permalink]

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29 Oct 2015, 03:39
Straight algebra

L=2w
L(w-2)=160
Lw -2l =160
L^2/2 -2l =160 => l^2 -4l -320=0 . so l=20 or -16. Ans :C
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Re: The length of a rectangular floor is twice its width. The [#permalink]

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21 Nov 2015, 18:25
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I'm terrible at GMAT math so I always look for shortcuts...

Floor Area = 2w^2
Carpet Area = 160 which is slightly less than the floor.

So to guesstimate 2w^2=160..... w^2=80......w = around 9 ...
Length is a little bigger than 2*9....... 20 is closest answer.
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Re: The length of a rectangular floor is twice its width. The [#permalink]

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06 Jan 2017, 13:23
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Re: The length of a rectangular floor is twice its width. The [#permalink]

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20 Jan 2017, 08:46
Complete Rectangular floor
Width(W) = 10, Length = 2W
Carpet :
Width = W-2
same Length = 2W
A = 160 = 2W (W-2)
80 = W^2 - 2W
w^2 - 2W - 80 = 0
W = 10
Length = 2w = 20
C
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Re: The length of a rectangular floor is twice its width. The [#permalink]

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20 Jan 2017, 11:33
Jem2905 wrote:
The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor?

A. 8
B. 16
C. 20
D. 24
E. 32

Floor :

Length = $$2w$$
Width = $$w$$

Area = $$2w^2$$

Carpet :

Length = $$2w$$
Width = $$w-2$$

Area = $$2w^2 - 4w$$

Quote:
If the area of the carpet is 160 sq. feet

$$2w ( w - 2 ) = 160$$

Or, $$w(w-2) = 80$$

So, $$w = 10$$

So, Length of the floor is $$2w = 20$$

Hence the length of floor is 20 , correct answer must be (C) 20
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Re: The length of a rectangular floor is twice its width. The   [#permalink] 20 Jan 2017, 11:33
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