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

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

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...

There is a simpler solution-
Let Table area = l*2l --- (where l=width and 2l=length) ---- (1)
Therefore Cloth area = (l-2)*2l ------(2)
So all we need is the value of 2l .

From the given information in (2) , we get (l-2)*2l = 160
Simplifying we get (l-2)*l =80
From the above eq. we can easily workout (l-2)*l = 8*10
This give l=10 .
Now all we need is 2l= 20 .
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Re: The length of a rectangular floor is twice its width. The [#permalink]
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Re: The length of a rectangular floor is twice its width. The [#permalink]
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