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

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

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.

Let's TEST Answer B:

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).

Let's TEST Answer C:

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.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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 .
Hence answer = C

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.

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

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..

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.

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

Floor :

Length = \(2w\)
Width = \(w\)

Area = \(2w^2\)


Carpet :

Length = \(2w\)
Width = \(w-2\)

Area = \(2w^2 - 4w\)




\(2w ( w - 2 ) = 160\)

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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