Length of Floor

Hi bml1105,

There are a couple of different ways to go about answering this question. Beyond the algebraic approach, here's how you can solve by TESTing THE ANSWERS:

We're told a few facts:

1) The floor's length is twice it's width. So, L = 2W

2) A carpet on this floor as the same length as the floor, but it's width is 2 feet LESS.

3) The area of the carpet is 160 sq. ft.

We're asked for the LENGTH of the FLOOR.

Let's TEST THE ANSWERS by starting with B.

If L = 16, then the dimensions of the carpet would be 16 x 10.
We're told that the width of the carpet is 2 feet LESS than width of the floor, so the floor would be… 16 x 12.
However, this DOES NOT match (we're told the length is TWICE the width). This means that the length is not "long enough"
Eliminate B and A.

If L = 20, then the dimensions of the carpet would be 20 x 8
This would made the dimensions of the floor….20 x 10
This is a MATCH (since the length is TWICE the width).

Final Answer: C

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

Hi bml1105,

There's nothing inherently wrong with tackling this question with algebra. The math can get "thick" though; the more math that needs to be done, the greater the chance that a silly mistake can occur. If I'm given a choice between a long math approach or a shorter tactical approach, then I tend to go with the shorter/easier option.

Here's the algebra approach.

We're told the floor's length is twice its width.

L = 2W

Area of floor = LW = (2W)W = 2(W^2)

We're told the carpet's length matches the length of the floor, but its width is 2 feet LESS.

Length = 2W
Width= (W-2)

Area of carpet = 2W(W-2) = 2(W^2) - 4W

We're also told that the area of the carpet is 160

2(W^2) - 4W = 160

Divide each term by 2 and move the 160 "to the left"

W^2 - 2W - 80 = 0

This can be factored into:

(W-10)(W+8) = 0

W = 10 or -8

Since we're dealing with geometry, there's no such thing as a "negative side length", so W MUST = 10. The length of the floor is TWICE its width, so L = 2(10) = 20

Final Answer: C

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