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 length of the floor whose width is 2 feet less than the width of the floor. If the area of the carpet is 160 square feet, what is the length, in feet, of the floor?
(A) 8
(B) 16
(C) 20
(D) 24
(E) 32
OA: C
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Length of Floor
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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
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
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bml1105
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Thanks! I keep forgetting to just try and plug in the answers. I keep trying to come up with formulas to make it work and I got stuck at w^2 - w - 80. It was either 16 or 20, and my best guess wasn't right.
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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
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
