A rectangular floor

[didieravoaka]

Thanks to help.

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Hi didieravoaka,

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

[MartyMurray]

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 and 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

Another way to do this one is to translate the information given in the question and solve.

Floor Length - L
Floor Width - W

L = 2W

Carpet Length = L
Carpet Width = W - 2

Carpet Area = 160 = L x (W - 2) = 2W x (W - 2)

160 = 2W² - 4W
80 = W² - 2W

Factor

W² - 2W - 80 = 0
(W - 10)(W + 8) = 0

W = 10 or -8 A width cannot be negative. So W = 10

L = 2W = 20

The correct answer is C.

[didieravoaka]

Thanks Rich and Marty!

Marty,

Actually I tried to solve by using your method but got stuck with the quadratic equation.

I got W2-2W+80=0, then (W-40)(W+2)=0. This is where I got stuck. instead I should have (W-10)(W+8). This is how I lose many points sometimes. And when I look at corrections, I see that I was on the right path and got confused while solving.

I feel like I struggle with factorization though.

[MartyMurray]

I feel like I struggle with factorization though.

From what you said it looks as if you need to see the logic of the math more.

If the W coefficient is -2, then logically the difference in the absolute value of the factors of -80 has to be 2. So they can't be 2 and -40. They have to be 8 and -10.

Keep that in mind and practice a little more, if you have any time.

In general, being more logic driven will serve you well.

[[email protected]]

Hi didieravoaka,

If you find that using approaches to Quant questions that involve 'technical' steps lead you to make mistakes, then you might want to look to other approaches. On a fundamental level, between the two approaches that I used and Marty used, which one is technically 'easier'? It might be that you're trying to deal with the Quant section with too much 'math' and not enough Tactics.

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