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by [email protected] » Thu Mar 10, 2016 4:40 pm
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

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by MartyMurray » Thu Mar 10, 2016 11:17 pm
didieravoaka 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 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.
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by didieravoaka » Mon Mar 14, 2016 7:51 pm
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.
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by MartyMurray » Mon Mar 14, 2016 8:36 pm
didieravoaka wrote: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.
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by [email protected] » Mon Mar 14, 2016 9:35 pm
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.

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