Length of Floor

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bml1105: Master | Next Rank: 500 Posts; Posts: 113; Joined: Sun Nov 24, 2013 9:19 pm; Thanked: 1 times; Followed by:5 members

Length of Floor

by bml1105 » Tue Jun 03, 2014 2:31 pm

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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Source: Beat The GMAT — Problem Solving | Tue Jun 03, 2014 2:31 pm

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Tue Jun 03, 2014 3:14 pm

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

Contact Rich at [email protected]

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bml1105: Master | Next Rank: 500 Posts; Posts: 113; Joined: Sun Nov 24, 2013 9:19 pm; Thanked: 1 times; Followed by:5 members

by bml1105 » Tue Jun 03, 2014 3:56 pm

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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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Tue Jun 03, 2014 5:41 pm

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

Contact Rich at [email protected]