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17 Oct 2008, 09:36
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a square patio surrounded by a walkway of width x meters. If the area of the walkway is 132 square meters and the width of the patio is 5 meters greater than the width of the walkway, what is the area of the patio, in square meters?
A. 56
B. 64
C. 68
D. 81
E. 100
A. 56
B. 64
C. 68
D. 81
E. 100
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06 Dec 2008, 19:15
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I'm pretty sure that this is not an official GMAT question (which I will explain shortly) but here it goes:
Imagine a square (the patio) which is "framed" by a larger square (the walkway).
x is the width of the walkway, so each side of the patio is x+5 meters long.
The outer edges of the walkway will be (x+5)+x+x or simple 3x+5
The area of the larger, outer square MINUS the area of the patio will EQUAL the area of the walkway.
So, our equation is (3x+5)^2 - (x+5)^2 = 132
If we simply this we get 8x^2 + 20x = 132
Set equal to zero to get 8x^2 + 20x - 132 = 0
Divide both sides by 4 to get 2x^2 + 5x - 33 = 0
Here's where I conclude that this is not an official GMAC question. Even though GMAC suggests that students need to know how to solve quadratics where the coefficient of the x^2 is not zero (and the quadratic is neither a square or a difference of squares) I have never seen an official question that tests this skill, and I've looked a lot of GMAT questions. That said, perhaps it is a real GMAT question (750+ level at that), so let's solve this quadratic. It's not that hard to factor.
Factor to get (x-3)(2x+11)=0
We get x=3 or x=some negative number.
Since x must be positive, x must equal 3.
This means the sides of the patio are 8 meters long, which means the area of the patio is 64 square meters.
Imagine a square (the patio) which is "framed" by a larger square (the walkway).
x is the width of the walkway, so each side of the patio is x+5 meters long.
The outer edges of the walkway will be (x+5)+x+x or simple 3x+5
The area of the larger, outer square MINUS the area of the patio will EQUAL the area of the walkway.
So, our equation is (3x+5)^2 - (x+5)^2 = 132
If we simply this we get 8x^2 + 20x = 132
Set equal to zero to get 8x^2 + 20x - 132 = 0
Divide both sides by 4 to get 2x^2 + 5x - 33 = 0
Here's where I conclude that this is not an official GMAC question. Even though GMAC suggests that students need to know how to solve quadratics where the coefficient of the x^2 is not zero (and the quadratic is neither a square or a difference of squares) I have never seen an official question that tests this skill, and I've looked a lot of GMAT questions. That said, perhaps it is a real GMAT question (750+ level at that), so let's solve this quadratic. It's not that hard to factor.
Factor to get (x-3)(2x+11)=0
We get x=3 or x=some negative number.
Since x must be positive, x must equal 3.
This means the sides of the patio are 8 meters long, which means the area of the patio is 64 square meters.
