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A certain highway is to be divided

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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A certain highway is to be divided

by AJWILL » Sat Aug 04, 2012 1:18 pm
A certain highway is to be divided into 3 lanes. For this purpose two yellow stripes are to be painted so that strips divide the highway into 3 lanes. If 3 gallons of paint covers an area of 2P square feet of highway, how many gallons of paint will be needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet, and 1 feet = 12 inches)

[A] 220xm/p

5280xmp/12

[C] 1320mx/p

[D] 440xm/p

[E] 220mp/x


OA C

[spoiler]
Area = (xm5280)/12 * 2 (2 lanes) dont know what to do after this[/spoiler]
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by eagleeye » Sat Aug 04, 2012 1:30 pm
AJWILL wrote:A certain highway is to be divided into 3 lanes. For this purpose two yellow stripes are to be painted so that strips divide the highway into 3 lanes. If 3 gallons of paint covers an area of 2P square feet of highway, how many gallons of paint will be needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet, and 1 feet = 12 inches)

[A] 220xm/p

5280xmp/12

[C] 1320mx/p

[D] 440xm/p

[E] 220mp/x


OA C

[spoiler]
Area = (xm5280)/12 * 2 (2 lanes) dont know what to do after this[/spoiler]


We are told that 2P square feet is covered by 3 gallons. Hence one square foot is covered by 3/(2P) gallons. Let's convert everything to square feet so that we can simply multiply the total area by 3/2P.

Now area = (2 strips)*(m*5280 feet)*(x/12 feet) = mx*2*5280/12
Then paint needed = 3/(2P)* mx*2*5280/12 = mx*5280/(4P) = mx* 1320/P.

C is correct :)
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by truplayer256 » Sun Aug 05, 2012 1:03 pm
Area of each strip = length x width = (stretch of highway) x (width of strip) = (x/12)(5280m) ft^2
Number of gallons of paint needed for each strip = (5280mx/(12*2P)) * 3 = (5280mx)/(8P)
Since there are two strips => (5280mx)/(4P) gallons of paint is needed or 1320mx/P gallons.
Choose C.
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