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# A solid yellow stripe is to be painted in the middle of a

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A solid yellow stripe is to be painted in the middle of a [#permalink]  12 Jul 2008, 08:04
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76% (02:10) correct 24% (02:11) wrong based on 98 sessions
A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of p square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)

A. (5,280 mt) / 12 p
B. (5,280 pt) / 12m
C. (5,280 pmt) /12
D. (5,280)(12m) / pt
E. (5,280)(12p) / mt
[Reveal] Spoiler: OA

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Re: A solid yellow stripe [#permalink]  12 Jul 2008, 10:50
Quote:
A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of p square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1mile = 5,280 feet and 1 foot = 12 inches)

Let’s translate all measure units to feet and calculate the area of the stripe:

Area = (m*5280)*(t/12) square feet. Now, all we need is to divide this by p – this will give us the number of gallons:

N of gallons = 5280*mt/12p. This is A.

(I wonder why they didn’t ask us to divide 5280 by 12… The result is 440, an integer)
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Re: A solid yellow stripe [#permalink]  12 Jul 2008, 11:04
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POE

unit of m = distance
unit of t = distance
unit of p = area = distance X distance

we are looking for an answer in gallon ... so all units of distance should cancel each other ...
eliminate B, C, D, .. between A and E

p sq feet ------------- 1 gallon
xyz sq feet ----------- xyx/p gallon ---> p should come in denominator

30 seconds ... max
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Re: A solid yellow stripe [#permalink]  12 Jul 2008, 11:12
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one thing i've noticed about algebra and problem solving on the GMAT is that when you have a problem that appears to require a lot of multiplication of large numbers, it's best to just keep those number un-multiplied and then set up the equation. It also helps to take a look at the answer choices and get a feel for what format the answers are in. If you did the multiplication and did 5280 * 12, and then divided by 144, or whatever, you'd have the correct answer, but you would have a hard time identifying it in the answer choices.

You'd come up with \frac{440tm}{p}

Like here

t = how many feet wide the stripe is. 5280 = feet long in 1 mile, m = length of the yellow stripe in 1 mile

so 5280 * 12 = number of inches in a mile.

5280 * 12 * t = number of square inches per mile of yellow stripe.

5280 * 12 * t * m = total number of squre inches we need to cover...but the coverage is in square feet p so 144 * p = number of inches per square foot the paint will cover.

\frac{5280 * 12 * t * m}{144p}
becomes
\frac{5280 * t * m}{12p}
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Re: A solid yellow stripe [#permalink]  19 Dec 2010, 16:02
Can you please describe how to attack this problem? I just stuck to the p's, m's and t's and did a quick calculation on where they end up, but the p square feet is throwing me off. How does this compare to the inch wide yellow line? thanks.
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Re: A solid yellow stripe [#permalink]  20 Dec 2010, 00:55
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gettinit wrote:
Can you please describe how to attack this problem? I just stuck to the p's, m's and t's and did a quick calculation on where they end up, but the p square feet is throwing me off. How does this compare to the inch wide yellow line? thanks.

A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of p square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1mile = 5,280 feet and 1 foot = 12 inches)
A. (5,280 mt) / 12 p
B. (5,280 pt) / 12m
C. (5,280 pmt) /12
D. (5,280)(12m) / pt
E. (5,280)(12p) / mt

Given that: 1 gallon of paint covers an area of p square feet. Question: how many gallons of paint will be needed ...

In any case you will have: (total are in square feet)/(gallons per feet)=(total are in square feet)/p, so p must be in the denominator: eliminate all but A and D.

Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=t inches as 1 feet=12 inches then t inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.

Direct way: (total are in square feet)/(gallons per feet)=(total are in square feet)/p=?

(area in square feet)=(width in feet)*(length in feet)=(t/12)*(5,280m) --> (total are in square feet)/p=(5,280mt)/(12p).

Hope it's clear.
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Re: A solid yellow stripe [#permalink]  23 Dec 2010, 18:19
Thanks Bunuel very clear!
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Re: A solid yellow stripe is to be painted in the middle of a [#permalink]  05 Nov 2013, 13:16
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Re: A solid yellow stripe is to be painted in the middle of a   [#permalink] 05 Nov 2013, 13:16
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