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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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Difficulty:

35% (medium)

Question Stats:

74% (02:18) correct
26% (02:09) wrong based on 260 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

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)

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 \(\frac{5280 * t * m}{12p}\) _________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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.

A solid yellow stripe is to be painted in the middle of a [#permalink]
20 Dec 2010, 00:55

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Expert's post

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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 psquare feet. Question: how many gallons of paint will be needed ...

In any case you will have: (total area in square feet)/(gallons per feet)=(total area 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.

Answer: A.

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).

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]
10 Feb 2015, 15:12

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Re: A solid yellow stripe is to be painted in the middle of a [#permalink]
12 Feb 2015, 12:49

Expert's post

Hi All,

I'm a big fan of TESTing VALUES in these types of questions. This question is written in such a way though that you can solve it with just a few math concepts...

There are two "logic shortcuts" to this question that can help you to zero-in on the correct answer.

First, we're dealing with "square feet" of a stripe, which implies the area formula for a rectangle (L x W)….

In this case, we have a length of M MILES, so L = M(5280 feet) We have a width of T INCHES; since we're dealing in SQUARE FEET though, we have to convert inches to feet: W = T/12

So, if we just focus on the area, we'll have 5280(M)(T) / 12. Eliminate B, D and E.

Second, we're told that 1 gallon of paint covers P SQUARE FEET. This is "ratio data", so to calculate the number of gallons…..whichever side of the fraction has the area….the other side has the P. This means that the P must be in the denominator. Eliminate C.

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