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

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12 Jul 2008, 08:04

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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

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)

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$$.

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.

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]

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05 Nov 2013, 13:16

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A solid yellow stripe is to be painted in the middle of a [#permalink]

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10 Feb 2015, 15:12

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

Re: A solid yellow stripe is to be painted in the middle of a [#permalink]

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21 May 2016, 20:44

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A solid yellow stripe is to be painted in the middle of a [#permalink]

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22 May 2016, 10:26

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TheBigCheese wrote:

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

area of the strip = m miles *t inches 5280m * t/12 square feet 1 gallon is required to paint p square feet, then 5280 mt/12p is required to paint the whole stretch.

A should be the answer.
_________________

I welcome critical analysis of my post!! That will help me reach 700+

Re: A solid yellow stripe is to be painted in the middle of a [#permalink]

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03 Jun 2016, 10:14

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TheBigCheese wrote:

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

Visualize the problem -

Attachment:

Road.png [ 1.66 KiB | Viewed 4153 times ]

Notice you have three denominations -

(A) 1 gallon of paint covers an area of p square feet of highway (B) A stripe of t inches wide (C) The stretch of highway m miles long

Given 1 Mile = 5,280 feet ;

So, Length of m miles = 5280m feet And , Breadth of t inches = t/12 feet

Area = 5280 mt/12 sq Feet

Quote:

1 gallon of paint covers an area of p square feet of highway

So, quantity of paint required = 5280 mt/12p

Hence answer will be (A) _________________

Thanks and Regards

Abhishek....

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