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

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Q49  V42
Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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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 is to be painted in the middle of a certain high [#permalink]
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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 is to be painted in the middle of a certain high [#permalink]
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 is to be painted in the middle of a certain high [#permalink]
Thanks Bunuel very clear!
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Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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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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Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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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.

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Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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Attached is a visual that should help.
Attachments

Screen Shot 2016-06-03 at 10.09.50 AM.png [ 185.09 KiB | Viewed 51914 times ]

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Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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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 51522 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

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Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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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. $$\frac{5,280 mt}{12 p}$$

B. $$\frac{5,280 pt}{12m}$$

C. $$\frac{5,280pmt}{12}$$

D. $$\frac{5,280*12m}{pt}$$

E. $$\frac{5,280*12p}{mt}$$

We need to find the number of gallons to paint the strip, so start by what is given :

p sq. ft = 1 gallon

1 sq. ft = 1/p gallon

x sq. ft = x/p gallons ---- (where "x" is the area we want to paint) ------- (I)

From this we can eliminate all options that have p in the numerator as it can save time.

Now we just need to find the value of "x".

As we have a rectangular section, area would be "L x B"

Solve for length :

L = "m" miles (we need the length in feet)

1 mile = 5,280 feet

"m" miles = 5280 * m feet ----- (II)

Solve for width :

W = "t" inches (we need the width in feet)

1 foot = 12 inches

1 inch = 1/12 feet

"t" inches = t/12 feet ----- (III)

Therefore, (I) = (II) * (III)

x sq. ft = x/p gallons

=$$\frac{5280 *m*t}{12*p}$$
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Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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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. $$\frac{5,280 mt}{12 p}$$

B. $$\frac{5,280 pt}{12m}$$

C. $$\frac{5,280pmt}{12}$$

D. $$\frac{5,280*12m}{pt}$$

E. $$\frac{5,280*12p}{mt}$$

We are given that 1 gallon of paint covers p square feet of highway. Thus, thus the “coverage rate” is:

(p square feet)/(1 gallon)

We need to determine how many gallons are needed to cover a total area of:

(t inches)(m miles)

Converting inches to feet and miles to feet, we have:

(t/12 feet)(5,280m feet) = 5,280mt/12 square feet

Now we can determine how many gallons we need to cover the particular stretch of highway:

gallons needed = area/rate

[5,280mt/12 square feet]/[(p square feet)/(1 gallon)]

5,280mt/12p gallons

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Re: A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
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This question seems really confusing with all of the different variables, and furthermore I realized what makes this problem even trickier than other conversion problems. The gallons of paint is given in SQUARE feet aka $$ft^{2}$$, which means we should be applying geometrical formula AND unit conversions to the stripe measurements.

Our unit of measurement for gallons of paint is $$\frac{1 gal}{p ft^{2}}$$

Let's find the area of the stripe of t inches by m miles by (1) converting each to the same unit of inches, and then (2) multiplying them together to get the area of the stripe.

(1) convert to inches
t in* $$\frac{1 ft}{12 in}$$
$$= \frac{t}{12}$$ft
m mi * $$\frac{5,280 ft}{1 mi}$$
$$= m * 5,280$$ft

(2) multiply together to get area
$$\frac{t}{12} ft * m * 5,280$$ft
$$= \frac{5,280 mt ft^{2}}{12}$$

Finally multiply the area by gallons of paint rate.
$$\frac{1 gal}{p ft^{2}} * \frac{5,280 mt ft^{2}}{12}$$
$$= \frac{5,280 mt}{12p}$$gal

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. $$\frac{5,280 mt}{12 p}$$

B. $$\frac{5,280 pt}{12m}$$

C. $$\frac{5,280pmt}{12}$$

D. $$\frac{5,280*12m}{pt}$$

E. $$\frac{5,280*12p}{mt}$$
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A solid yellow stripe is to be painted in the middle of a certain high [#permalink]
Lets take it one step at a time by converting all the measurements to feet:

m miles = $$5,280m$$ ft

$$t inches = \frac{t}{12} ft$$

You can think of the yellow stripe as a very long rectangle.

Now we multiply the length and the width of the rectangle:

$$\frac{5,200 * m * t }{ 12}$$

So now we have the area of the rectangle; we simply need to divide by p (1 gallon of paint covers an area of p square feet):

$$\frac{5,200 * m * t }{ 12p}$$ = number of gallons required

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