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

Question

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. \(\frac{5,280*12p}{mt}\)

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}

Bunuel · Accepted Answer

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 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) .

Answer: A.

Hope it's clear.

durgesh79 · Answer

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

Answer A,

30 seconds ... max

greenoak · Answer

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)

jallenmorris · Answer

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}

gettinit · Answer

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.

gettinit · Answer

Thanks Bunuel very clear!

EMPOWERgmatRichC · Answer

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.

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

Divyadisha · Answer

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.

mcelroytutoring · Answer

Attached is a visual that should help.

Abhishek009 · Answer

Visualize the problem - Road.png 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 So, quantity of paint required = 5280 mt/12p Hence answer will be (A)

AkshdeepS · Answer

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}

ScottTargetTestPrep · Answer

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/12p gallons

Answer: A

jmwon · Answer

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

Basshead · Answer

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

Answer is A.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia