Gallons of paint needed

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Mon May 19, 2014 6:36 pm

Hello,

Can you please help with this:

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 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) / (12p)
B. (5,280 pt) / (12m)
C. (5,280 pmt) / 12
D. (5,280)(12m) / (pt)
E. (5,280)(12p) / (mt)

OA: A

Thanks,
Sri

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Source: Beat The GMAT — Problem Solving | Mon May 19, 2014 6:36 pm

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by GMATGuruNY » Mon May 19, 2014 8:19 pm

gmattesttaker2 wrote:Hello,

Can you please help with this:

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 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) / (12p)
B. (5,280 pt) / (12m)
C. (5,280 pmt) / 12
D. (5,280)(12m) / (pt)
E. (5,280)(12p) / (mt)

Let p = 5280 square feet.
Thus, for every 5280 square feet, 1 gallon of paint is needed.

Let t = 12 inches.
Let m = 2 miles.
Since 12 inches = 1 foot, and 2 miles = 10560 feet, the area of the yellow stripe = (1 foot)(10560 feet) = 10560 square feet.
Since an area of 5280 square feet requires 1 gallon of paint, the amount of paint required for 10560 square feet = 2 gallons. This is our target.

Now plug p=5280, t=12, and m=2 into the answers to see which yields our target of 2.
Only A works:
(5,280 mt) / (12p) = (5280*2*12)/(12*5280) = 2.

The correct answer is A.

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by [email protected] » Mon May 19, 2014 9:16 pm

Hi Sri,

I'm a big fan of TESTing VALUES, which is the approach that Mitch used to answer this question. There's another way to solve it though that just requires you to know some 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)
We have a width of T INCHES; since we're dealing in SQUARE FEET, 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

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Thu Jul 24, 2014 11:05 pm

This question at the max should take 30 seconds should you use dimensional analysis thaught in physics ....

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,

here is a cool link to refresh the concept of dimensional analysis in case you require it-

https://www.youtube.com/watch?v=XHZHHgNJt1c

solving maths in a unconventional manner ... and getting inspired by Mitch Hunt !!!

https://graceeducation1613.wordpress.co ... questions/

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Fri Jul 25, 2014 3:05 am

gmattesttaker2 wrote:Hello,

Can you please help with this:

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 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) / (12p)
B. (5,280 pt) / (12m)
C. (5,280 pmt) / 12
D. (5,280)(12m) / (pt)
E. (5,280)(12p) / (mt)

OA: A

Thanks,
Sri

Area to be Painted = Length x Width = (5280m feet) x (t/12 feet) = (5280 mt)/12 square feet

Paint needed for p square feet = 1 gallon
Paint needed for (5280 mt)/12 square feet = (5280 mt)/(12p) gallon

Answer: Option [spoiler]A[/spoiler]

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by Scott@TargetTestPrep » Tue Dec 12, 2017 11:30 am

gmattesttaker2 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 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) / (12p)
B. (5,280 pt) / (12m)
C. (5,280 pmt) / 12
D. (5,280)(12m) / (pt)
E. (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 sqaure feet)/(1 gallon)]

5,280mt/12p gallons

Answer: A

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Founder and CEO
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