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
Gallons of paint needed
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Let p = 5280 square feet.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)
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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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 !!!
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 !!!
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Area to be Painted = Length x Width = (5280m feet) x (t/12 feet) = (5280 mt)/12 square feetgmattesttaker2 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
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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We are given that 1 gallon of paint covers p square feet of highway. Thus, thus the "coverage rate" is: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)
(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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