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A home owner must pick between paint A, which costs $6.00

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A home owner must pick between paint A, which costs $6.00 [#permalink] New post 17 Aug 2009, 14:08
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A home owner must pick between paint A, which costs $6.00 per liter, and paint B, which costs $4.50 per liter.Paint B takes one third longer to apply than paint A. If the home owner must pay the cost of labor at the rate of $36 per hour, which of the two paints will be cheaper to apply???

1> The ratio of the area covered by one liter of paint A to the area covered by one liter of paint B is 4:3.

2> Paint A will require 40 liters of paint and 100 hours of labor.



Kindly post a detailed and explained solution, and also the approach to crack.

If you like this question, consider for kudos!!!
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Re: Which paint is cheaper to apply [#permalink] New post 17 Aug 2009, 15:22
[quote="gmac25"]A home owner must pick between paint A, which costs $6.00 per liter, and paint B, which costs $4.50 per liter.Paint B takes one third longer to apply than paint A. If the home owner must pay the cost of labor at the rate of $36 per hour, which of the two paints will be cheaper to apply???

1> The ratio of the area covered by one liter of paint A to the area covered by one liter of paint B is 4:3.

2> Paint A will require 40 liters of paint and 100 hours of labor.


a,b is number of liters
6a+36t ..................4.5b+36*4/3t = 4.5b+48t

am not sure if we can assume that the no of liters is directly proportional to the area covered but i am assuming so.

a/b = 4/ 3 ie: 3a = 4b thus 6a = 8b

the equation become 8b+36t as compared to 4.5b+48t.... i d say suff

from b

obviously insuff

i d say A
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Re: Which paint is cheaper to apply [#permalink] New post 17 Aug 2009, 15:34
gmac25 wrote:
A home owner must pick between paint A, which costs $6.00 per liter, and paint B, which costs $4.50 per liter. Paint B takes one third longer to apply than paint A. If the home owner must pay the cost of labor at the rate of $36 per hour, which of the two paints will be cheaper to apply???

1> The ratio of the area covered by one liter of paint A to the area covered by one liter of paint B is 4:3.

2> Paint A will require 40 liters of paint and 100 hours of labor.

Kindly post a detailed and explained solution, and also the approach to crack.
If you like this question, consider for kudos!!!


1. One liter of paint A covers 4x square meter of area, whose cost = 6
One liter of paint B covers 3x square meter of area but to paint 4x square meter of area needs 1.3333 (4x/3x) liters of paint B. The cost of 1.3333 liters of paint B = 1.3333 x (4.5) = 6
Now it is suff since paint B costs more labor cost.

2. Statement 2 tells nothing details about the costs of each paints. NSF>

A is the answer.
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Re: Which paint is cheaper to apply [#permalink] New post 18 Aug 2009, 07:37
Even i marked A as answer, but kaplan math workbook solution suggests E as answer.

I think we cannot assume area covered to be directly proportional to liters of paint.
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Re: Which paint is cheaper to apply [#permalink] New post 23 Apr 2011, 02:07
answer is E

because we cannot say how much time does paint A takes
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Re: Which paint is cheaper to apply [#permalink] New post 23 Apr 2011, 07:34
gmac25 wrote:
A home owner must pick between paint A, which costs $6.00 per liter, and paint B, which costs $4.50 per liter.Paint B takes one third longer to apply than paint A. If the home owner must pay the cost of labor at the rate of $36 per hour, which of the two paints will be cheaper to apply???

1> The ratio of the area covered by one liter of paint A to the area covered by one liter of paint B is 4:3.

2> Paint A will require 40 liters of paint and 100 hours of labor.



Ian / Karishma

Your opinion on this one please? I think the first ratio is enough to answer the question

From statement 1
It is actually the ratio of quantity of paint A used : quantity of paint B used = 3:4

If a = quantity of paint A used
b = quantity of paint B used
t1 = time required to apply paint A
t2 = time required to apply paint B

We are given that t2 = 4/3 or t2 = 1.33t1

and

a = 3/4 b = 0.75 b

The question becomes is 6a + 36 t1 < 4.5b + 36 t2
Or 6 * 0.75b + 36t1 < 4.5b + 36 t2
4.5b + 36t1 < 4.5b + 36t2

or The question becomes - Is t1 < t2 ?
We know that this is true. Sufficient

From statement 2

We don't know the quantity of paint B used. Insufficient.

Answer A
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Re: Which paint is cheaper to apply [#permalink] New post 23 Apr 2011, 10:52
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gmat1220 wrote:
Ian / Karishma

Your opinion on this one please?


First, I think it's a ridiculous question, because most people would (very reasonably) assume that one liter of paint A covers the same area as one liter of paint B. According to Statement 1, that's not the case. Second, with Statement 1 alone, we can answer the question: if we need 4 liters of paint B to cover the same area as 3 liters of paint A, then it will cost 4(4.50) = 18 dollars to cover that area with paint B, and 3(6) = 18 dollars to cover that area with paint A. So the paint costs are the same; the total cost will only be different because of labor costs. Since paint B takes longer to apply, paint B will cost more to apply, and Statement 1 is sufficient.

I have no idea how they can give E as an answer here, since if you use both Statements, you can work out exactly how many liters of each paint you'd need and how many hours each paint would take to apply.
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Re: Which paint is cheaper to apply [#permalink] New post 23 Apr 2011, 11:05
Thanks Ian. That was quick :-D +1
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Re: A home owner must pick between paint A, which costs $6.00 [#permalink] New post 08 Jan 2012, 06:00
Lets evaluate statement 2:

PAINT A

Cost of paint A ---> 40*6=240

Cost of painter A --->100*36=3600

Total cost A ---> 240+3600=3840

PAINT B

Since 100 hours of labor must be used for paint A, and paint B takes 1/3 longer to apply ---> 100*4/3=400/3 hours to apply.

cost of painter B---->(400/3)*36=12*400=4800

Since (Total cost A) < (cost of painter B) ---> (Total cost A) < (Total cost B)

Therefore, despite the fact that we can't estimate how much we would have to pay for paint B, we can see statement 2 is sufficient.

Therefore the correct answer is D.
Re: A home owner must pick between paint A, which costs $6.00   [#permalink] 08 Jan 2012, 06:00
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