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Wrong OA?

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Wrong OA?

by pakaskwa » Thu Mar 05, 2009 7:35 pm
A home owner must pick between paint A, which costs $6 per liter, and paint B, which costs $4.5 per liter. Paint B takes 1/3 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 o9ne liter of paint B is 4:3;
2) Paint A will require 40 liters of paint and 100 hours of labor.

OA answer is E, but my answer is C. I don't understand. Someone help me please?

By the way, the question comes from Kaplan GMAT Math Workbook, 6th edition, page 324.
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by rseeker2 » Sun Mar 08, 2009 2:11 am
I'm getting it as D....

This is how I have approached...

A B

Cost 6$/l 4.5$/l

Let paint A take 'h' hours --> B takes h + h/3 = 4h/3 hours.

So now the table stands as

A B

Cost 6$/l 4.5$/l

Time h hrs 4h/3 hrs


Cost of labor -- 36$/hr

Total cost to the owner = Cost of paint + Cost of labor

----------------------------------------------------------------------

1) Say, the area covered by one liter of paint A is '4x' --> the area covered by one liter of paint B is '3x'.

Let the total area to be painted be 'y'

'4x' area is covered by one liter of A. Therefore 'y' area is covered by 'y/4x' liters of paint A

So the cost to the owner in case of A would be --> 6*y/4x(cost of paint) + 36*h(cost of labor) = 1.5y/x + 36h

---

'3x' area is covered by one liter of B. Therefore 'y' area is covered by 'y/3x' liters of paint B

So the cost to the owner in case of B would be --> 4.5*y/3x(cost of paint) + 36*4h/3(cost of labor) = 1.5y/x + 48h


Cost if A is used -- 1.5y/x + 36h
Cost if B is used -- 1.5y/x + 48h

Clearly, A is cheaper. Therefore the owner must pick paint A.
Hence 1 is sufficient.


2)
A B

Cost 6$/l 4.5$/l

Time h hrs 4h/3 hrs


Cost of labor -- 36$/hr

Total cost to the owner = Cost of paint + Cost of labor


Now, Paint A will require 40 liters of paint and 100 hours of labor.
If Paint A requires 100 hours of labor i.e. h, paint B would require 4h/3 i.e., 4(100)/3 hours

--> Cost to the owner in case of A = 40*6(cost of paint) + 36*100(cost of labor) = 240 + 3600 = $3840


Say paint B requires 'b' liters of paint

--> Cost to the owner in case of B = b*4.5(cost of paint) + 36*400/3(cost of labor) = 4.5b + 4800, which is always greater than $3840 (of paint A).

Hence the owner should choose paint A. Hence 2 alone is sufficient.


Since each of the statements alone is sufficient, I would say D.

Please let me know if I am wrong somewhere.
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Re: Wrong OA?

by Vemuri » Sun Mar 08, 2009 3:38 am
Interesting, I would want to see an explanation on why E is the answer. I too thought C was the answer. But, I am sure I did not get into the details.
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by moadhia » Sun Mar 08, 2009 1:24 pm
I want to see why its E as well. Couldnt figure it out
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by pakaskwa » Sun Mar 08, 2009 1:55 pm
I don't have the book with me, otherwise I'll copy its explanation here. It doesn't make sense to me. It basically says 2 stmts together are not sufficient.

That's why I post it here and see if anybody can figure it out. If not, I think it's a wrong OA, especially when the question isn't that complicated.
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