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A home owner must pick between paint A, which costs $6 p/l, [#permalink]

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27 Oct 2005, 09:07

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A home owner must pick between paint A, which costs $6 p/l, and paint B, which costs $4.50 p/l. Paint B takes 1/3 longer to apply than paint A. If the home owner must pay labor costs, which of the two paints will be cheaper to apply?

1. The ratio of the area covered by paint A to B is 4:3.
2. Paint A will require 40 liters of paint and 100 hrs of labor.

I guessed E because I couldn't solve the problem with the information given in the two statements. I would love for one of the VPs or CEOs to solve this one as I'm still a fledgling with DS.

Made a minor edit to correct B paint cost from 6 to 4.5.

I got E.

Cost to apply paint A= 6*(#liters of paint A) + (#painting hrs using A)*(Painting labor rate) = 6*L + H*r

Cost to apply paint B= 4.5*(#liters of paint B) + (#painting hrs using B)*(Painting labor rate) = 4.5*l + h*r
But it's given that paint B takes one-third longer or h=(1 + 1/3)H = (4/3)H
Therefore, Cost to apply paint B = 4.5*l + (4/3)*H*r

Q: Which paint is cheaper to apply?
Or 6*L + H*r > 4.5*l + (4/3)*H*r ?

2) says, L=40 and H=100
We don't know the values for r, l.
NOT SUFF => ACE

1) says Area coverage by A/B = 4/3.
Since there's no info in the Q to suggest any relation between coverage area to Paint Quantity (L, l) or Painting time (H, h), this info is of no use!
NOT SUFF => CE

1+2) We still don't know what r, l are.
NOT SUFF => E

Last edited by mbaqst on 28 Oct 2005, 10:52, edited 1 time in total.

As I posted in my other thread, I dont see why you need to find the exact cost of applying either of the paints. You only need to find out which one is cheaper to apply! They cost the same amount per meter square and one is applied slower than the other.

Quote:

Personally I would answer A (statement 1 is enough). This is because we can work out how much 1 liter of each paint covers in meters square: 1 liter of A covers 4 m2 1 liter of B covers 3 m2 we can in turn find out that the paints cost the same amount per meter square; $4.5/3 = $1.5/m2 $6/4 = $1.5/m2 So if they cost the same amount per amount of area needed painting, the only difference will be the amount of time it takes to apply the paint, and since the question stem says that B is applied one third slower than A, we know that A would be the cheaper alternative. Unfortunately the OA says that both statements are not enough (E). Where am I going wrong, or is it an error with the answer in the book? Thanks

Your subject title says that this is from the Kaplan math book. Could post the official explanation? I agree with you that Statement 1 is sufficient, and that the answer should be A.

Using algebra, what I came up with indicated the cost differences would be based entirely off amount of labor required.

The generic equation for this is c = pl + hr = pl + 36h
where:
c = cost
p = price per liter
l = liters of paint required
h = hours required to paint
r = labor rate, which is stated as 36
(for simplicity I'll use capital letters for the variables of paint A, and lower case for the variables of paint B)

If P is the price per liter of paint A, and p is the price per liter of paint B, then:

P/p = 4/3

Meanwhile, the ratio liters of paint A needed to the liters of paint B needed are (this is the inverse of the coverage of A to the coverage of B):

L/l = 3/4

So, the pl portion of the equation c = pl + 36h is equal for either kind of paint.

We know that the ratio of hours required painting with paint A to hours painting with paint B is:

H/h = 3/4

Thus, we are left with the following cost equations:

Cost of paint A: C = PL + 36H
Cost of paint B: c = PL + 48H

where P, L, and H are for both equations stated in terms for paint A.

Last edited by BumblebeeMan on 28 Oct 2005, 05:39, edited 2 times in total.

A home owner must pick between paint A, which costs $6 p/l, and paint B, which costs $4.50 p/l. Paint B takes 1/3 longer to apply than paint A. If the home owner must pay labor costs, which of the two paints will be cheaper to apply?

1. The ratio of the area covered by paint A to B is 4:3. 2. Paint A will require 40 liters of paint and 100 hrs of labor.

Statement 1 gives the ratio but not the labour rate or the total litres required hence not sufficient.

Statement 2 gives all the required details for paint A. And only infer that paint b would take 300 hrs of labours. But does not give how much of paint B is required or the cost of labour for paint B hence not sufficient.

Combining both we get A to be 40 L and B to be 30 L and cost of labour for A is 100 but nothing is specified about the labour for B. Hence combined statements aren't sufficient.

Statement 1 gives the ratio but not the labour rate or the total litres required hence not sufficient.

Why do you need the labour rate or total litres required? Since the only difference between the two paints is that B is applied slower, and hence will use up more labour. Surely only if the paints differed in cost per square meter (ie efficiency of coverage or price) would the amount of application time be important.

Here is the OE, which I dont find too helpful. Considering contacting kaplan with comments. I found that a few of the questions in the book had errors and some of the answers were missing in the OE section! (IE they had the same explanation for 2 completely different questions, probably misprints but nevertheless)

"To make an intelligent decision we need to know which requires more paint and how much more, how long each will take, and we need some information on the labor costs. Statement 1 gives us information on which requires more paint, however, we still need the actual amounts, the number of hours, and the labor costs.
Statement 2 tells us the amount of one paint and the amount of labor: we can find from the question stem the amount of labor needed for the other paint, but we still dont know how much labor costs, or how much of paint B is needed. Using both statements together, we still cannot find the klaor costs. Both statements together are insufficient."

I also missed this point earlier... bit i agree totally with you, we can certainly decide with the information given in statemnt A that paint B shall cost more. And statement B alone is not sufficient so answer should be A.
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