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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]

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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.

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Re: Which paint is cheaper to apply [#permalink]

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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]

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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>

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Re: Which paint is cheaper to apply [#permalink]

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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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A home owner must pick b/n paint A, which cost \$6.00 per [#permalink]

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14 Sep 2009, 09:30
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A home owner must pick b/n paint A, which cost \$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 labour at the rate \$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 labour.

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Re: paint A and paint B [#permalink]

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14 Sep 2009, 10:05
E.
Nothing can b deduced from "(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."
Although "(2) Paint A will require 40 liters of paint and 100 hours of labour." provides sufficient info for calculating the total cost for paint A (A = 40*6 + 100*36, B = (100+100/3)*36 + X*4.5 where X= quantity of paint B is missing)but we so not have info regarding the quantity of Paint B.
Hence E.

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Re: paint A and paint B [#permalink]

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14 Sep 2009, 10:10
sacmanitin wrote:
A home owner must pick b/n paint A, which cost \$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 labour at the rate \$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 labour.

C?

1. You know the ratio of the area but you dont know how long it will take to paint... so INSUFF?
2. you know A will require 40 liters and 100 hours of labour. For B you know it will take 133.33 hours to apply since it takes 1/3 longer to apply. But still insuff. since you dont know how many liters of paint B you need

Combine:
so you know A's price through the paint and the labour. B you know the labour price but need the number of liters of paint. 1 gives you the ratio of the area - so the area painted using A's paint is 40 X4= 160. with that you can figure out that B needs 160/3 = 53.33 = 54 liters of paint. So SUFF.
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Re: paint A and paint B [#permalink]

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14 Sep 2009, 10:49
According to my understanding if 1 liter paint A : 1 liter paint B =4:3 in terms of area covered,

then let say A covers 4x sq feet so to cover 1 sq feet paint A required =1 /4x
B covers 3x sq feet so to cover 1 sq feet paint B requied =1/3x

so the paint required for any fixed area to cover will be 1/4x:1/3x=1/4:1/3=3:4

now we know paint A require =40 liter ,so paint B require 4/3 *40=160/3

so we know the two amounts and we know the hours also 100 hrs and 133.33 hrs
-what you guys things

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Re: paint A and paint B [#permalink]

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14 Sep 2009, 23:58
sacmanitin wrote:
A home owner must pick b/n paint A, which cost \$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 labour at the rate \$36 per hour ,which of the two paints will be cheaper to apply ?

\$6 * A_liters + \$36 * Time_needed VS \$4.50 * B_liters + \$36 * 4/3 * Time_needed
6A + 36T vs 4.5B + 48T

(1) Gives us ratio of A to B, but we don't know T, not enough
(2) Gives us A and T, we don't know B

Together suffiecient

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Re: paint A and paint B [#permalink]

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18 Sep 2009, 08:13
Also get C

From the original data :
Ca=\$6/lt; Cb=\$4.5/lt
Tb=4/3Ta
Lc=\$36/h

Q: which one cheaper?

St(1) Gives Aa/lt:Ab/lt=4:3 -->insuff
St(2) Gives Va=40lt; Lh=100h, only can get Total cost of using paint A no correlation to B -->insuff

St(1)&(2) Found the Total cost of A=40.\$6+100.\$36
Found the Vb=Aa.Va/Ab=4/3.40
Found the Tb=4/3Ta
Found total cost of B=4/3.40.\$4.5+4/3.100.\$36 --> suff, hence C

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Re: paint A and paint B [#permalink]

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18 Sep 2009, 10:14
"Paint B takes one third longer to apply than paint A" --> Let the time taken for paint A is t then the time taken for paint B is 1.33t

From statement 1,
Ratio of area covered by one liter of paint A to area covered by one liter of paint B is 4:3
So the ratio of paint used to paint the same area for paint A to paint B = 3:4
So cost incurred to paint a given area using paint A = quantity * time * cost
= 3 * t * 6 = 18t
Cost incurred to paint a given area using paint B = 4 * 1.33t * 4.5 = 24t

So it is cheap to use A compared to B

From statement 2,
Quantity of paint used and time taken for paint A are given. Using this cost incurred using A can be deduced but we cannot conclude on the cost for B.
So 2 alone is not sufficient.

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Re: paint A and paint B [#permalink]

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29 Sep 2009, 03:44
sacmanitin wrote:
A home owner must pick b/n paint A, which cost \$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 labour at the rate \$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 labour.

1: price of paint per unit of area is the same \$6.00:\$4.50=4:3 but price of applying paint B is more expensive -> The home owner should buy paint A.
2: no info about how much of paint B required and how much labor required

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Re: paint A and paint B [#permalink]

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30 Sep 2009, 07:34
pl check the resource :Kaplan Math workbook

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Re: paint A and paint B [#permalink]

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30 Sep 2009, 22:31
OA should be E, as nothing can be deduced from the st1 and st2 individually. Even if we combine the statements getting the area covered by 1 litre of paint we are able to do calculate the cost just for A and not for paint B. Hence, option C is incorrect.

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Re: paint A and paint B [#permalink]

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30 Sep 2009, 23:36
Based on the information given, I also believe the correct answer to be A (as per maratikus' logic). Was there any explanation provided as to why E is the correct answer?

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A homeowner must pick between paint A, which costs \$6 per [#permalink]

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19 Apr 2010, 12:59
A homeowner must pick between paint A, which costs \$6 per liter, and paint B, which costs \$4.50 per liter. Paint B takes one-third longer to apply than paint A. If the homeowner 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 paint B is 4:3.

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

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19 Apr 2010, 14:03
IMO C
Whats the OA?

Total cost of A = 6x+ 36Ta
Total cost of B = 4.5y+ 36Tb = 4.5y+ 48 Ta ( Given Tb = 4/3 * Ta )

where x and y are quantity required.

Statement 1: This just give area covered by 1 L of A and B in ratio , thus not sufficient.
Statement 2: This gives x= 40 and Ta = 100, not sufficient as we need y as well

using statement 1 and 2 we can calculate y
let area of be painted is z,
number of liter required for A = total area/ area per litre = z/4k = 40
number of liter required for B = z/3k = 40*4/3 = y

Thus C - Both together are sufficient.
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19 Apr 2010, 14:31
E

The explanation reasons that, because labor costs are unknown, both statements are insufficient. I arrived at C as well.

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19 Apr 2010, 14:36
Please read the question again, labor cost is given to be 36\$. We just need labor hours.
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19 Apr 2010, 14:57
I've read it more than a few times. Here is the explanation verbatim:

"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 amount, 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 don't know how much labor costs, or how much of paint B is needed. Using both statement together, we still cannot find the labor costs. Both statements together are insufficient."

Clearly, there is an error. This is the last DS question in the Kaplan GMAT Math WorkBook.

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Re: DS-question   [#permalink] 19 Apr 2010, 14:57

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