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A construction company was paid a total of $500,000 for a [#permalink]
22 Jul 2010, 10:55

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Difficulty:

55% (medium)

Question Stats:

47% (01:58) correct
52% (01:40) wrong based on 65 sessions

A construction company was paid a total of $500,000 for a construction project. The company's only costs for the project were for labor and materials. Was the company's profit greater than $150,000?

(1) The company's total cost was three times its cost for materials.

(2) The company's profit was greater than its cost for labor

Re: Cost/Profit Problem - is my explanation correct? [#permalink]
22 Jul 2010, 11:04

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Expert's post

asch13 wrote:

A construction company was paid a total of $500,000 for a construction project. The company's only costs for the project were for labor and materials. Was the company's profit greater than $150,000?

(1) The company's total cost was three times its cost for materials.

(2) The company's profit was greater than its cost for labor

Given: c=l+m Question is p=500-c>150 true?

(1) c=3m --> is 500-3m>150 true? --> is m<\frac{350}{3}\approx{117} true? Not sufficient.

(2) 500-(l+m)>l --> 500>2l+m. Not sufficient.

(1)+(2) Question became is m<\frac{350}{3}\approx{117} true? From (1) c=l+m=3m --> l=2m. From (2) 500>2l+m=4m+m=5m --> m<100. Sufficient.

Re: Cost/Profit Problem - is my explanation correct? [#permalink]
22 Jul 2010, 11:05

Cost(C) = Labor(L) + Materials(M) Profit(P) = 500,000-C is 500,000 - C > 150,000? is C < 350,000

(1) C = 3M C = 3M = L + M, L = 2M

(2) P > L Substitute 2M for L P > 2M multiply both sides by 3/2 (3/2)P > 3M Substitute C for 3M (3/2)P > C plug 150,000 in for P (3/2)(150,000) > C 225,000 > C

So, C < 350,000 and the answer is yes, so then (1) and (2) together are sufficient

Re: Cost/Profit Problem - is my explanation correct? [#permalink]
22 Jul 2010, 11:05

Bunuel wrote:

asch13 wrote:

A construction company was paid a total of $500,000 for a construction project. The company's only costs for the project were for labor and materials. Was the company's profit greater than $150,000?

(1) The company's total cost was three times its cost for materials.

(2) The company's profit was greater than its cost for labor

Given: c=l+m Question is p=500-c>150 true?

(1) c=3m --> is 500-3m>150 true? --> is m<\frac{350}{3}\approx{117} true? Not sufficient.

(2) 500-(l+m)>l --> 500>2l+m. Not sufficient.

(1)+(2) Question became is m<\frac{350}{3}\approx{117} true? From (1) c=l+m=3m --> l=2m. From (2) 500>2l+m=4m+m=5m --> m<100. Sufficient.

Answer: C.

wow, that was fast, I was just typing my explanation, but yours looks much simpler. thanks

Re: Cost/Profit Problem - is my explanation correct? [#permalink]
22 Jul 2010, 11:53

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My solution:

1) Total cost = 3M, Labor = 2M, NS

2) Profit >= Labor, NS

1) and 2) Profit >= 2M, therefore profit must be at least 2M/(2M+M+2M)*$500,000 = 2/5*$500,000, therefore profit >= $200,000. Sufficient.
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Re: Cost/Profit Problem - is my explanation correct? [#permalink]
23 Jul 2010, 05:57

Gladly.

Since from:

1) we know that Labor (L) = 2 * Materials (M), and 2) we know that Profit (P) >= L 1) and 2) combined show that P >= 2M

There are only three components of the $500,000: P, L and M, so P+L+M = $500,000. The minimum amount of P is the case that P = L = 2M. In order to find what fraction P is of P+L+M we simply take P/(P+M+L) = 2M/(2M+M+2M) = 2M/5M = 2/5. Now that we know what fraction of the $500,000 is P, we simply multiply 2/5 * $500,000 to get $200,000. Sufficient.
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Combining 1 and 2; T=M+L=L/2+L T=(3/2)L P=500-T=500-(3/2)L P=500-(3/2)L P>L 500-(3/2)L>L 500>(5/2)L (5/2)L<500 L<200 Since M is half L. M should be <100 Even if we consider maximum of these; Total maximum expenditure = 200+100=300<350. Thus profit will always be >150.

Actually, you may not want to use so many variables and then plug values. Chances of error are very high in this case. Preferably, stick to algebra or reason it out as follows:

>>> A construction company was paid a total of $500,000 for a construction project. The company's only costs for the project were for labor and materials.

500,000 is divided into 3 parts - Labor costs, material costs and profit.

>>> Was the company's profit greater than $150,000?

Was profit > 150,000?

>>> (1) The company's total cost was three times its cost for materials.

labor cost + material cost = 3 * material cost labor cost = 2* material cost

So now we know that 500,000 is divided into 3 parts - 2*material costs (labor), material costs and profit. But no idea what these costs and profit are. Not sufficient.

>>> (2) The company's profit was greater than its cost for labor Profit > labor cost but no idea how much labor cost or material cost was. Not sufficient.

Together, Profit > 2 material cost so even if it was greater than 2*material cost by a very very small amount, 500,000 would have been split into 3 parts: 2*material cost (labor), material cost and 2*material cost (profit) So 2*material cost would be at least 200,000. Hence profit is at least 200,000. Sufficient. Answer (C).
_________________

1. L+M = 3M => L = 2M. No info on M or L values, insuff. 2. L < 150K. M=? insuff

Together, L<150K, which means M<75K, which implies that the labor cost is 3M<3x75K=225K. Obviously, this means that profit > 150K. Suff.
_________________

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DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Re: A construction company was paid a total of $500,000 for a [#permalink]
13 Oct 2013, 01:45

Hello from the GMAT Club BumpBot!

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Re: A construction company was paid a total of $500,000 for a [#permalink]
23 Feb 2014, 22:50

Hi all. Bumping this topic because I didn't find an adequate answer explanation.

Here's mine:

Given :

Profit = 500,000 - TC

TC = L + M

St. 1: (N.S.)

TC = 3M 3M = L + M 2M = L

St. 2: (N.S.)

P > L , since L = 2M , Profit > 2M

Both Statements:

P = 500,000 - 3M [TC = 3M from st. 1] 2M = 500,000 - 3M [P > L , P > 2M ] . Substitute 2M into the profit formula, knowing that the Profit number must be greater than 2M.

solve for M: ... M = $100,000. Plug into profit formula :

2($100,000) = $500,000 - 3($100,000)

Profit > $200,000

Answer choice C.

gmatclubot

Re: A construction company was paid a total of $500,000 for a
[#permalink]
23 Feb 2014, 22:50