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A construction company was paid a total of $500,000 for a [#permalink] ### Show Tags 22 Jul 2010, 10:55 3 This post received KUDOS 21 This post was BOOKMARKED 00:00 Difficulty: 85% (hard) Question Stats: 56% (02:16) correct 44% (01:18) wrong based on 371 sessions ### HideShow timer Statistics 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 [Reveal] Spoiler: OA Math Expert Joined: 02 Sep 2009 Posts: 37079 Followers: 7242 Kudos [?]: 96299 [7] , given: 10732 Re: Cost/Profit Problem - is my explanation correct? [#permalink] ### Show Tags 22 Jul 2010, 11:04 7 This post received KUDOS Expert's post 17 This post was BOOKMARKED 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. _________________ Intern Joined: 03 Jun 2010 Posts: 16 Followers: 0 Kudos [?]: 22 [0], given: 0 Re: Cost/Profit Problem - is my explanation correct? [#permalink] ### Show Tags 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 Intern Joined: 03 Jun 2010 Posts: 16 Followers: 0 Kudos [?]: 22 [0], given: 0 Re: Cost/Profit Problem - is my explanation correct? [#permalink] ### Show Tags 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 Intern Joined: 16 Jul 2010 Posts: 18 Followers: 1 Kudos [?]: 18 [2] , given: 9 Re: Cost/Profit Problem - is my explanation correct? [#permalink] ### Show Tags 22 Jul 2010, 11:53 2 This post received KUDOS 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]

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23 Jul 2010, 05:28
dauntingmcgee wrote:
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. Could you please explain why profit must be at least 2M/(2M+M+2M)*500,000? Intern Joined: 16 Jul 2010 Posts: 18 Followers: 1 Kudos [?]: 18 [1] , given: 9 Re: Cost/Profit Problem - is my explanation correct? [#permalink] ### Show Tags 23 Jul 2010, 05:57 1 This post received KUDOS 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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Re: Cost/Profit Problem - is my explanation correct? [#permalink]

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19 Feb 2011, 13:59
Total budget = 500

Is profit > 150

Or is expenditure < 350

1) Total cost = Material+Labor
T = M+L
T = 3M
3M = M+L
2M = L

Labor cost is twice that of material.

If M=1, L=2; T=3. Expenditure < 350. Yes
M=150; L=300; T=450; Expenditure > 350. No.
Not sufficient.

2) Company's Profit P>L
M=0; L=249; P=251. Expenditure <350. Yes
M=399; L=1; P=100. Expenditure <350. No.
Not sufficient.

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.

Ans: "C"
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Re: Cost/Profit Problem - is my explanation correct? [#permalink]

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19 Feb 2011, 19:27
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fluke wrote:
Total budget = 500

Is profit > 150

Or is expenditure < 350

1) Total cost = Material+Labor
T = M+L
T = 3M
3M = M+L
2M = L

Labor cost is twice that of material.

If M=1, L=2; T=3. Expenditure < 350. Yes
M=150; L=300; T=450;

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.
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Re: A construction company was paid a total of $500,000 for a [#permalink] ### Show Tags 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

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04 Jun 2015, 03:39
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.

Hi Bunuel,
In Statement 1 we concluded that m< 350/3= 116.66 So we can substitute the result in the equation 500-(3*116)=152>150. We can choose number lower than 116. Choose 115 and apply in the equation 500-(3*115)=155 > 150 any number lower than 350/3 will result in P>150. So Statement A should be Sufficient.

What is wrong in my work?
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18 Jun 2016, 16:23
Hi all. I’m not very good at mathy explanations (more of a verbal guy), but I got this question right first time in about 2 minutes. Here is my logic to it:

The question stem tells us that the company was paid $500k for the project, and states that only labor and material are the costs. It then asks if the company’s profit is greater than 150k. Another way of thinking of that is asking if the costs were greater than$350k. (Since $500k payment –$350k cost = $150k profit) Statement 1 tells us that the ratio of total cost to cost of material is 3 to 1. Because the question stem states the only other cost is labor, we know that the ratio of labor cost to material cost is 2:1. For every dollar of material there is 2 dollars of labor. Not sufficient on its own. Statement 2 tells us the company profit is greater than its cost of labor. An important part of that is that it means profit is indeed a positive number! Not sufficient on its own. With the statements combined we know that profit is greater than labor, and the ratio of labor to material is 2:1. The limit ends up being$200k profit, $200k labor, and$100k materials. The company’s actual costs have to be lower than this limit. Even the limit only has $300k of cost, which is much lower than$350k as asked in the question stem.

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A construction company was paid a total of $500,000 for a [#permalink] ### Show Tags 26 Oct 2016, 10:20 Converting the question into equations is the key to solving this question under two mins. What does the question stem say -> Cost (C) = Labour ( L ) + Material ( M ) Cost = 500 ( dividing by 1000, makes the calculations appear less daunting ) Is Profit > 150 ? What is profit ? -> Money Earned - Money Spent Money Earned is -> 500 So Profit ( P) = 500 - C Now, Rephrasing the question stem, Is 500 - C > 150 which means, Is C < 350 ? Now, lets look at both the options. A) C=3M No numerical given, so there is no way to ascertain the answer to our main question. B) Profit is > Cost of Labour -- Which in mathematical terms, means the following 500 - C > L now as we already know that C= L + M, L= C -M Substituting, 500 -C > C - M , 500 > 2C - M ( Again no numerical value available to prove C< 350 ) Now , Lets combine A and B 500 >2C - M and C= 3M, Lets get everything in terms of C as our main question is in terms of C. 500 > 2C - C/3 , This gives us -- > C < 300 , which is sufficient to answer our main question , Is C< 350 . Answer is C. A construction company was paid a total of$500,000 for a   [#permalink] 26 Oct 2016, 10:20
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