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A construction company was paid a total of $500,000 for a

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A construction company was paid a total of $500,000 for a [#permalink] New post 22 Jul 2010, 10:55
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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
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Re: Cost/Profit Problem - is my explanation correct? [#permalink] New post 22 Jul 2010, 11:04
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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.
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Re: Cost/Profit Problem - is my explanation correct? [#permalink] New post 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
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Re: Cost/Profit Problem - is my explanation correct? [#permalink] New post 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
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Re: Cost/Profit Problem - is my explanation correct? [#permalink] New post 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] New post 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?
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Re: Cost/Profit Problem - is my explanation correct? [#permalink] New post 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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Re: Cost/Profit Problem - is my explanation correct? [#permalink] New post 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] New post 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.
Answer (C).
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Re: GMATprep DS1 [#permalink] New post 27 Dec 2011, 13:07
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when you combine
TC (total cost)= 3m (material)
TC= L (labor) + m = 3m so L=2M

500-TC>2m (aka L)
500>5m
m<100

500 - less then 300= greater then 200k

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Re: GMATprep DS1 [#permalink] New post 10 Jan 2012, 14:01
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Rephrase: 500K - [L+M] >= 150K
L+M <= 350K?

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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Re: A construction company was paid a total of $500,000 for a [#permalink] New post 13 Oct 2013, 01:45
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Re: A construction company was paid a total of $500,000 for a [#permalink] New post 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.
Re: A construction company was paid a total of $500,000 for a   [#permalink] 23 Feb 2014, 22:50
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