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hard question,

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hard question,

by tanviet » Tue Sep 29, 2009 4:55 am
a contruction company was paid a total of 500,000 usd for a construction project. The company's only costs for the project were for labor and materials. Was the company's profit for the project greater than 150,000?

a, the company's tatal cost was three times its cost for materials

b, the company's profit was greater than its cost for labor

pls, help with this.
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Source: — Data Sufficiency |
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by fiercepoint » Tue Sep 29, 2009 5:35 am
I think both statements together are sufficient.

The first statement tells you that the ratio of cost of materials to cost of labour is 1:2 but nothing about profit. Let's say cost of materials is x, then cost of labour is 2x.
The second statement tells you that profit was greater than cost of labour or greater than 2x.
Costs plus profit must equal 500 000. 2x + 2x + x = 500 000 or x = 100 000, now since profit was greater than 2x this means profit must be over 200 000. The equation isn't perfect because profit is actual larger than 2x but it's sufficient to answer the question.
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by gnet » Tue Sep 29, 2009 6:52 am
C(osts) = L(abor) + M(aterials)
P(rofit) = 500,000 - C(osts)

Question: Is 500,000 - C > 150,000

( So, if we could show that total costs were less (or more) than 350,000 then we have an answer! )

(a) C = 3M
or 3M = L + M
or L = 2M

Could take any values -> not sufficient

(b) P > L
or 500,000 - C > L
or 500,000 - (L + M) > L
or 500,000 - L - M > L
or 500,000 - M > 2L

could take any values
- eg. if M = 400,000 then 100,000 > 2L -- or, L < 50,000 (in which case our costs have gone above 350K)
- another example: if M = 100,000 then L < 200,000 (in which case our costs stay below 350 K)
So, not sufficient.

(c) combine the two eqns from a and b
L = 2M
500,000 - M > 2L

or 500,000 - M > 4M
or 500,000 > 5M
or M < 100,000

Since L = 2M
therefore L/2 < 100,000
or L < 200,000

combining the above two results

M + L < 100,000 + 200,000
L + M < 300,000

i.e. total costs were less than 300,000 - therefore profits were more than 200,000 - which answers (Yes) the question asked.

Both statements together sufficient in my view. Please let us know the OA.
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