From Gmat Prep 1, Q#28

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 for the project 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.

Highlight for OA: C


Thoughts:
Given: Profit = 500,000 – Total Cost
*****Profit = 500,000 – Labor - Materials
Need to find out: P > 150,000

From (1)…Total Cost = 3*Materials
Doesn't say anything about labor.

From (2)...Profit > Labor
What about materials?

From (1) and (2)...I'm getting stuck here. How do I combine these two?

(1) alone:
since total cost = L + M, this means that L + M = 3M, or L = 2M.
so, rephrased, statement 1 says that labor cost twice as much as materials.
still, this is insufficient, as picking values will show: if M = $1 and L = $2, the answer is yes, but if M = $150,000 and L = $300,000, the answer is no.

(2) alone:
great, but no information at all about materials. so, if L = M = $1, then yes; if L = $1 and M = $499,997 (so that profit = $2), then no.
insufficient

together:
we have
P > L
which, using the rephrasing found above, rephrases to
P > 2M
also,
P = 500,000 - 3M (because total cost = 3M)
so
500,000 - 3M > 2M
500,000 > 5M
100,000 > M
since M is less than 100,000, it follows that profit, which is 500,000 - 3M, must be more than 500,000 - 3(100,000) = 200,000.
answer = yes
sufficient

this is a hard problem!

Thanks on this one as well Ron! Makes sense.

Could you do the problem this way as well

Stmt 1) Labor cost is twice the cost of material -> 2M+M = 500000 => M=500000/3 => L = 2* 500003/3 = 333333.333. Nothing is known about Profit. INSUFF

Stmt 2) Profit is larger than Labor cost -> But nothing is know about the labor cost. INSUFF

Combine (1) and (2) -> Profit is greater than L => P > 333333.333. Hence P > 150000. SUFF
(C)

nope, can't do it that way.

the company's revenue for the construction project, not its total cost, was $500k.
the m + 2m = 3m is the total cost of materials and labor; if you set 3m equal to $500k, you're implying that the total costs are $500k. in that case, since you already know that the revenue is $500k, you'd have zero profit.

remember: profit = revenue - cost
(this is the only thing you'll ever have to know on the gmat that pertains even remotely to business)
the whole point of statement (1) is that you have no actual dollar value for the total cost. if you had a concrete dollar value - any dollar value, regardless of the actual amount - you'd be able to calculate the profit.