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.

Individually, statements are insufficient.
Combining the statements:

1) Assume no profit: i.e. Maximum cost = 500,000 --> Cost of labor = 1/3 X 500,000
Which means cost of labor is LARGER THAN $150,000 (worst case scenario)

Now:
2) Profit > Labor > $150,000 (worst case scenario)*

Combined it is sufficient.


*The worst case scenario makes sense because if things are going better, costs will be lower, which means profit will be higher.

whoa there.
no.

the fact that your "profit" is SIMULTANEOUSLY zero (in statement one) and more than $150k (in statement two) should, to put it mildly, worry you.
you can't have two contradictory values of the same variable in the same problem.

(it should be obvious that statement (2) rules out the possibility of zero profit.)

--

important message:
hard word problems like this are usually, well, hard. THERE ARE NOT USUALLY "SHORTCUTS" ON PROBLEMS SUCH AS THIS ONE.
if you think you've found such a "shortcut", think very carefully about whether there's a bug in the shortcut.

Hi Ron,
I have a question here. The problem is specifically asking if the profit is greater than 150000? But after taking into account the information from both the stems, we conclude the profit has to be greater than 200000. So is it still sufficient to answer the question?

For example if a question asks is x>10 and we found out x>15, is it still OK to say we have enough information to answer the question?

Many thanks in advance
Ramesh

if you know that a kid is over 15 years old, can you say that the kid is definitely over 10 years old?
yes, you can.

same thing applies here.

-- ron

Why would I even bother to do any calculation and not choose E as the correct answer? The question asks about figuring out company's profit for the project but the options (1) and (2) talk about (all the projects of) the entire company.

aagar2003, no. if the problem actually had a wording that suggested that interpretation -- e.g., the company's profit for all projects -- then you would have a case here. however, in situations such as this one, you should assume that the wording can be interpreted in a way that is most relevant to whatever is described.

If 3m=total cost of project. Than the most m can represent is 166,666. or 1/3 of 500,000. we know that m+L= cost of project which means L cant exceed 166,666r because we know P>L we know that profit is greater than labor. So yes profit is greater than 150,000

hi -- if you are going to work out data sufficiency problems on the forum, please indicate which statements you are using when. thanks.

Hi Ron,

Thanks for the great approach! I've learned so much from your replies and your lecture :)

I thought up two other ways to tackle this when we combine both statements (given that I already know that either statement alone isn't sufficient), please let me know if my reasoning is correct, thanks!

approach # 1
GT=greater than LT=less than
500=3M + GT 2M <--p
if GT 2M or p equals 2M, then 500=5M or 100=M. That's the maximum value that M can get, even so, p which is GT 2M must be GT 2(100) or GT 200. If we reduce M, then "GT 2M" or p will only get even more bigger than 200 in order for us to have 500 in total, hence sufficient.

My inspiration for using this method came from you and other's solution in this problem:
last-month-15-homes-were-sold-in-town-x-t4373.html

approach # 2: since the problem asks for: is p>150K, if I can prove that both the case of p<150k and p>150 work in the statement's condition, or the combined statements' condition, then it proves the statement's insufficiency in giving me a specific value (for value DS question) or a specific range of possible values (for yes/no DS question) for the unknown.

I make p>150 a preferred answer/yes to the question
and p<150 a not preferred answer/no to the question
And try both preferred and not preferred values in the statement to see if both work, if so, then the statement isn't sufficient.

so: 500=3M + GT 2M <----p
try a preferred value, say p > 150
then equation becomes:
500=3M + GT 150
3M = LT 350
3M <350
M<350/3

then try a not preferred value, say p < 150
500=3M + LT 150
500=GT 350 + LT 150 or 3M = GT 350
thus 3M > 350
M> 350/3
since depends on the value we choose, M's value changes, it means that the combined statement must give us a specific range of possible values for M, thus sufficient.

I know this sounds very complicated, but I've always had trouble with inequality and YES/NO DS until this post inspired me to use this method to knock off insufficient statement.

if-1-000-is-deposited-in-a-certain-bank-account-t3209.html

I like how someone uses r<8 and r>8 to try on statements to prove insufficiency.

Sorry for writing so much, your response is much appreciated!

sorry I forgot to quote you in my reply, hopefully you will see my response!