DS - For Manufacturer M, the cost C of producing x units of

[Steve G]

From GMATPrep 2,

For Manufacturer M, the cost C of producing x units of its product per month is given by C = kx + t, where C is in dollars and k and t are constants. Last month, if Manufacturer M produced 1,000 units of its product and sold all the units for k + 60 dollars each, what was Manufacturer M’s gross profit on the 1,000 units?

(1) Last month, Manufacturer M’s revenue from the sale of the 1,000 units was $150,000.
(2) Manufacturer M’s cost of producing 500 units in a month is $45,000 less than its cost of producing 1,000 units in a month.

Highlight for OA: E

Gross Profit = Revenue - Cost
Gross Profit = 1000*(k+60) - (k*1000 + t)

From 1, you can solve for k, but not t. Insufficient.
From 2, you have cannot solve for k and t since you have 2 equations, and three unknowns. Insufficient.

From (1) and (2), you can solve for k in (1), and then you can solve for t in (2). I marked C, but obviously that's not the correct answer.
Is the only reason that C is not the correct because statement 2 doesn't talk about the last month in particular, while the question asks for the gross profit for the last month? If statement 2 did indeed talk about last month, is there any other reason why C could not be correct? Thanks!

[RonPurewal]

it looks like you're doing everything in your power to avoid writing the equation for statement (2). hint: that's a bad idea. in the time you spent rationalizing your decision not to set up the equation, you could easily set up the equation and just see what happens.

to wit:
statement (2) translates as
(500k + t) + 45,000 = (1000k + t)
500k + 45,000 = 1000k
oops
can't solve for t here, either
insufficient

look how little work that was; i guarantee you it's less work than coming up with the rationale you've posted here.

--

lesson to be learned here:
if you're dealing with simultaneous equations, don't sit around and philosophize; just set up the equation and see what happens.

the gmat test writers looooooooooove to write questions on which traditional algebra rules, such as 'n equations can solve for n variables', give incorrect answers. so don't assume anything; just write the equation and do the work. you'll find it's less work than you think.

[Steve G]

Thanks Ron...makes sense. Thanks for the tip as well.

[rfernandez]

[nikshep]

I'm a little confused on this..

the revenue = 1000(K+60) - (1000K + t) = 60,000 - T. So we need T to solve

S1 - gives us K ..still not T
S2 - 500 units cost 45K less than 1000, therfefore can I assume 500 units cost 45K to manufacture? Based on this

45000 = 500K + T..

I derived K from S1, substitute for K to derive T. Answer C

What's wrong with this approach???

Thanks

nix

[RonPurewal]

S2 - 500 units cost 45K less than 1000, therfefore can I assume 500 units cost 45K to manufacture?

no.
that would only work if C was just kx, not kx + t.
in real-life terms, "k" represents the per-unit cost of manufacturing, while "t" represents the overhead costs -- the costs of things like electricity, etc., which would be incurred even if 0 units were manufactured. therefore, your assumption is invalid unless the overhead costs are zero (i.e., t = 0).

did you read the post above?
this one:
post9696.html#p9696
in that post, i derived the correct equation for statement 2.