Data Sufficiency

For Manufacturer M, the cost C of producing X Units of its product per month is given by C = k X + 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.


OA E

X = 1000
Revenue = 1000*(k + 60)
Cost = kX + t

Profit = 1000k + 60,000 - kX - t

Statement 1:
Revenue = 150,000 = 1000k + 60,000.

we can evaluate k. however we still don't know t. Insufficient.

Statement 2:
500k + t + 45,000 = 1000k + t.
5k + 450 = 10k

we can evaluate k, however we still won't know t. Insufficient.

Both statements together:
Since both statements will only provide info on k, and t remains unknown, both statements are insufficient.

Choose E.

-BM-

Can someone please help me understand where the GrossProfit calculation could be simplified as follow:

GrossProfit = (k+60)*x-(kx+t) --> kx+60x-kx-t --> 60x-t

Thanks for helping.

Hi dario.brignone,

Yes. The Gross Profit can be simplified that way, which tells us that the Gross Profit is only dependent on 'x' and 't'.
Next Step: Since the question is for x = 1000, Gross Profit depends only on 't'.

Good work!

Gross profit is a function of t and x. In the question x is known. The satatement which gives the value of t is suficient.

S1. t cannot be calculated

S2. t cannot be calculated

Combining also we don't' get t

(E)