Data Sufficiency

abhasjha wrote: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 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?

1) Last month, manufacturer M's revenue from sale of 1000 units was $150,000
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.

Given that c = kx+t

Revenue from the sale of 1000 units = 1000*(k+60) = 1000k+60,000
Cost of 1000 units = 1000k+t

Thus, Gross profit from the sale of 1000 units = (1000k+60,000) - (1000k+t) = 60,000-t

So, the rephrased question is: What is the value of t?

It is important to note that whether we get/do not get the value of k, it would have no impact on the question.

S1: Last month, manufacturer M's revenue from the sale of 1000 units was $150,000.

Revenue from the sale of 1000 units = 1000k+60,000 = 150,000 => k = 90. We do not have the value of t. Insufficient.

S2: Manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.

Difference of 'cost of producing 1000 units' and 'cost of producing 500 units' = (1000k+t) - (500k+t) = 500k = 45,000 => k =90. We do not have the value of t. Insufficient.

S1 and S2:

Even after combining both the statements, we cannot get the value t.

Answer: E

-Jay
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abhasjha wrote: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 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?

1) Last month, manufacturer M's revenue from sale of the 1000 units was $150,000
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.

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 1000 units of its product and sold all the units for k+60 dollars each, what was manufacturer M's gross profit on the 1000 units?

1) Last month, manufacturer M's revenue from sale of the 1000 units was $150,000.
2) manufacturer M's cost of producing 500 units in a month is $45000 less than its cost of producing 1000 units in a month.

We are given the formula c = kx + t, in which c is in dollars, x is the number of units produced per month, and k and t are constants. We are also given that last month manufacturer M produced 1000 units of its product and sold all the units for k + 60 dollars each. We need to determine manufacturer M's gross profit on the 1000 units. Thus, we have:

c = k(1,000) + t

Furthermore, since the manufacturer sells 1000 units for k + 60 dollars each, its revenue was 1000(k + 60) = 1000k + 60000. So, the gross profit is 1000k + 60000 - (1000k + t ) = 60000 - t. As we can see, if we can determine the value of t, then we can answer the question.

Statement One Alone:

Last month, manufacturer M's revenue from sale of the 1000 units was $150,000.

Using the information in statement one, we can create the following equation:

1000k + 60,000 = 150,000

1000k = 90,000

k = 90

Although we have a value for k, we have no information about the value of t. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

Manufacturer M's cost of producing 500 units in a month is $45,000 less than its cost of producing 1000 units in a month.

Using the information in statement two, we can create the following equation:

k(1,000) + t - [k(500) + t] = 45,000

1,000k + t - 500k - t = 45,000

500k = 45,000

k = 90

Although we have a value for k, we still do not have enough information to determine the value of t. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Since each statement allows us to find only the value of k (recall k = 90 in each statement), we still do not have enough information to determine the value of t, so we cannot determine the profit last month.

Answer: E