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The cost of production of a certain instrument increases with the numb

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The cost of production of a certain instrument increases with the numb  [#permalink]

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New post 06 May 2017, 11:05
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Source: Nova GMAT

The cost of production of a certain instrument increases with the number of units produced. What is the cost of production for 270 units?

(1) The cost of production for 300 units is $300.
(2) The cost of production is directly proportional to the number of units produced.

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Re: The cost of production of a certain instrument increases with the numb  [#permalink]

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New post 06 May 2017, 11:26
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SajjadAhmad wrote:
Source: Nova GMAT

The cost of production of a certain instrument increases with the number of units produced. What is the cost of production for 270 units?

(1) The cost of production for 300 units is $300.
(2) The cost of production is directly proportional to the number of units produced.



IMO, answer is (C) ,i.e., both statements together are sufficient to answer this.

It is given that the cost of production of a certain instrument increases with the number of units produced.
Using statement (1) alone, we cannot find the cost of production for 270 units since there is no relation between the cost of production and the number of units produced.

Using statement (2) alone, we can say that, C = k*n, where c= Cost of production and n = number of units produced.
Using only this, we cannot find the cost of production for 270 units

Combining both statements (1) and (2), C = k*n => 300 = 300*k => k = 1

So, cost of 270 units = 270 * k = 270

Thus, (C) is the answer.

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Re: The cost of production of a certain instrument increases with the numb  [#permalink]

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New post 25 May 2017, 06:42
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From Statement (1) alone, we have that the cost of production for 300 units is $300. Suppose the cost
of production (in dollars) is calculated as 100 + 2/3  quantity. Then the cost of production of 300 units
equals 300 dollars, and the cost of production of 270 units equals 100 + 2/3  270 = 100 + 180 = 280.
Now, suppose it were calculated as 200 + 1/3  quantity, then the cost of production for 270 units would
equal 200 + 1/3  270 = 200 + 90 = 290 dollars.
Since we do not have a unique value, Statement (1) alone is not sufficient.
From Statement (2) alone, the cost of production is proportional to the number of units produced. Hence,
we have the equation The Cost of Production = k  Quantity, where k is some constant. The Cost of
Production of 270 units equals k  270. But we do not know the value of k. So, Statement (2) alone is not
sufficient.
Now, from the statements together, we have that 300 units cost 300 dollars. Putting this in the
proportionality equation yields 300 = k  300. Solving the equation for k yields k = 300/300 = 1. Since we
now know the value of k, we can evaluate the cost of production of 270 items. Hence, the statements
together answer the question. Hence, the answer is (C). The answer is the cost = k  270 = 1  270 = 270
dollars.
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Re: The cost of production of a certain instrument increases with the numb &nbs [#permalink] 25 May 2017, 06:42
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