OG13 141

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OG13 141

by massi2884 » Thu May 10, 2012 10:44 am
Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

(1) The company's total revenue from the sale of product X last year was greater than $110,000

(2) For each unit of product X sold last year, the company's revenue was $5

OA B
Source: — Data Sufficiency |

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by aneesh.kg » Thu May 10, 2012 11:30 am
Given:
Total expenses, E = 100000 + 0.05*R
R > E (since there is profit)
Asked:
Is n > 21000?

Statement(1):
R > 110000
This will tell us that E is greater than a certain value. But, there is no way to get any information on n.
INSUFFICIENT

Statement(2):
R = 5n
E = 100000 + 0.05*5n = 100000 + 0.25n
Since R > E,
5n > 100000 + 0.25n
We've an inequality in n, from which the required information on n can be obtained.
SUFFICIENT

[spoiler](B)[/spoiler] is the answer
Aneesh Bangia
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by massi2884 » Fri May 11, 2012 4:17 am
Hi aneesh,
thanks for your reply. However, how can you please confirm that we need to go ahead and make the calculation to find n?
Because if for example the result were n > 20,000, that statement wouldn't be sufficient I guess.

Thanks.

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by aneesh.kg » Fri May 11, 2012 4:20 am
You're right. We need to be sure if n > 21000 or not.

We need to go one step further in that inequality.
5n > 100000 + 0.25n
n > 100000/4.75 > 21000
Aneesh Bangia
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