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Last year, a certain company began manufacturing product X [#permalink]

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05 Jun 2012, 15:09

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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% 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 21000 units of product X?

(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

Re: Last year, a certain company began manufacturing product X [#permalink]

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05 Jun 2012, 22:09

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Hi,

It is given that the total expense for the company = 100,000 + 5% of total revenue (let say, x) Also, the project made profit. Profit = Total revenue - expenses = x - (100000 + 0.05x) = 0.95x - 100000 Since profit > 0 therefore, 0.95x - 100000 > 0 ...(a)

using (1) The company's total revenue from the sale of product X last year was greater than $110,000, we can only check whether 0.95x - 100000 is positive or not. Insufficient.

using (2) For each unit of product X sold last year, the company's revenue was $5, lets find the minimum number of units, number of units = total revenue/5 = x/5 or 0.95(x/5) - 100000 >0 ....(from (a)) or x > 21052, thus x is greater than 21000. Sufficient.

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% 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 21000 units of product X?

(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

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?

Since the company made a profit, then R-(100,000+0.05R)>0 --> R>2,000,000/19=~105,000.

(1) The company's total revenue from the sale of product X last year was greater than $110,000 --> R>110,000. Its possible that company sold just one unit for say $120,000 or 120,000 units for $1. Not sufficient.

(2) For each unit of product X sold last year, the company's revenue was $5. If total of n units were sold, then the total revenue would be $5n, so R=5n --> 5n>2,000,000/19 --> n>400,00/19>21,000. Sufficient.