Walkabout wrote:
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.
Given:
1. Last year, a certain company began manufacturing product X and sold every unit of product X that it produced.
2. 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.
3. The company made a profit on product X last year
Asked: Did the company sell more than 21,000 units of product X last year?
Let the units of product sold by company X last year be x units and selling price be p
(1) The company's total revenue from the sale of product X last year was greater than $110,000.
Total revenues = R = xp > $110,000
Total expenses = E = $100,000 + 5%xp
Total profit = R - E = xp - ($100,000 + 5%xp) = 95%xp - $100,000 > 0
xp > (100/95) * 100,000 = $10,000,000/95
NOT SUFFICIENT
(2) For each unit of product X sold last year, the company's revenue was $5.
p = $5
Total revenues = R = 5x
Total expenses = E = $100,000 + 5%*5x
Total profit = R - E = 5x - ($100,000 + 5%*5x) = 95%*5x - $100,000 > 0
x> 10,00,000/95*5 = 21052.63 > 21000
SUFFICIENT
IMO B
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