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Question
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 100,000plus5percentofthecompany′stotalrevenuefromallunitsofproductXsold.IfthecompanymadeaprofitonproductXlastyear,didthecompanysellmorethan21,000unitsofproductXlastyear?(1)Thecompany′stotalrevenuefromthesaleofproductXlastyearwasgreaterthan110,000.
(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 100,000plus5percentofthecompany′stotalrevenuefromallunitsofproductXsold.IfthecompanymadeaprofitonproductXlastyear,didthecompanysellmorethan21,000unitsofproductXlastyear?(1)Thecompany′stotalrevenuefromthesaleofproductXlastyearwasgreaterthan110,000.
(2) For each unit of product X sold last year, the company's revenue was $5.
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Solution
The correct option is A Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
- For a company that made a profit last year from selling product X and had total expenses for product X of 100,000+0.05R,whereRisthetotalrevenueforsellingproductX,determinewhetherthecompanysoldmorethan21,000unitsofproductXlastyear.Notethatsincethecompanymadeaprofit,revenue−cost,whichisgivenbyR−(100,000 + 0.05R) = 0.95R − $100,000, must be positive.
- It is given that R > 110,000.ItispossibletovarytheunitpriceandthenumberofunitssoldsothatR>110,000 and more than 21,000 units were sold, and also so that R > $110,000 and less than 21,000 units were sold; Thus, NOT sufficient.
- It is given that the company’s revenue for each unit of product X was 5.IfthecompanymanufacturedandsoldxunitsofproductX,thenitsrevenuewas5x. Because the company made a profit, 0.95 * (5x)−100,000 > 0, and so
0.95 * (5x)−100000 > 0;4.75x−100000 > 0;4.75x>100000;x > 21052; Thus, sufficient. - To avoid long division in the last step, note that 4.75 * (21,000) = 99,750, and thus from 4.75x > 100,000 it follows that x > 21,000. The correct answer is B; statement 2 alone is sufficient.
- For a company that made a profit last year from selling product X and had total expenses for product X of 100,000+0.05R,whereRisthetotalrevenueforsellingproductX,determinewhetherthecompanysoldmorethan21,000unitsofproductXlastyear.Notethatsincethecompanymadeaprofit,revenue−cost,whichisgivenbyR−(100,000 + 0.05R) = 0.95R − $100,000, must be positive.
- It is given that R > 110,000.ItispossibletovarytheunitpriceandthenumberofunitssoldsothatR>110,000 and more than 21,000 units were sold, and also so that R > $110,000 and less than 21,000 units were sold; Thus, NOT sufficient.
- It is given that the company’s revenue for each unit of product X was 5.IfthecompanymanufacturedandsoldxunitsofproductX,thenitsrevenuewas5x. Because the company made a profit, 0.95 * (5x)−100,000 > 0, and so
0.95 * (5x)−100000 > 0;
4.75x−100000 > 0;
4.75x>100000;
x > 21052; Thus, sufficient.
- To avoid long division in the last step, note that 4.75 * (21,000) = 99,750, and thus from 4.75x > 100,000 it follows that x > 21,000. The correct answer is B; statement 2 alone is sufficient.
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