As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold k bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2k
II. y > k
III. y > 3 Pick: A) I only B) II only C) I and II D) II and III E) I, II, and III
This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -   0 Bikes - $20   6 Bikes - $56   12 Bikes - $128   More than 12 bikes - 128 + 18*(k-12) where k is the total number of bikes sold (when k&gt;12). K = cycles sold last week   KS = Salary last week.   Y = cycles sole this week   YS = Salary this week.   given YS&gt;2KS   lets test all statements with K=0;   KS = 20   YS &gt;40   True when Y = 4   satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C   lets test all statements with K=1;   KS = 26   YS&gt;52   True when Y=6   Still satisfies all the statements - Nothing achieved   lets test all statements with K=6;   KS = 56   YS&gt;112   True when Y = 11   This proves statement i wrong, hence eliminate E so we are left with   Answer II and III
<result>D</result>
As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold k bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2k
II. y > k
III. y > 3