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 n bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2n
II. y > n
III. y > 3  Choose the correct choice from the following answers
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*(n-12) where n is the total number of bikes sold (when n&gt;12).   XN = cycles sold last week   NS = Salary last week.   Y = cycles sole this week   YS = Salary this week.   given YS&gt;2NS   lets test all statements with N=0;   NS = 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 N=1;   NS = 26   YS&gt;52   True when Y=6   Still satisfies all the statements - Nothing achieved   lets test all statements with N=6;   NS = 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 n bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2n
II. y > n
III. y > 3