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