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As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink]
08 Dec 2007, 10:36
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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 x bicycles last week and y bicycles this week, which of the following statements must be true?
I did III first because I thought it'd be easiest.
III. y >3
since he makes $20/week base, assuming he sells 0 bikes last week. He would still need to sell > 3 bikes to double his salary of $20 (since 3 bikes would only net him $18). III must be true.
if III is true then only D and E are left. Since II shows up in both answers, we don't need to worry about it at all (although it's fairly obvious that y>x, how could he make more money by selling fewer bike?)
now onto I. y > 2x
plug in 6 for x (I chose 6 because it's at a price cutoff, all the extra bikes he sells this week will be worth more. if there's a scenario where he doesn't need to sell 2x bikes, it would be here)
Week 1: $20 + 6(6) = 56 (so week two must be > $112)
Week 2: $20 + 6(6) + 6(12) = $128
this is more than double by $16. He could have sold 6 bikes in X and 11 bikes in Y and still come out ahead by $2. This proves I doesn't have to be true.