Question

As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he 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. y>2x
II. y>x
III. y>3

A. I only
B. II only
C. I and II
D. II and III
E. I, II, III

Answer 1

A. I only

I. y>2x

Explanation:

I. y>2x

He sold x bicycles last week and y bicycles this week, this week, he earned more than twice as much as he did last week. Therefore more than twice means greater than 2 x or

y>2x

II. y>x This is not true because y could be greater than x and less than twice of x (2x)

III. y>3 This is also not true because the least he would be earning would be $ 20 and he could get earn greater than 3 and less than $ 20 which would again be contradictory to the given statement