MGMAT quistion

[ankurmit]

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. y > 2x

II. y > x

III. y > 3

[arora007]

tough one.... is the answer II and III ?

[anshumishra]

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. y > 2x

II. y > x

III. y > 3

Here II is obviously right, no need to check for it. To earn more you got to sell more.

Lets test I :
y> 2x

x = 5, dollars earned = 20+5*6 = 50
y = 10, dollars earned = 20+6*6+4*12 = 20+36+48 = 124 (but, y is not greater than 2x).


Lets test III:

If y=3:
Max dollars earned = 20+3*6 = 38
Minimum value of x = 0 => Minimum dollar earned = 20 (more than half of dollars earned by selling 3 bicycles)
So, y has to be more than 3.

Hence, II and III.

[ankurmit]

U are right .

[spoiler]II. y > x

III. y > 3

are correct [/spoiler]