Problem Solving

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


I only

II only

I and II

II and III

I, II and III

I want to understand how to pick numbers for such questions?

I didn't pick numbers. Maybe some one can show how to pick numbers.

From this question stem itself you know that y > x b/c he must have sold greater number of vehicles this week for his revenue to be twice as great.

so (II) is true.

set up the equation. 20 + 6*6 + 12(y-6) + 18(y-12) = This week.

This week = 2*Last week; Last week = x, so this week is 2x

20 + 6*6 + 12(y-6) + 18(y-12) = 2x.

20 + 36 + 12y - 72 + 18y - 216 = 2x.

30y - 232 = 2x

x = 15y - 106.

from the above equation, you can find out that he at least sold 8 more bicycles this week than last week b/c if he sold 7 more, you would get a negative value for x and that is not possible.

(-1) = 15*7 - 106.

14 = 15*8 - 106

Now we know the least amount of vehicles he sold was definitely y > 3

so (III) is also true.

(I) doesn't always have to be true. He makes twice as much not sells twice as much.

IMO D.

Its D

You can be easily folled by forgetting about the $20/wk,

If you forgot about that, then A would be true.

As x(2) = 1bike for x = $6.00
Y being 3 , 3(6)=$18

But with the $20/wk

Its $26 and $38

Don't forget to translate X bikes x 6.

B: There is no way y can be smaller than X.

C. Y has to be atleast 4 to get over the half way hump even if X sells 0 bikes the week before.
X = 0 = $20
Y = 4 X 6 = $24.00 + 20 = $44.00