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

[spoiler]
The OA is II and III; This can be solved by assuming different values of x and y, however can anybody tell me how can this be solved algebraically, under exam pressure and time constraint of 2 mins!!! [/spoiler]
Source: Manhattan GMAT CAT

See if my approach shown in the attached images is of help.

I personally don't like this problem as far as its relevance to the GMAT is concerned. I haven't seen anything like this on the GMAT so far, perhaps the writers of the problem have.

Here is one that I like that tests a related concept but in a very GMAT style, it is from the Official GMATPrep software:

https://www.beatthegmat.com/how-many-ite ... 19019.html

Dabral

How profit is it 38 when Y=3 ??

If Y < 6, Earnings = 20 + 6*Y
If 6 < Y < 12, Earnings = 20 + 6*6 + 12*(Y-6)
If Y > 12, Earnings = 20 + 6*6 + 12*6 + 18*(Y-12)

If Y = 3(<6), Earnings = 20 + 6*Y = 20 + 6*3 = 20+18 = 38. Hope that helps!