Coming up with numbers - math

[fbmagnumopus]

Hey Tommy,

I was wondering if you could guide me on how I could have known which numbers to try out to disprove the first option for this 'select all that apply' question. It's really difficult to think straight under pressure during the exam and select the right numbers to plug in - How would one know for this problem, to try out x=4 and then x=6 or any other possible numbers that disprove the first option?

On what criteria does one go about selecting the right numbers in general on such problems?

Here's the question from practice test 3, section 1:
10 Norman's Bicycle Sales Devilish 4:26 17:07 DQ Inequalities & Absolute Values


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? Indicate all that apply.

[tommywallach]

Hey FB,

I'm not going to go through the whole question, given that I'm sure you've seen the solution provided on the website.

Basically, you just need to think about the possible things that could happen in terms of ranges. Think about what happens if he doesn't sell even 6 bikes. Think about what happens if he's between 6 and 12. Think about what happens if he's between 12 and 18. And finally, you could think about what happens if he sells a bazillion bicycles (exaggeration for effect).

There are ranges here, so we expect things to change in the different ranges, so that's what we'd want to consider. The inequalities you set-up based on the given information also help to inform how you want to think about it.

It's a devilish question, so don't agonize over it or anything. But the way you "know" what numbers to test is by thinking about what numbers would "change" the situation/relationships.

Hope that helps a bit!

-t