As a bicycle salesperson, Norman earns a fixed salary of $20

[igordudchenko]

Ok, the answer choices II and III are obvious, but your explanation reg. the choice I assumes the testing of numbers 'let's say X is 4...'. Is there any shortcut which allows to test the answer choice I?
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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
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OA: II and III

[jnelson0612]

Ok, the answer choices II and III are obvious, but your explanation reg. the choice I assumes the testing of numbers 'let's say X is 4...'. Is there any shortcut which allows to test the answer choice I?

igor, to me, number testing is the shortcut. Upon seeing this problem, I would immediately put together a chart with the number of bicycles sold and the corresponding pay, from 0 sold to 10 sold. It would take me about twenty seconds to write this chart. At the point I could see that I is not necessarily true, but that II and III must be true.

[JbhB682]

Hi - I tried doing this via algebra but not able to get 1 right ...

Could you please tell me where am i going wrong here

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Hi - i did the following but not able to get option 1 ...experts please let me know why this is wrong

2* Money earned last week = Money earned this week

2* (x+20) = (y +20)

2x + 40 = y + 20

2x + 20 = y

With this algebraic equation, obviously 2 and 3 have to be right

But per this algebraic equation, even 1 has to be right as the equation is 2x + 20 = y ....so Y has to go above and beyond 2x for the algebraic equation to hold true .... hence i selected 1 also ...

Please let me know where am i going wrong ..

Thank you !

[Sage Pearce-Higgins]

This is a tricky question, but one that shows (again) how algebra can get you into trouble on GMAT. Whenever I see "which of the following must be true?" I immediately start thinking about counterexamples. It's this kind of thinking that got me into trouble at high-school (I was always trying to find the exception to the teacher's rule!), but that helps me out on GMAT.

Try writing out the table as Jamie suggested, with "no. of bicycles" in one column and "money earned" in the other and see if that helps you.