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

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As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] New post 02 Nov 2009, 03:03
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48% (02:26) correct 52% (02:59) wrong based on 65 sessions
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

A. I only
B. II only
C. I and II
D. II and III
E. I, II, and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: as-a-bicycle-salesperson-norman-earns-a-fixed-salary-of-111038.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Sep 2013, 07:40, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Bicycles [#permalink] New post 02 Nov 2009, 09:28
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This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -

0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(x-12) where x is the total number of bikes sold (when x>12).

X = cycles sold last week
XS = Salary last week.
Y = cycles sole this week
YS = Salary this week.

given YS>2XS

lets test all statements with X=0;
XS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C

lets test all statements with X=1;
XS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved

lets test all statements with X=6;
XS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with

Answer D
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Re: Bicycles [#permalink] New post 26 Sep 2013, 07:38
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Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] New post 26 Sep 2013, 07:41
Expert's post
As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he 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

A. I only
B. II only
C. I and II
D. II and III
E. I, II, III

II and III are obviously always true:

II. y>x --> since this week, Norman earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);

III. y>3 --> if Norman sold 3 bicycles this week then this week he earned 20+3*6=$38, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $20. So y must be more than 3;

I. y>2x --> if y=12 and x= 6 then this week Norman earned 20+6*6+6*12=$128, and the last week he earned 20+6*6=$56. $128 is more than twice as much as $56, so the condition in the stem holds but y=2x, which means that III is not always true.

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: as-a-bicycle-salesperson-norman-earns-a-fixed-salary-of-111038.html
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Re: As a bicycle salesperson, Norman earns a fixed salary of $20   [#permalink] 26 Sep 2013, 07:41
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