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As a bicycle salesperson

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phoenixio
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As a bicycle salesperson [#permalink] New post   25 Aug 2016, 02:59
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As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first three bicycles he sells, $12 per bicycle for the next three bicycles he sells, and $18 per bicycle for every bicycle sold after the first six. In Week 2, Norman earned more than twice as much as he did in Week 1. If he sold x bicycles in Week 1 and y bicycles in Week 2, which of the following statements must be true?

Indicate all that apply

A) x < 5
B) y > x
C) y > 3
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B,C
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Re: As a bicycle salesperson [#permalink] New post   29 Aug 2016, 15:25
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phoenixio wrote:
As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first three bicycles he sells, $12 per bicycle for the next three bicycles he sells, and $18 per bicycle for every bicycle sold after the first six. In Week 2, Norman earned more than twice as much as he did in Week 1. If he sold x bicycles in Week 1 and y bicycles in Week 2, which of the following statements must be true? Indicate all that apply

A) x < 5
B) y > x
C) y > 3

Show: ::
B,C


I'd create a version of a "growth table" to show possible earnings.

Bikes sold: Earnings
0: $20
1: $26
2: $32
3: $38
4: $50
5: $62
6: $74
7: $92
8: $110
.
.
.
Now check the three statements:

A) x < 5
This need not be true.
Norman could have sold 6 bikes in the first week (x = 6) and then sold 1000 bikes in the second week (y = 1000)
ELIMINATE A

B) y > x
This must be true. If, in week 2, Norman earned more than twice as much as he did in Week 1, then he must have sold more bikes in the second week than in the first week.
So, y MUST be greater than x
B is TRUE

C) y > 3
Norman's minimum earnings is $20 (if he sells 0 bikes)
Even if Norman earns the minimal amount ($20) in week 1, he still must sell 4 or more bikes in week 2 in order to earn more than twice as much as he did in Week 1
So, y MUST be greater than 3
C is TRUE

Answer: B, C
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Sonalika42
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Re: As a bicycle salesperson [#permalink] New post   25 Aug 2016, 22:13
hey its a good qs
it took me around 6 mins to solve this, is there an easier and quicker way to solve it.
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phoenixio
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Re: As a bicycle salesperson [#permalink] New post   26 Aug 2016, 03:28
Since in second week, his earning is more than double than 1st week, therefore y>x
and then if we go by logic, if Norman sells less than 3 bikes in 1st week, his salary will be 20$, so in order to make more than double money in 2nd week, he needs to sell more than 3 bikes, i.e. y>3
Since no. of bikes he can sell in 2nd week is unlimited, no. of bikes he can sell in 1st week is also unlimited, x>5 making option 1 wrong.
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Re: As a bicycle salesperson [#permalink] New post   01 Oct 2020, 01:17
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Bump for further discussion
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akumar24
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Re: As a bicycle salesperson [#permalink] New post   07 Oct 2020, 17:55
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This problem seems tricky but doesn't need a lot of calculations to begin with,
let's check out the answer choices,
A. x < 5 :: there is no limit to bicycles sold in the second week so x need not be less than 5 , note the question asks for statements must be, x need not be < 5

B. y > x ::obviously, if you're making more salary then more bikes has to sold because fixed salary is 20

C. y > 3 :: this is where we might need some calculation, Total Salary would be 20 + 3(6) = 38, now assuming he didn't sell any bikes in week1 his salary still would be 20 and 38 is < than twice week 1 so C has to be true.
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Re: As a bicycle salesperson [#permalink] New post   25 Jul 2022, 08:02
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For the first week
20+ 6(3) +12(3)+18 (X-6) = A

18X - 34 = A

So 2nd week will be

18X - 34 = 2A
Combining the two gives
18X - 9Y = 17
From this we can see that
Y is greater than X
Y is greater than 3
And X must be greater than 5.
Answer B and C.
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Re: As a bicycle salesperson [#permalink] New post   03 Apr 2024, 11:43
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: As a bicycle salesperson [#permalink]
03 Apr 2024, 11:43
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