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As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] ### Show Tags 17 Mar 2011, 05:39 13 This post was BOOKMARKED 00:00 Difficulty: 65% (hard) Question Stats: 51% (02:23) correct 49% (01:09) wrong based on 415 sessions ### HideShow timer Statistics 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 [Reveal] Spoiler: OA _________________ target:-810 out of 800! Last edited by Bunuel on 31 Mar 2012, 16:39, edited 2 times in total. Edited the OA Math Expert Joined: 02 Sep 2009 Posts: 37105 Followers: 7251 Kudos [?]: 96474 [10] , given: 10751 Re: word problem [#permalink] ### Show Tags 31 Mar 2012, 17:03 10 This post received KUDOS Expert's post 5 This post was BOOKMARKED jj97cornell wrote: Can someone verify the OA? I get D as well. Correct answer is D. OA edited. 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. _________________ Director Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing. Affiliations: University of Chicago Booth School of Business Joined: 03 Feb 2011 Posts: 920 Followers: 14 Kudos [?]: 346 [3] , given: 123 Re: word problem [#permalink] ### Show Tags 17 Mar 2011, 06:07 3 This post received KUDOS 2 This post was BOOKMARKED I will throw in the values of x and y since its going to be tough using algebra. For first 6 bicycles - he gets$6 / bicycle
For next 6 bicycles - he gets $12 / bicycle For > 12 bicycles - he gets$18 / bicycle

Constraint : This week he earned more than twice as much as he did last week.

Paraphrase I: Did he double the quantity of bicycles sold to earn more than double the revenue from last week?

I dont think so. Reasons -

Lets say last week he sold 13 bicycles.

Last week revenue = 20 + 6*6 + 6*12 + 1*18 = 146

146*2 + 1 = 292 + 1 = 293. To make this revenue he could sell (293 - 128)/18 = 165/18 i.e. 10 more than 12 bicycles

Total bicycles sold this week = 12 + 10 = 22 (which is less than twice the bicyles sold last week)

Hence I is ruled out. That leaves the options - B and D.

B Vs D. I have to verify statement III

Paraphrase III: Did he double the revenue from last week by selling minimum of 4 bicycles this week?

Lets assume the contradiction is true. He sold 3 bicycles this week and 1 bicycle last week.

Last week revenue = 20 + 6*1 = 26
This week revenue = 20 + 6*3 = 38

38 is less than twice 26. So the contradiction fails. Hence III is true.

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11 May 2012, 10:37
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piyushksharma wrote:
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

I think II and III are pretty straight forward and I am assuming you have no problem deciding about those.

Let me add here what I thought about I. One way is that you can try to find a case where he earns twice as much but doesn't sell twice as many bikes.
Another is a more intuitive approach. You know that initially, he has to sell more bikes to make some money (he earns only $6 from first 6 bikes and$12 from next 6 bikes. First $20 is too small an amount). Later on, he gets$18 per bike which means he makes money at a much faster rate. Hence, later on, he can double the amount he made previously very quickly and by selling far fewer bikes.
Hence it is not essential that he needs to sell twice as many bikes to make twice as much money. Hence y may not be greater than 2x.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7185 Location: Pune, India Followers: 2167 Kudos [?]: 14020 [2] , given: 222 Re: As a bicycle salesperson, Norman earns a fixed salary of$20 [#permalink]

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16 Feb 2016, 22:08
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Sunil01 wrote:
Hi Karishma and Bunuel,

In order to prove the third statement 1.e y>3, you are assuming x=0.
Is this allowed to assume x=0.

Thanks & regards,
Sunil01

So we need to figure out whether y must be greater than 3. So I think to myself - what is so great about y = 3 that it cannot happen while y = 4 can probably happen?
That is why I put y = 3 and see the numbers I get.

If y = 3, total earning = 20 + 3*6 = 38
I know that this week he earned more than twice of last week. So if he sold 3 bikes this week, he must have earned less than $19 last week. But last week he MUST have earned at least$20, right? That is his fixed salary. This is the reason y cannot be 3 or less. It MSUT be more than 3.
We don't assume that x is 0. We say that even if x = 0, his last week's salary cannot be $19. This means he sold at least 4 bikes this week. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] ### Show Tags 17 Feb 2016, 01:54 2 This post received KUDOS Expert's post Sunil01 wrote: VeritasPrepKarishma wrote: Sunil01 wrote: Hi Karishma and Bunuel, In order to prove the third statement 1.e y>3, you are assuming x=0. Is this allowed to assume x=0. Thanks & regards, Sunil01 So we need to figure out whether y must be greater than 3. So I think to myself - what is so great about y = 3 that it cannot happen while y = 4 can probably happen? That is why I put y = 3 and see the numbers I get. If y = 3, total earning = 20 + 3*6 = 38 I know that this week he earned more than twice of last week. So if he sold 3 bikes this week, he must have earned less than$19 last week. But last week he MUST have earned at least $20, right? That is his fixed salary. This is the reason y cannot be 3 or less. It MSUT be more than 3. We don't assume that x is 0. We say that even if x = 0, his last week's salary cannot be$19. This means he sold at least 4 bikes this week.

Nicely explained thanks Karishma

Hi,
although the explanation is almost same as a post above this explanation, but since you did not understand my English, I got to start looking into my Verbal ..
Kidding... Till the time you are learning, its ok, and I am sure none is contributing for appreciation.
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Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] ### Show Tags 11 Jul 2016, 21:59 2 This post received KUDOS Expert's post target760gmat wrote: I got this as the last qn (7#) or one before last .. Is it better to mark last 3-4 qns randomly when the time left is around 3 minutes or attend a qn or two properly in those three minutes and and leave the last 1/2 qn ? Experts pls advise. If you are left with just a few mins with 3-4 questions in hand, try to give a quick shot to each. Read the question stem and you might be able to narrow down the choices based on some simple logic. Take a guess out of those and move on. It increases the probability of a correct answer. Don't leave 1-2 questions unanswered at the end. Try to take a smart guess. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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20 Jan 2014, 21:50
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jlgdr wrote:
I'm having some issues picking the correct numbers, how can I decide which numbers to use to prove this case not necessarily true?

Cheers!
J

There are no correct/incorrect numbers. You can just try to understand the logic using numbers.

6 bikes - $6 each i.e. total$36
next 6 bikes - $12 each i.e. total$72
So 12 bikes for a total sum of $108 But for every subsequent bike, he gets$18 so the next $108 he will be able to make by selling just 6 bikes. So even if he earns twice as much as before, he doesn't need to sell twice as many bikes. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] ### Show Tags 04 Aug 2014, 20:55 1 This post received KUDOS Expert's post russ9 wrote: VeritasPrepKarishma wrote: piyushksharma wrote: 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 I think II and III are pretty straight forward and I am assuming you have no problem deciding about those. Let me add here what I thought about I. One way is that you can try to find a case where he earns twice as much but doesn't sell twice as many bikes. Another is a more intuitive approach. You know that initially, he has to sell more bikes to make some money (he earns only$6 from first 6 bikes and $12 from next 6 bikes. First$20 is too small an amount). Later on, he gets $18 per bike which means he makes money at a much faster rate. Hence, later on, he can double the amount he made previously very quickly and by selling far fewer bikes. Hence it is not essential that he needs to sell twice as many bikes to make twice as much money. Hence y may not be greater than 2x. Hi Karishma, I'm intrigued by your intuitive approach. To backtrack a little -- word problems as a whole seem to be the biggest time suck for me. I spent 4 minutes on this problem, and although I got it right, I can't seem to figure out how to speed things up when it comes to word problems as such. Is there a strategy you recommend to tackle word problems in general? I know that this is a vague question but any help would be appreciated. Can you recommend other word problems to do to help with practice? Regarding what you said, to me, 2 seemed very straight forward but I still went and checked statement 3. Yes, in hindsight, all of this looks very simple after reading your explanation but I'm not as certain during the test. Any thoughts would be appreciated. Thanks Hey Russ, Familiarity creates intuition. When you see a lot of word problems, you are often able to see what is going to work and usually it is correct. Till a few years back, I use to rely on algebra (equations) to solve all word problems. Then, a mentor forced me to see the big picture, the reason behind every step and how the steps are meant for machines only - how we are quite capable of using reason and logic to solve most questions in a reasoning based test such as GMAT. Now the problem is that when you need to give a solution to someone, just saying that use intuition is not helpful. You can barely explain it in a face-to-face situation. Also, confidence comes with practice. You will start feeling confident in your inferences from the given data once you see that you are getting most of them right on practice questions. I will suggest you to start every word problem by trying to infer whatever you can from the given data. Try to minimize your use of equations (you can't let them go completely). Look for alternative solutions for every problem. Soon. you will start coming up with your own intuitive solutions. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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31 Mar 2012, 16:30
Can someone verify the OA? I get D as well.
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11 May 2012, 02:17
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
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29 Mar 2013, 00:19
AnkitK wrote:
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

Given:

1. The number of bicycles sold last week = x
2. The number of bicycles sold this week = y
3. Let earnings of last week and this week be s1 and s2 resp. s2> 2s1

Question:

1. Is y > 2x
2. Is y > x
3. Is y > 3

Basically the question asks us to relate number of bicycles sold in each of 2 weeks based on the relation between the earnings in those 2 weeks.

1. Earnings in the current week can be higher than that of the last week only when the number of bicycles sold
is higher in the current week. i.e., only when y>x
2. If the number of bicycles sold during the current week <4, then the earnings in the current week cannot be more than double that of the previous week.
3. Now let us assume y=2x. Since we are assuming twice the bicycles are sold this week over that of the previous week , if we take x=18, then y=36.
4. Let us calculate s1 and s2.
s1= earnings from the first 12 bicycles + earnings from the next 6 bicycles = 128+ 108= 236
s2= earnings from the 12 bicycles+ earnings from the next 24 bicycles= 128+ 432= 560
5. s2>2s1 even when y=2x

We see from (1) above statement II is true, from (2) above statement III is true, from (5) above statement I need not be true.

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17 Jan 2014, 04:10
Bunuel wrote:
jj97cornell wrote:
Can someone verify the OA? I get D as well.

Correct answer is D. OA edited.

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.

Bunuel, nice approach +1

On I though, I'm having some issues picking the correct numbers, how can I decide which numbers to use to prove this case not necessarily true?

Cheers!
J
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13 Sep 2014, 01:49
i still feel option (B) is correct because it says y>3 and you guys tested the condition with y=3 and x=1
but what about when y=4 and x=1 or 2
then the earning last week add up to 26 or 32 and the earnings this week is merely 44
and either ways the earnings last week is more than half of the earnings this week

Can you guys please clarify on this approach?
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17 Dec 2014, 15:46
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

What if you just do:
x=1 so y>2*1=2 so let's say y=3

20+(1*6)=26 = earnings last week
20+(3*6)=38 = earnings this week

He earned this week more than twice as much as last week so 38 must be bigger than 26*2.

38<52 so this means y>2x does not have to be true.

Is this correct or is this the wrong way?
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Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] ### Show Tags 17 Dec 2014, 22:12 Lars1988 wrote: 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 What if you just do: x=1 so y>2*1=2 so let's say y=3 20+(1*6)=26 = earnings last week 20+(3*6)=38 = earnings this week He earned this week more than twice as much as last week so 38 must be bigger than 26*2. 38<52 so this means y>2x does not have to be true. Is this correct or is this the wrong way? To prove that (I) needn't hold, you need to find numbers where he earned more than twice but y was not greater than twice of x. You have done the opposite - you have taken a case where y is greater than twice of x and shown that he did not earn more than twice. This doesn't prove that (I) needn't hold. The numbers you need to consider would be say x = 12, y = 24 (y is NOT MORE than twice of x) Last week's earning = 20 + 6*6 + 12*6 = 128 This week's earning = 20 + 6*6 + 12*6 + 12*12 = 128 + 144 (More than twice of last week's earning) So he could earn more than twice of last week's earning and still, y > 2x may not hold. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] ### Show Tags 18 Dec 2014, 03:24 VeritasPrepKarishma wrote: Lars1988 wrote: 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 What if you just do: x=1 so y>2*1=2 so let's say y=3 20+(1*6)=26 = earnings last week 20+(3*6)=38 = earnings this week He earned this week more than twice as much as last week so 38 must be bigger than 26*2. 38<52 so this means y>2x does not have to be true. Is this correct or is this the wrong way? To prove that (I) needn't hold, you need to find numbers where he earned more than twice but y was not greater than twice of x. You have done the opposite - you have taken a case where y is greater than twice of x and shown that he did not earn more than twice. This doesn't prove that (I) needn't hold. The numbers you need to consider would be say x = 12, y = 24 (y is NOT MORE than twice of x) Last week's earning = 20 + 6*6 + 12*6 = 128 This week's earning = 20 + 6*6 + 12*6 + 12*12 = 128 + 144 (More than twice of last week's earning) So he could earn more than twice of last week's earning and still, y > 2x may not hold. Oke I thought because y can be bigger than 2x and he can earn more than twice last week x=1 and y=6 for example than 56>52 but if y is 3, 4 or 5, which is bigger dan 2x, y<52 and he did not earn more than twice last week. So it can be true but also false. So that's why I thought y>2x does not stand at all time. I now understand that I have to find y=2x and that he earned this week more than twice last week but I thought the other way around could also solve the problem. Re: As a bicycle salesperson, Norman earns a fixed salary of$20   [#permalink] 18 Dec 2014, 03:24

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