Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Aug 2014, 19:35

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 11 Feb 2011
Posts: 148
Followers: 3

Kudos [?]: 22 [0], given: 21

GMAT Tests User
As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] New post 17 Mar 2011, 05:39
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

49% (02:24) correct 51% (01:17) wrong based on 150 sessions
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
3 KUDOS received
Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 931
Followers: 11

Kudos [?]: 190 [3] , given: 123

Reviews Badge
Re: word problem [#permalink] New post 17 Mar 2011, 06:07
3
This post received
KUDOS
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.

Answer D.
Intern
Intern
avatar
Joined: 29 Dec 2011
Posts: 7
Concentration: Finance
Schools: Yale '14
GMAT 1: 710 Q48 V38
GMAT 2: 720 Q49 V40
GPA: 3.3
Followers: 0

Kudos [?]: 2 [0], given: 6

GMAT ToolKit User
Re: word problem [#permalink] New post 31 Mar 2012, 16:30
Can someone verify the OA? I get D as well.
Expert Post
6 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22141
Followers: 3406

Kudos [?]: 24888 [6] , given: 2697

Re: word problem [#permalink] New post 31 Mar 2012, 17:03
6
This post received
KUDOS
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 21 Feb 2012
Posts: 117
Location: India
Concentration: Finance, General Management
GMAT 1: 600 Q49 V23
GPA: 3.8
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 26 [0], given: 15

MANHATTAN PS3 [#permalink] New post 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
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1080

Kudos [?]: 4847 [1] , given: 163

Re: MANHATTAN PS3 [#permalink] New post 11 May 2012, 10:37
1
This post received
KUDOS
Expert's post
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 14

Kudos [?]: 190 [0], given: 11

GMAT ToolKit User GMAT Tests User
Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] New post 01 Dec 2012, 22:00
Test the inequalities:
I. y>2x
Let x = 1 bicycle; Earnings: 26 dollars
Let y = 3 bicylce; Earnings: 38 dollars
Is 38 more than twice of 26? NO!
II. y > x
Surely, there must be more bicycles sold in the second week. Always true! YES!
III. y>3
Testing I, we found that when y = 3 and x = 1, we still couldn't achieve the condition that the second week's earning is more than twice the first. Therefore, y must be greater than 3. YES!

Answer: D
_________________

Impossible is nothing to God.

Senior Manager
Senior Manager
User avatar
Joined: 17 Dec 2012
Posts: 394
Location: India
Followers: 12

Kudos [?]: 173 [0], given: 9

Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] New post 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.

The answer is choice D.
_________________

Srinivasan Vaidyaraman
Sravna Test Prep
http://www.sravna.com/courses.php

Classroom Courses in Chennai
Online and Correspondence Courses

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1627
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 155 [0], given: 254

GMAT ToolKit User
Re: word problem [#permalink] New post 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.

Answer: D.


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 :)
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1080

Kudos [?]: 4847 [0], given: 163

Re: word problem [#permalink] New post 20 Jan 2014, 21:50
Expert's post
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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 268
Followers: 0

Kudos [?]: 10 [0], given: 23

Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] New post 03 Aug 2014, 15:19
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
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1080

Kudos [?]: 4847 [0], given: 163

Re: As a bicycle salesperson, Norman earns a fixed salary of $20 [#permalink] New post 04 Aug 2014, 20:55
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

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: As a bicycle salesperson, Norman earns a fixed salary of $20   [#permalink] 04 Aug 2014, 20:55
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic As a bicycle salesperson, Norman earns a fixed salary of $20 adarsh12345 3 02 Nov 2009, 03:03
As a bicycle salesperson, Norman earns a fixed salary of $20 dancinggeometry 1 13 Sep 2008, 01:52
3 As a bicycle salesperson, Norman earns a fixed salary of $20 JCLEONES 5 15 Jan 2008, 10:20
As a bicycle salesperson, Norman earns a fixed salary of $20 applecrisp 1 09 Dec 2007, 14:19
As a bicycle salesperson, Norman earns a fixed salary of $20 applecrisp 1 08 Dec 2007, 10:36
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.