• The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Admissions Success Stories As a bicycle salesperson, Norman earns a fixed salary of ...

This topic has 1 expert reply and 5 member replies

hengirl03 Senior | Next Rank: 100 Posts Default Avatar
Joined
05 Aug 2008
Posted:
86 messages
Upvotes:
7

As a bicycle salesperson, Norman earns a fixed salary of ...

Post Wed Sep 03, 2008 9:52 am
When I did this problem originally, use the picking numbers technique to find the answer. However, picking numbers didn't really work for I, since some numbers works and other didn't. My question is, how do you know that you are picking all of the numbers that you need to find the answer?

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

Answer: II and III
[/b]

  • +1 Upvote Post
  • Quote
  • Flag
mayur00 Senior | Next Rank: 100 Posts Default Avatar
Joined
23 Jun 2008
Posted:
35 messages
Upvotes:
2
Post Wed Sep 03, 2008 11:20 am
Plug in x= 1 to 5 and find closest value of y, you'll find that
1. None satisfy the given condition that his earning in one month was 2x the other.
2. Shows that x>3, since x=1 to 5 don't satisfy given condition
3. y>x (obvious)
4. As x increases from 1 to 5, y increases from 5 to something less than 10. Which shows that y < 2x

  • +1 Upvote Post
  • Quote
  • Flag
hengirl03 Senior | Next Rank: 100 Posts Default Avatar
Joined
05 Aug 2008
Posted:
86 messages
Upvotes:
7
Post Wed Sep 03, 2008 12:01 pm
For I: if x = 4 and y = 9. Then Norman earned ($20+24 = 44) this week, and ($20+36+36 = 92). So y> 2x.

However, if x = 6 and y = 11. Then Norman earned $56 in the first week, and 116 the next. In this case, $116 > 2 $56, yet y < 2x.



I still don't know how I can make sure that I choose all of the right answers when solving this problem. Then I first did this problem, I chose x = 4 and y = 9. But I didn't consider the situation where x=6 and y=11.

  • +1 Upvote Post
  • Quote
  • Flag
pepeprepa Legendary Member Default Avatar
Joined
08 Jul 2008
Posted:
661 messages
Upvotes:
48
Post Wed Sep 03, 2008 12:19 pm
It is clear that statement one is the most complicated.

y>2x must be true?
Let's try to find a counter-example, if we cannot so it must be true.
In your example, you want Norman to earn more than twice as much as he did last week.
If we chose x=10 and y=18 we have y<2x
Revenue with 10: 20 + 6*6 + 4*12 = 104
Revenue with 18: 20 + 6*6 + 6*12 + 6*18 = 236

We respect the conditions given by the question and we find that it is possible that Norman earns more than twice as much as he did last week and at the same time with y<2x
That's a counter-example to the statement "y>2x must be true".

  • +1 Upvote Post
  • Quote
  • Flag
pepeprepa Legendary Member Default Avatar
Joined
08 Jul 2008
Posted:
661 messages
Upvotes:
48
Post Wed Sep 03, 2008 12:22 pm
hengirl03 wrote:
For I: if x = 4 and y = 9. Then Norman earned ($20+24 = 44) this week, and ($20+36+36 = 92). So y> 2x.

However, if x = 6 and y = 11. Then Norman earned $56 in the first week, and 116 the next. In this case, $116 > 2 $56, yet y < 2x.



I still don't know how I can make sure that I choose all of the right answers when solving this problem. Then I first did this problem, I chose x = 4 and y = 9. But I didn't consider the situation where x=6 and y=11.
I did not precisely read your post.
Indeed, when a question asks you " X must be true", you only need to find a counter-example which respects all the conditions given by the question but wich contradicts X. That's what you did in your post, so do not chose I/

  • +1 Upvote Post
  • Quote
  • Flag
Post Sat Aug 04, 2018 1:46 am
Can we deploy some smart numbers to solve this problem without delving into algebra much?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Tue Aug 07, 2018 6:27 pm
Hi All,

To start, we will need to 5 answer choices for reference (as the ability to 'prove' or 'disprove' an answer can help us to eliminate answer choices):

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

This Roman Numeral question can be solved with "brute force"; let's map out the possibilities and look for patterns. Based on the given information, here's a table of how much money Norman would make in 1 week (based on the number of bikes sold):

Bikes = Money
0 = $20

1 = $26
2 = $32
3 = $38
4 = $44
5 = $50
6 = $56

7 = $68
8 = $80
9 = $92
10 = $104
11 = $116
12 = $128

13 = $144
14 = $162
Etc. ($18 per additional bike)

We're told that Norman sold X bicycles last week and Y bicycles this week. We also know that he earned MORE THAN TWICE the money he earned in the prior week, so we have to use THAT fact to evaluate what the possibilities could be (within the table above).

II. Y > X

Roman Numeral II is easiest, so we'll start there. Since Norman earned MORE MONEY, he had to have sold MORE bicycles. Thus Y MUST be greater than X (so no heavy work is required here).
Roman Numeral II is TRUE.

III. Y > 3

Here, we can look at the "top" of the table and talk through the possibilities.

If last week, Norman sold ___ bikes last week, then how many would he need to have sold this week, at the MINIMUM, to make MORE than twice the money?
0 bikes….4 or more bikes were sold
1 bike…..6 or more bikes were sold

The second number will just get bigger and bigger. This proves that Y MUST be greater than 3.
Roman Numeral III is TRUE.

I. Y > 2X

For this Roman Numeral, we can continue the work that we did in Roman Numeral II; we have to look to see whether Y is ALWAYS greater than 2X or not…

2 bikes….7 or more bikes were sold
3 bikes….8 or more bikes were sold
4 bikes….9 or more bikes were sold
At this point, notice the ratio of Y to X is getting smaller….?
5 bikes…10 or more bikes were sold.

This last example PROVES that Y isn't always greater than 2X.
Roman Numeral I is NOT ALWAYS TRUE.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 Jay@ManhattanReview 76 first replies
2 GMATGuruNY 61 first replies
3 Brent@GMATPrepNow 46 first replies
4 Rich.C@EMPOWERgma... 33 first replies
5 ceilidh.erickson 18 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

107 posts
2 image description GMATGuruNY

The Princeton Review Teacher

94 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

93 posts
4 image description Max@Math Revolution

Math Revolution

91 posts
5 image description Jay@ManhattanReview

Manhattan Review

88 posts
See More Top Beat The GMAT Experts