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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## As a bicycle salesperson, Norman earns a fixed salary of ... ##### This topic has 1 expert reply and 5 member replies ## As a bicycle salesperson, Norman earns a fixed salary of ... 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] Senior | Next Rank: 100 Posts Joined 23 Jun 2008 Posted: 35 messages Upvotes: 2 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 Senior | Next Rank: 100 Posts Joined 05 Aug 2008 Posted: 86 messages Upvotes: 7 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.

Legendary Member
Joined
08 Jul 2008
Posted:
661 messages
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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".

Legendary Member
Joined
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Posted:
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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/ Master | Next Rank: 500 Posts Joined 13 Sep 2016 Posted: 186 messages Can we deploy some smart numbers to solve this problem without delving into algebra much? ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10023 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 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 bikesâ€¦.4 or more bikes were sold 1 bikeâ€¦..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 notâ€¦ 2 bikesâ€¦.7 or more bikes were sold 3 bikesâ€¦.8 or more bikes were sold 4 bikesâ€¦.9 or more bikes were sold At this point, notice the ratio of Y to X is getting smallerâ€¦.? 5 bikesâ€¦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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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