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

Question

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

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

target760gmat · Answer

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.

KarishmaB · Answer

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.

gmat4varun · Answer

So it means we are sure that no sales no salary?

jabhatta2 · Answer

Hi - i did the following but not able to get option 1 ...experts please let me know why this is wrong

2* Money earned last week = Money earned this week

2* (x+20) = (y +20)

2x + 40 = y + 20

2x + 20 = y

With this algebraic equation, obviously 2 and 3 have to be right

But per this algebraic equation, even 1 has to be right as the equation is 2x + 20 = y ....so Y has to go above and beyond 2x for the algebraic equation to hold true .... hence i selected 1 also ...

Please let me know where am i going wrong ..

Thank you !

EMPOWERgmatRichC · Answer

Hi All,

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 (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).

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. 
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, 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

Prasannathawait · Answer

My head spun in this question. But after reading the explanation I get that this question is not that hard.
This is an example that an easy question can be disguised with difficult wording. 
Thanks for the nice and simple explanations.

Agree. D is the answer.

ScottTargetTestPrep · Answer

Statements II and III are easy, so let’s start with them.

Statement II: Since he sold y bicycles this week and x bicycles last week, and it is given that he earned more than twice this week as last week, then y must be greater than x. II is true.

Statement III: Let’s consider the case that y = 3. Then this week Norman would have earned 20 + (3 * 6) = $38. This cannot be true because we are given that he earned more than twice what he earned last week, but his minimum for last week would be the fixed $20 salary. Since $38 is not more than twice $20, we see that y must be greater than 3. III is true.

Statement I: The possible earnings are 20, 26, 32, 38, 44, 50, 56, 68, 80, 92, 104, 116, 128, 146, 164, etc. which respectively correspond to selling 0 bikes, 1 bike, 2 bikes etc.

Notice that an earning of 104 (which corresponds to the sale of 10 bikes) is more than twice of an earning of 50 (which is from the sale of 5 bikes). Thus, if we take x = 5 and y = 10, we see that the condition “the earnings this week are more than twice the earnings of last week” is satisfied, however, the condition y > 2x is not satisfied. Therefore, we see that I is not always true.

Answer: D

mangamma · Answer

I. UNCERTAIN: It depends on how many bicycles Norman sold.

For example, if x = 4, then Norman earned $44   last week. In order to double his earnings, he would have to sell a minimum of 9 bicycles this week (y = 9), making $92  . In that case, y > 2x.

However, if x = 6 and y = 11, then Norman would have earned $56   last week and $116   this week. In that case, $116 > 2 × $56, yet y < 2x.

So, it is possible for Norman to more than double his earnings without selling twice as many bicycles.

II. TRUE: In order to earn more money this week, Norman must sell more bicycles.

III. TRUE: If Norman did not sell any bicycles at all last week (x = 0), then he would have earned the minimum fixed salary of $20. So he must have earned at least $40 this week. If y = 3, then Norman earned $38   this week. If y = 4, then Norman earned $44   this week. Therefore, Norman must have sold at least 4 bicycles this week, which can be expressed y > 3.

The correct answer is D.

lwx939431 · Answer

For option II: y>x
Says this week he sell 7 and last week sold 6, this satisfied the condition y>x.
Then last week he earned 20+6(6) = 56 and this week he earned 20 +6(6) + 12 = 68. From here we see if y is far greater than x, then for sure he will earned more than twice last week. But if y=7 and x=6, he will not earned more than twice of last week.
I didn't choose option II because option II is "might be true", not "must be true".

EMPOWERgmatRichC · Answer

Hi lwx939431,

The prompt defines how Norman is paid - and in simple terms, the MORE bicycles he sells, the MORE he gets paid. Thus, since he made more money this week than he did last week, the number of bicycles he sold this week (the "Y") has to be greater than the number he sold last week (the "X"). 
 
The prompt tells us that "he earned MORE than TWICE as much as he did last week" - and while that helps to define the minimum difference between Y and X, it does not change the fact that Y is always greater than X.

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

sanjayparihar16 · Answer

I. UNCERTAIN: It depends on how many bicycles Norman sold.

For example, if x = 4, then Norman earned $44   last week. In order to double his earnings, he would have to sell a minimum of 9 bicycles this week (y = 9), making $92  . In that case, y > 2x.

However, if x = 6 and y = 11, then Norman would have earned $56   last week and $116   this week. In that case, $116 > 2 × $56, yet y < 2x.

So, it is possible for Norman to more than double his earnings without selling twice as many bicycles.

II. TRUE: In order to earn more money this week, Norman must sell more bicycles.

III. TRUE: If Norman did not sell any bicycles at all last week (x = 0), then he would have earned the minimum fixed salary of $20. So he must have earned at least $40 this week. If y = 3, then Norman earned $38   this week. If y = 4, then Norman earned $44   this week. Therefore, Norman must have sold at least 4 bicycles this week, which can be expressed y > 3.

The correct answer is D.

EMPOWERgmatRichC · Answer

Hi sanjayparihar16,

It appears that you copy/pasted mangamma's explanation (from 11 months ago) as your post - without adding any of your own thoughts. Did you have any questions about this prompt or the approach that was taken in that post?

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

sanjayparihar16 · Answer

I thought that thread does not have the official explanation, so I pasted it. Now realising that it did exist, I am deleting my post. Thanks for pointing out.

Posted from my mobile device

Rahul3484 · Answer

Can we solve it like this:

I assumed both of them sold more than 12 bicycles so we get- 18(y-12)>2*18(x-12) The rest of the salary part gets cancelled out as they are same.

Solving the above equation further we get: y >2x-12, which shows y is not necessarily greater than 2x always.

Experts Need your opinion.

Thanks,
Rahul K Nair

nithyak · Answer

Question:
What about when x=0, then y will always be > 2x. 
In this case I becomes a must be true as well right?

muralis18 · Answer

KarishmaB 
I think the statement3 Y>3 is not a 'MUST' be true but a 'CAN' be true.

Because it says Y>3. If Y=4 and X=3, then Yrev = 44 and Xrev = 38 which is not twice more. So how can we say Statement 3 is a MUST be a true option?

Am I missing something? Experts, please let me know.

EMPOWERgmatRichC · Answer

Hi muralis18, Since the prompt tells us that Norman "earned MORE than twice as much as he did last week", we cannot randomly choose values for X and Y (as you've noted, if X =3, Y cannot equal exactly 4 - it would have to be at least 8); there will be some limits on the possibilities because the money earned in each of those two calculations has to "fit" with the information that we're given. Thankfully, this question can be solved with a bit "brute force"; we can map out the possibilities and look for patterns. Based on the given information, here's a table of how much money Norman would make (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) III. Y > 3 Here, we can look at the "top" of the table and talk through the possibilities. If last week, Norman sold ___ bikes, then how many would he need to have sold this week, at the MINIMUM, to make MORE than twice the money? If he sold 0 bikes last week (re: he made $20)…. then he would have had to have sold AT LEAST 4 bikes this week (re: to make MORE than $40). If he sold 1 bike last week (re: he made $26)…. then he would have had to have sold AT LEAST 6 bikes this week (re: to make MORE than $52). As X gets larger, the value of Y will also get larger. This proves that Y MUST be greater than 3 - and Roman Numeral III is TRUE. GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com

KarishmaB · Answer

muralis18

When we say 'y must be greater than 3,' we are saying that 'y cannot be 0/1/2/3.' 
We are NOT saying that 'all values of y greater than 3 must work.'

Take another example. Say we know that n is a prime number. I can say that 'n must be greater than 1.' This holds. It means every value that satisfies n must be greater than 1 (i.e. 2 > 1, 3 > 1, 5> 1, 7 > 1, 11> 1 etc). 
It does NOT mean that every value greater than 1 satisfies n.

Does this help?

pratyush3284 · Answer

if y =4 & x = 3; he doesnt earn more than twice.

this rejects II & III.

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

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

Prep Toolkit

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