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A shoe Cobbler charges n dollars

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A shoe Cobbler charges n dollars [#permalink] New post 03 Jan 2013, 00:09
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A shoe cobbler charges n dollars to repair a single pair of loafers. Tomorrow, he intends to earn 240 dollars repairing loafers. If he were to reduce his fee per pair by 20 dollars, he would have to repair an additional pair of the loafers to ear the same amount of revenue. How many pair of loafers does he intend to repair tomorrow?

Choices:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[Reveal] Spoiler: OA

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PraPon

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Last edited by PraPon on 04 Jan 2013, 08:29, edited 2 times in total.
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Re: A shoe Cobbler charges n dollars [#permalink] New post 03 Jan 2013, 01:33
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Expert's post
PraPon wrote:
A shoe cobbler charges n dollars to repair a single pair of loafers. Tomorrow, he intends to earn 240 dollars repairing loafers. If he were to reduce his fee per pair by 20 dollars, he would have to repair an additional pair of the loafers to ear the same amount of revenue. How many pair of loafers does he intend to repair tomorrow?

Choices:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

See if you can solve it without using algebraic calculations. Explain your shortest method.


240/n=240/(n-20)-1 --> n=80 --> 240/n=240/80=3.

Answer: C.

P.S. Please provide OA's for the questions and tag them correctly.
_________________

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Re: A shoe Cobbler charges n dollars [#permalink] New post 27 Jun 2013, 18:08
Wouldn't the answer actually be D - 4?

The question is asking for how many pair of loafers does he intend to repair tomorrow?

This is (x + 1) (because he would have to repair an additional pair)
So shouldn't the answer be (x + 1 = 3 + 1 = 4 = D ??)

Thanks for the help
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Re: A shoe Cobbler charges n dollars [#permalink] New post 27 Jun 2013, 19:25
Expert's post
jjack0310 wrote:
Wouldn't the answer actually be D - 4?

The question is asking for how many pair of loafers does he intend to repair tomorrow?

This is (x + 1) (because he would have to repair an additional pair)
So shouldn't the answer be (x + 1 = 3 + 1 = 4 = D ??)

Thanks for the help


We are told that the cobbler charges n dollars to repair a pair of shoes. Then we are told that IF he charged n-20 dollars he would have to repair an additional pair. Notice that we are not told that he WILL charge n-20 dollars, just IF.

Hope it's clear.
_________________

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

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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.


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Re: A shoe Cobbler charges n dollars [#permalink] New post 29 Jun 2013, 10:53
Bunuel wrote:
jjack0310 wrote:
Wouldn't the answer actually be D - 4?

The question is asking for how many pair of loafers does he intend to repair tomorrow?

This is (x + 1) (because he would have to repair an additional pair)
So shouldn't the answer be (x + 1 = 3 + 1 = 4 = D ??)

Thanks for the help


We are told that the cobbler charges n dollars to repair a pair of shoes. Then we are told that IF he charged n-20 dollars he would have to repair an additional pair. Notice that we are not told that he WILL charge n-20 dollars, just IF.

Hope it's clear.


So technically, they have given the future scenario for the cobbler just so we can solve the problem.
I mean without that specific sentence we would have too many unknowns.

I think I was over thinking the problem.
Thanks,
Math Expert
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Re: A shoe Cobbler charges n dollars [#permalink] New post 29 Jun 2013, 11:50
Expert's post
jjack0310 wrote:
Bunuel wrote:
jjack0310 wrote:
Wouldn't the answer actually be D - 4?

The question is asking for how many pair of loafers does he intend to repair tomorrow?

This is (x + 1) (because he would have to repair an additional pair)
So shouldn't the answer be (x + 1 = 3 + 1 = 4 = D ??)

Thanks for the help


We are told that the cobbler charges n dollars to repair a pair of shoes. Then we are told that IF he charged n-20 dollars he would have to repair an additional pair. Notice that we are not told that he WILL charge n-20 dollars, just IF.

Hope it's clear.


So technically, they have given the future scenario for the cobbler just so we can solve the problem.
I mean without that specific sentence we would have too many unknowns.

I think I was over thinking the problem.
Thanks,


Correct. Only that "n-20 dollars" case is not a future scenario it's a hypothetical scenario.
_________________

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.


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Senior Manager
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Re: A shoe Cobbler charges n dollars [#permalink] New post 16 Oct 2013, 01:45
Price x Qty = Total
===============================================================

n x 1 = n


n x 240/n = 240

Per condition given:


(n-20) x 240/n + 1 = 240

Solving above equation gives value of n = 80, Answer = 3
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Re: A shoe Cobbler charges n dollars [#permalink] New post 16 Oct 2013, 10:35
The loafer charges n per pair, and he is intending to make 240 from x pairs:

240 = x * n

If he wants to reduce the price by 20 (n - 20) he needs to repair 1 more ( x + 1)

240 = (n-20)(x+1)
xn = (n-20)(x+1)
xn = xn + n - 20x -20
n - 20x = 20......

what am I doing wrong?
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Re: A shoe Cobbler charges n dollars [#permalink] New post 16 Oct 2013, 10:40
Bunuel wrote:
PraPon wrote:
A shoe cobbler charges n dollars to repair a single pair of loafers. Tomorrow, he intends to earn 240 dollars repairing loafers. If he were to reduce his fee per pair by 20 dollars, he would have to repair an additional pair of the loafers to ear the same amount of revenue. How many pair of loafers does he intend to repair tomorrow?

Choices:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

See if you can solve it without using algebraic calculations. Explain your shortest method.


240/n=240/(n-20)-1 --> n=80 --> 240/n=240/80=3.

Answer: C.

P.S. Please provide OA's for the questions and tag them correctly.


Should it be +1 ?
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Re: A shoe Cobbler charges n dollars [#permalink] New post 16 Oct 2013, 10:50
Expert's post
Skag55 wrote:
The loafer charges n per pair, and he is intending to make 240 from x pairs:

240 = x * n

If he wants to reduce the price by 20 (n - 20) he needs to repair 1 more ( x + 1)

240 = (n-20)(x+1)
xn = (n-20)(x+1)
xn = xn + n - 20x -20
n - 20x = 20......

what am I doing wrong?


This is not a best way to solve the problem but you could still get the correct answer:
From 240=xn --> x=240/n --> substitute: n - 20*240/n= 20 --> solve: n=80 --> 240/80=3.
_________________

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?
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Re: A shoe Cobbler charges n dollars [#permalink] New post 16 Oct 2013, 10:50
Expert's post
Skag55 wrote:
Bunuel wrote:
PraPon wrote:
A shoe cobbler charges n dollars to repair a single pair of loafers. Tomorrow, he intends to earn 240 dollars repairing loafers. If he were to reduce his fee per pair by 20 dollars, he would have to repair an additional pair of the loafers to ear the same amount of revenue. How many pair of loafers does he intend to repair tomorrow?

Choices:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

See if you can solve it without using algebraic calculations. Explain your shortest method.


240/n=240/(n-20)-1 --> n=80 --> 240/n=240/80=3.

Answer: C.

P.S. Please provide OA's for the questions and tag them correctly.


Should it be +1 ?


Let me ask you a question: which is greater 240/n or 240/(n-20)?
_________________

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?
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Re: A shoe Cobbler charges n dollars [#permalink] New post 16 Oct 2013, 10:59
Bunuel wrote:

Let me ask you a question: which is greater 240/n or 240/(n-20)?


I got confused with the stem. It should be 240/(n+20) + 1 as I imagined it...
I think that's enough for me for today! :lol:
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Re: A shoe Cobbler charges n dollars [#permalink] New post 28 Mar 2014, 02:42
I was able to work out (240/n)+1=240/(n-20)
but somehow got stuck on the equation:n(n-20)=4800.
How do I solve it quickly?
Bunuel,please help!
Re: A shoe Cobbler charges n dollars   [#permalink] 28 Mar 2014, 02:42
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