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A shoe Cobbler charges n dollars

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A shoe Cobbler charges n dollars [#permalink]

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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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Last edited by PrashantPonde on 04 Jan 2013, 09:29, edited 2 times in total.
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Re: A shoe Cobbler charges n dollars [#permalink]

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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]

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New post 27 Jun 2013, 19:08
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]

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New post 27 Jun 2013, 20:25
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.
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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 29 Jun 2013, 11:53
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,
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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 29 Jun 2013, 12:50
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.
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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 16 Oct 2013, 02:45
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]

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New post 16 Oct 2013, 11:35
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]

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New post 16 Oct 2013, 11:40
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]

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New post 16 Oct 2013, 11:50
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.
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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 16 Oct 2013, 11:50
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)?
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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

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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 16 Oct 2013, 11:59
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]

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New post 28 Mar 2014, 03:42
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!
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Re: A shoe Cobbler charges n dollars [#permalink]

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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 01 Mar 2016, 04:35
Bunuel, can I plug in from answer choices starting with the middle answer choice ?
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Re: A shoe Cobbler charges n dollars [#permalink]

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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 01 Mar 2016, 05:59
PrashantPonde 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


Hi,
Since you have asked without algebric calculations, one method which will depend on the INFO we INFER from Q..
1) since price per loafer is reduced by 20, the earlier price >20..
2) Also 240 is teh total cost, the OLD and REDUCED price must be factor of 240..
3) From th e above two points, the OLD and REDUCED price must be one of 24,30,40,48,60,80,120,240..
4) We have to choose two prices amongst the value above which have a difference of 20..
5) so our ansewr is either 40 and 60 or 60 and 80..
6) if its 40 and 60 .. he earlier purchased 240/60=4 and now can purchase 240/40=6..
the difference is 2, but as per Q its 1..
2) if its 80 and 60 .. he earlier purchased 240/80=3 and now can purchase 240/60=4..
the difference is 1.. this is our answer


This was to explain the procedure ..
but a straight requirement to find the CORRECT answer is..
two pair of factors of 240 equalling 240, with change in one of them by 20 leading to lowering the other factot by 1..

240 =80*3
240=60*4..
so this is the answer
he would do 3..

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Re: A shoe Cobbler charges n dollars [#permalink]

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New post 05 Mar 2016, 07:22
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.




Hi Experts / Bunuel / chetan2u,

First, the approach discussed
240/n=240/(n-20)-1
If I solve this equation I am getting equation as n^2 -20n = 4800
Don't know how to solve further... :roll:

Second, I did this question by creating 2 equations

N= Price of repair
X= No of shoes to be repaired

==> N*X= 240
and (N-20) (X+1) = 240
X= -4 or 3
-4 not possible
So it should be 3.

Question asks How many pair of loafers does he intend to repair tomorrow?

it should be 3+1 = 4

eg---> 80*3= 240
(80-20) * ( 3+1) = 240

so tomorrow he is intended to repair 4 pair of loafers
But, the ans is 3...

Please help....I am totally stucked
What I am doing wrong....
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Re: A shoe Cobbler charges n dollars   [#permalink] 05 Mar 2016, 07:22
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