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# A shoe Cobbler charges n dollars

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Senior Manager
Joined: 27 Jun 2012
Posts: 371
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
A shoe Cobbler charges n dollars  [#permalink]

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Updated on: 04 Jan 2013, 08:29
3
5
00:00

Difficulty:

65% (hard)

Question Stats:

66% (02:43) correct 34% (03:17) wrong based on 233 sessions

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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

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Originally posted by PrashantPonde on 03 Jan 2013, 00:09.
Last edited by PrashantPonde on 04 Jan 2013, 08:29, edited 2 times in total.
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Joined: 02 Sep 2009
Posts: 52385
Re: A shoe Cobbler charges n dollars  [#permalink]

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03 Jan 2013, 01:33
2
3
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.

P.S. Please provide OA's for the questions and tag them correctly.
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Joined: 04 May 2013
Posts: 44
Re: A shoe Cobbler charges n dollars  [#permalink]

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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
Math Expert
Joined: 02 Sep 2009
Posts: 52385
Re: A shoe Cobbler charges n dollars  [#permalink]

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27 Jun 2013, 19:25
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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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
Joined: 02 Sep 2009
Posts: 52385
Re: A shoe Cobbler charges n dollars  [#permalink]

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29 Jun 2013, 11:50
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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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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Posts: 154
Re: A shoe Cobbler charges n dollars  [#permalink]

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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?
Manager
Joined: 26 Feb 2013
Posts: 154
Re: A shoe Cobbler charges n dollars  [#permalink]

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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.

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

Should it be +1 ?
Math Expert
Joined: 02 Sep 2009
Posts: 52385
Re: A shoe Cobbler charges n dollars  [#permalink]

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16 Oct 2013, 10:50
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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16 Oct 2013, 10:50
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.

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

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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!
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Posts: 231
Location: India
Re: A shoe Cobbler charges n dollars  [#permalink]

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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?
Manager
Joined: 20 Apr 2014
Posts: 89
Re: A shoe Cobbler charges n dollars  [#permalink]

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01 Mar 2016, 03:35
Bunuel, can I plug in from answer choices starting with the middle answer choice ?
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Posts: 52385
Re: A shoe Cobbler charges n dollars  [#permalink]

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01 Mar 2016, 04:43
hatemnag wrote:
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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01 Mar 2016, 04:59
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..
he would do 3..

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

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05 Mar 2016, 06:22
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.

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...

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...

What I am doing wrong....
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A shoe Cobbler charges n dollars  [#permalink]

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20 Feb 2017, 09:36
The problem seems relatively straightforward, until we try solving it algebraically. Let's assign x to represent the number of pair of loafers he intends to repair tomorrow. Using the equation for revenue:
nx = 240

Furthermore, reducing his fee by \$20 would result in the need to repair an additional pair of shoes for the same amount of revenue:
(n –20)(x + 1) = 240
Even though the problem is relatively simple to understand, the algebra gets complicated very quickly. Let's switch to a different approach—testing the answer choices:

We're done! Only answer choice C results in the correct amount of revenue. In fact, with practice, you
wouldn't have to fill out the whole table.
Attachments

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

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Re: A shoe Cobbler charges n dollars &nbs [#permalink] 18 Apr 2018, 07:44
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