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A merchant purchased a jacket for $60 and then determined

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A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post Updated on: 05 Feb 2012, 13:55
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A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?

(A) $0
(B) $3
(C) $4
(D) $12
(E) $15

Originally posted by Sarang on 06 Nov 2010, 13:32.
Last edited by Bunuel on 05 Feb 2012, 13:55, edited 1 time in total.
Edited the question and added the OA
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Re: Profit from a Jacket  [#permalink]

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New post 06 Nov 2010, 20:34
11
5
Sarang wrote:
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?

(A) $0
(B) $3
(C) $4
(D) $12
(E) $15


No, answer A is not correct. Note that we are told that: "markup ... was 25 percent of the selling price".

Step by step:

Let the markup be \($x\), so \(x\) must be 25% of the selling price \(60+x\): \(x=0.25(60+x)\) --> \(x=20\) --> selling price will be \(60+20=80\).

The price after discount of 20% will be \(80*0.8=64\) --> gross profit on the sale will be final selling price - cost of the jacket = \($64 - $60 = $4\).

Answer: C.
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Re: Profit from a Jacket  [#permalink]

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New post 06 Nov 2010, 13:38
1
60*1.25=75
75*0.8=60
60-60=0
the answer is A
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Re: A merchant purchased a jacket for $60 and then determined a selling pr  [#permalink]

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New post 02 Apr 2011, 06:40
Markup = x

x = 0.25(60 + x)

=> 3x/4 = 15

=> x = 20

So SP = 80

But Actual SP = 0.8 * 80 = 64

So profit = $4

Answer - C
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Re: A merchant purchased a jacket for $60 and then determined a selling pr  [#permalink]

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New post 02 Apr 2011, 06:45
Acer86 wrote:
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A) $0
(B) $3
(C) $4
(D) $12
(E) $15


Selling price is sp, so
\(sp=60+0.25*sp\), where \(m*0.25\) is a markup
sp=80
Discounted the sp by 20% means \(sp-0.2sp=0.8sp\)
\(0.8sp=0.8*80=64\)
Gross profit = 64-purchase price = 64-60=4
(C)
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Re: A merchant purchased a jacket for $60 and then determined a selling pr  [#permalink]

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New post 02 Apr 2011, 07:00
Acer86 wrote:
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A) $0
(B) $3
(C) $4
(D) $12
(E) $15


First of all, the question has very ambiguous language. They have to distinguish between marked price and selling price and they fail to do that. This is what the question needs to change:

A merchant purchased a jacket for $60 and then determined a mark-up price that equaled the purchase price of the jacket plus a markup that was 25 percent of the mark-up price. During a sale, the merchant discounted the mark-up price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?

Here, mark up was 25% of mark-up price so purchase price was 75% of mark-up price i.e. purchase price was increased by 33.33% to get mark up price (25 is 33.33% of 75)

\((1 + Mark Up%) * (1 - Discount%)= (1 + Profit%)\)
\((1 + \frac{1}{3})*(1- \frac{1}{5}) = (1 + Profit%)\)
\(Profit% = \frac{1}{15}\)
Hence you get a profit of $1 for every $15 of purchase price. Since purchase price is 4*15, profit will be 4.

For more on the formula and concept of Mark up, discount, check:
http://www.veritasprep.com/blog/2011/02 ... nt-profit/
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Re: A merchant purchased a jacket for $60 and then determined a selling pr  [#permalink]

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New post 02 Apr 2011, 11:14
Actual Cost = $60
SP = Actual Cost + Mark up

= Actual Cost + 25% SP

= 60*100/75

on sale SP = 80/100(60*75/100) = 64

Gross profit = $4

Answer is C
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Re: percentages  [#permalink]

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New post 11 Dec 2011, 20:50
5
This is a bit tricky, it's all in the details.

I suspect you read the question like this:
Merchant purchases jacket for $60
Merchant prices jacket at 25% more than purchase price. 20% more than $60 = $75
Merchant sells jacket at %20 off. 20% off of $75 = $60
Merchant makes $0 because he bought and sold at $60

But the question actually reads like this:
Merchant purchases jacket for $60
Merchant prices jacket at purchase price + 25% of selling price. Note the difference.

Let's break this down.
Selling price = purchase price + 25% of selling price
75% of Selling price = purchase price
Selling price = $60/75% = $80

Now we can finish the question...
Merchant sells jacket at %20 off. 20% off of $80 = $64
Merchant makes $4 because he bought at $60 and sold at $64.

I hope that helps!
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Re: percentages  [#permalink]

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New post 11 Dec 2011, 21:38
2
OA is C
purchase price + 25% selling price= 100% selling price
60+ 25% SP= 100% SP
60= 75% SP

s0 100 % SP =80

now 20 % sale means 20 % of 80 = 16
so he sold the jacket at 80-16 = 64 $
total profit = 64-60 = 4 $
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Re: percentages  [#permalink]

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New post 12 Dec 2011, 08:41
2
Let the cost price is C,selling price is S.
C=60.
S=C+0.25(S)
0.75(S)=C
3/4(S)=60
S=60*4/3=80.
seller gave a discount of 20% on selling price which is 80. 80*1/5=16(discount price)
Selling price -Discount price=80-16=64 (selling price after discount)
Gross profit= selling price after discount- cost price.=64-60=4
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 25 Nov 2013, 22:03
2
Let selling price = x
So, x = 60 + 25x/100
Calculating above, x = 80
Selling price = 80

20% Discount on Selling price = 64
So, profit = 64-60 = 4 Answer = C
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 18 Jul 2015, 00:39
SP = 60 + 0.25SP

SP = 80
20% discount
Discounted SP = 80 * 0.8 = 64

Profit = 4
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 06 Dec 2016, 19:09
PP = purchasing price
SP = selling price

PP=$60
SP=PP+0.25SP --> 0.75SP=0.60 -->SP=$80

20% off SP = 0.80(80) = $64 (price customer paid)

64-60 = $4 profit

C.
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 15 May 2017, 21:28
hey, is this really 700+ level question in gmat?
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 15 May 2017, 22:10
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 15 May 2017, 22:15
Bunuel wrote:
saarthak29 wrote:
hey, is this really 700+ level question in gmat?


The difficulty level is calculated automatically based on the timer stats from the users which attempted the question. So, yes it is a 700-level question.


hey, is it possible to send you private message?
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 15 May 2017, 22:18
saarthak29 wrote:
Bunuel wrote:
saarthak29 wrote:
hey, is this really 700+ level question in gmat?


The difficulty level is calculated automatically based on the timer stats from the users which attempted the question. So, yes it is a 700-level question.


hey, is it possible to send you private message?


If you have a question or query it's better to post directly on the forum.
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 19 May 2017, 05:20
Sarang wrote:
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?

(A) $0
(B) $3
(C) $4
(D) $12
(E) $15


We are given that a jacket was purchased for 60 dollars. The jacket was sold for a price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. We can let the selling price = p, and thus the selling price is 60 + 0.25p. We can create the following equation and solve for p:

p = 60 + 0.25p

Multiply the equation by 4, we have:

4p = 240 + p

3p = 240

p = 80

Since the selling price was then discounted 20%, the discounted price was:

0.8(80) = 64

Thus, the profit on the sale was 64 - 60 = $4.

Answer: C
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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 17 Jun 2017, 22:05
Hello VeritasPrepKarishma,

Firstly, apologies for asking a clarification on an old post!!

I am not able to follow the highlighted part of the solution. I do understand that you have used the successive percentage formula. But unable to understand why is - \((1 + \frac{1}{3})*(1- \frac{1}{5}) = (1 + Profit)\)%?

Can you please explain in a bit more detail.

Thanks in advance!



VeritasPrepKarishma wrote:
Acer86 wrote:
A merchant purchased a jacket for $60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
(A) $0
(B) $3
(C) $4
(D) $12
(E) $15


First of all, the question has very ambiguous language. They have to distinguish between marked price and selling price and they fail to do that. This is what the question needs to change:

A merchant purchased a jacket for $60 and then determined a mark-up price that equaled the purchase price of the jacket plus a markup that was 25 percent of the mark-up price. During a sale, the merchant discounted the mark-up price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?

Here, mark up was 25% of mark-up price so purchase price was 75% of mark-up price i.e. purchase price was increased by 33.33% to get mark up price (25 is 33.33% of 75)

[m](1 + Mark Up%) * (1 - Discount%)= (1 + Profit%)[/m]
\((1 + \frac{1}{3})*(1- \frac{1}{5}) = (1 + Profit%)\)
\(Profit% = \frac{1}{15}\)
Hence you get a profit of $1 for every $15 of purchase price. Since purchase price is 4*15, profit will be 4.


For more on the formula and concept of Mark up, discount, check:
http://www.veritasprep.com/blog/2011/02 ... nt-profit/

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Re: A merchant purchased a jacket for $60 and then determined  [#permalink]

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New post 06 Mar 2018, 13:53
Hi All,

This question is essentially just a "math" question. How you set up the math (and work through the steps) is up to you though (you can use fractions, decimals or percents):

Purchase price = $60
Selling price = $60 + 25% of the Final Price
Final Price = X

$60 + .25X = X
$60 = .75X
$60 = (3/4)(X)

Now, multiply both sides by 4/3
$60(4/3) = (4/3)(3/4)X
$240/3 = (12/12)X
$80 = X

During the sale, the selling price was discounted by 20%

$80 - 20%($80) = Final Selling Price
$80 - 1/5($80) =
$80 - $16 =
$64

The Gross Profit = Final Price - Purchase Price
$64 - $60 = $4

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Re: A merchant purchased a jacket for $60 and then determined &nbs [#permalink] 06 Mar 2018, 13:53

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