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# What percentage loss will a merchant incur if he marks his goods up by

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Intern
Joined: 04 Oct 2014
Posts: 11
GMAT 1: 650 Q44 V35
What percentage loss will a merchant incur if he marks his goods up by  [#permalink]

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Updated on: 04 Nov 2014, 09:28
4
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:54) correct 26% (02:02) wrong based on 109 sessions

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What percentage loss will a merchant incur if he marks his goods up by x% over his cost price and then offers a discount of x% on his selling price?

A. 0 %
B. 2x/100 %
C. x^2/100 %
D. x %
E. 2x %

Originally posted by jgk on 04 Nov 2014, 05:19.
Last edited by jgk on 04 Nov 2014, 09:28, edited 1 time in total.
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Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: What percentage loss will a merchant incur if he marks his goods up by  [#permalink]

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04 Nov 2014, 08:58
2
jgk wrote:
What percentage loss will a merchant incur if he marks his goods up by x% over his cost price and then offers a discount of x% on his selling price?

A. 0 %
B. 2x/100 %
C. x^2/100 %
D. x %
E. 2x %

Taking smart numbers:

Let, C.P = 100$and X = 20% over C.P then Mark Up = 120$

After discount of X%

S.P= 80% of 120
S.P = 96$Therefore Loss is 4$ and hence Loss in % = 4%

Plugging numbers in options.
A. 0 % ---------------------------Not true because loss is 4%

B. 2x/100 % --------------------2*20/100 = 0.4%. Hence Not True

C. x^2/100 % ------------------ 20^2/100 = 4%. True

D. x % --------------------------- 20%. Hence Not True

E. 2x % -------------------------- 2*20 = 40%. Hence Not True

Intern
Joined: 04 Oct 2014
Posts: 11
GMAT 1: 650 Q44 V35
Re: What percentage loss will a merchant incur if he marks his goods up by  [#permalink]

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04 Nov 2014, 09:32
1
Hi Ashishmathew01081987 I also agree with your approach. The OA is C indeed!!
Intern
Joined: 17 Oct 2014
Posts: 28
Re: What percentage loss will a merchant incur if he marks his goods up by  [#permalink]

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04 Nov 2014, 15:15
1
1
Ashish's method is a very efficient one; I recommend taking advantage of the answer choices and multiple choice format whenever possible. Well done!

I'll add a little bit of math background, since I know that many students prefer to understand the underlying mathematics.

The question asks for the loss suffered by the author. That is to say, subtract from 100% the final percentage price after applying the x% markup. and the x% discount.

To find the price after the x% markup and x% discount, multiply: [1 + (x / 100)] * [1 - (x / 100)].

This equation looks a little messy, but it's actually a classic quadratic. (a + b) (a - b) = a^2 - b^2. So, the multiplier for the sale price is:
[1 - (x/100)^2]

Multiply by 100% to convert to percent, then subtract from 100%, to determine the loss:
100% - [1 - (x/100)^2] * 100%
100% - 100% - [(x^2) / 100]%
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Re: What percentage loss will a merchant incur if he marks his goods up by  [#permalink]

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13 Nov 2014, 02:39
2
Actually in such problems, whenever we add x% & then subtract x% from values, we end back in a quadratic equation>>

Original Price >> 100

Total >> 100+x

Subtract x% >> $$(100+x)* \frac{x}{100}$$

Coming back to the problem....

In the OA given, only quadratic option given is C

Had there been more addition of x%, discount of x%, power of x would increase.....................

It may not be applicable here directly, however there is a formula for liquid displacement from where I took hint in solving this......

$$Final Concentration = Initial Concentration ( 1 - \frac{replace}{Total})^{Number of replacements}$$
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Re: What percentage loss will a merchant incur if he marks his goods up by  [#permalink]

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01 Apr 2018, 14:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What percentage loss will a merchant incur if he marks his goods up by   [#permalink] 01 Apr 2018, 14:41
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