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### Show Tags

Updated on: 28 Jun 2013, 08:01
1
12
00:00

Difficulty:

(N/A)

Question Stats:

76% (01:33) correct 24% (02:35) wrong based on 74 sessions

### Show Tags

28 Jun 2013, 09:49
10
Hi Trushit,

If the original price of an item is $100 and you increment it by 20%, the final price is$100 + 20/100 * 100 = 100+20 = 120

If you discount the final price of $120 by 20%, we assume it to be$100 but it is not so.

The reason is: $120 - 20/100 * 120 = 120 - 24 =$94

You notice... 20% of 120 is 24 not 20 so you are deducting more than what you actually added hence when you discount by the same value (20%), you wont get the same number.

In question you have posted, the author says - "A dress is marked up by 16 2/3% to make the final price of $140" "marked up" means hiked the price... what you tried to do was "discount" the price by same % on the final price.. which is incorrect. Hence, the problem has to be solved as follows: let x be original price % increase is = 16 2/3% of x = 50/3% of x final price =$ 140

==> x + 50/3 * x% = 140

==> x + 50/300 * x = 140

==> x + x/6 = 140

==> 7x/6 = 140

==> x = 120

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##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 56239
Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] ### Show Tags 28 Jun 2013, 08:19 2 trushit wrote: A dress is marked up $$16\frac{2}{3}%$$ to a final price of$140. What is the original price 3 of the dress?

OA:
120

My concern:
How the answer is 120? According to me the answer should be 140- 16 \frac{2}{3}% x 140 = 116.66

Reference: Chapter 5: FDPs (Manhattan GMAT guide 1: Fractions, Decimals, & Percents)

$$16\frac{2}{3}=\frac{50}{3}$$, thus $$16\frac{2}{3}$$ percent is $$\frac{(\frac{50}{3})}{100}=\frac{1}{6}$$ (the same ways as 10% is 10/100=0.1).

Say the price of the dress is $x, then the markup is 1/6*x, so we have that $$x + \frac{1}{6}*x=140$$ --> $$x=120$$. Hope it's clear. _________________ Manager Joined: 12 Jan 2013 Posts: 145 Re: A dress is marked up 16 2/3% to a final price of$140. What  [#permalink]

### Show Tags

21 Jul 2013, 14:33
Thank you Bunuel, I completely missed the percent...
Intern
Joined: 13 Oct 2011
Posts: 4
A dress is marked up 16 2/3% to a final price of $140. What [#permalink] ### Show Tags 01 Oct 2016, 13:32 1 I have a bit shorter answer. Since, Markup= Selling price- Cost, and (16 2/3 % = 1/6) so, 1/6x =$140- x
1/6 x + x = $140 7/6 x=$140
x= $120 Intern Joined: 11 Mar 2018 Posts: 3 Re: A dress is marked up 16 2/3% to a final price of$140. What  [#permalink]

### Show Tags

01 Apr 2018, 10:57
Could anybody please explain in more detail how to convert 16 2/3 % into 1/6?
Math Expert
Joined: 02 Sep 2009
Posts: 56239

### Show Tags

02 Apr 2018, 14:07
liho wrote:
Could anybody please explain in more detail how to convert 16 2/3 % into 1/6?

$$16\frac{2}{3}=\frac{50}{3}$$.......We need transform percent to fraction:

$$16\frac{2}{3}$$ percent is $$\frac{(\frac{50}{3})}{100}= \frac{50}{3} * \frac{1}{100}= \frac{50}{300} = \frac{1}{6}$$
Director
Joined: 27 May 2012
Posts: 811
Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] ### Show Tags 15 May 2019, 07:24 trushit wrote: A dress is marked up $$16\frac{2}{3}$$% to a final price of$140. What is the original price 3 of the dress?

OA:
120

My concern:
How the answer is 120? According to me the answer should be 140- 16 \frac{2}{3}% x 140 = 116.66

Reference: Chapter 5: FDPs (Manhattan GMAT guide 1: Fractions, Decimals, & Percents)

Thought the question is asking for the original price for 3 of the dresses, hence 120*3 = 360
What is the significance of the 3 ( three ) given in the question?
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