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A dress is marked up 16 2/3% to a final price of $140. What

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A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post Updated on: 28 Jun 2013, 08:01
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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
Please explain.

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

Originally posted by trushit on 28 Jun 2013, 07:11.
Last edited by Bunuel on 28 Jun 2013, 08:01, edited 1 time in total.
Edited the question.
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Re: A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 28 Jun 2013, 09:49
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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

Hope I resolved your concern
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Re: A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 28 Jun 2013, 08:19
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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
Please explain.

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.
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Re: A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 21 Jul 2013, 14:33
Thank you Bunuel, I completely missed the percent...
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A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 01 Oct 2016, 13:32
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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
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Re: A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 01 Apr 2018, 10:57
Could anybody please explain in more detail how to convert 16 2/3 % into 1/6?
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Re: A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 01 Apr 2018, 11:13
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Re: A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 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 \(\frac{(\frac{50}{3})}{100}= \frac{50}{3} * \frac{1}{100}= \frac{50}{300} = \frac{1}{6}\)
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Re: A dress is marked up 16 2/3% to a final price of $140. What  [#permalink]

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New post 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
Please explain.

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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Re: A dress is marked up 16 2/3% to a final price of $140. What   [#permalink] 15 May 2019, 07:24
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