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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 28 Jun 2013, 07:11
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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:
[Reveal] Spoiler:
120


My concern:
[Reveal] Spoiler:
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)

Last edited by Bunuel on 28 Jun 2013, 08:01, edited 1 time in total.
Edited the question.

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Manhattan GMAT Discount CodesEMPOWERgmat Discount CodesMagoosh Discount Codes
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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:
[Reveal] Spoiler:
120


My concern:
[Reveal] Spoiler:
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 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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FDPs: how is 16*(2/3) = 1/6? [#permalink]

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New post 21 Jul 2013, 13:55
Hi!

Im doing the FDPs book by MGMAT currenty and right at the end of ch 5, this pops up:

Quote:
Question: "A dress is marked up \(16\frac{2}{3}%\) to a final price of $140. What is the original price of the dress?"

Answer: From the previous page, you know that \(16\frac{2}{3}%\) is equivalent to \(\frac{1}{6}\). Thus, adding \(\frac{1}{6}\) of a number to 3 itself is the same thing as multiplying by \(1 + \frac{1}{6} = \frac{7}{6}\). The original price is $120


On what planet is 16(2/3) = 1/6?? What am I missing. If anything, 16(2/3) = 50/3 = 100/6... Or am I completelty missunderstanding?

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Re: FDPs: how is 16*(2/3) = 1/6? [#permalink]

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New post 21 Jul 2013, 13:58
aeglorre wrote:
Hi!

Im doing the FDPs book by MGMAT currenty and right at the end of ch 5, this pops up:

Quote:
Question: "A dress is marked up \(16\frac{2}{3}%\) to a final price of $140. What is the original price of the dress?"

Answer: From the previous page, you know that \(16\frac{2}{3}%\) is equivalent to \(\frac{1}{6}\). Thus, adding \(\frac{1}{6}\) of a number to 3 itself is the same thing as multiplying by \(1 + \frac{1}{6} = \frac{7}{6}\). The original price is $120


On what planet is 16(2/3) = 1/6?? What am I missing. If anything, 16(2/3) = 50/3 = 100/6... Or am I completelty missunderstanding?


Merging topics. Please refer to the posts above.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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
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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Re: A dress is marked up 16 2/3% to a final price of $140. What   [#permalink] 10 Oct 2017, 06:48
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