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

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trushit
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A dress is marked up 16 2/3% to a final price of $140. What [#permalink] 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:
Show Spoiler
120


My concern:
Show 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)

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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Bunuel
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] 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:
Show Spoiler
120


My concern:
Show 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] 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] New post   05 Oct 2020, 07:40
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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:
Show Spoiler
120


My concern:
Show 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)

Solution:

Let the original price of the dress be p. We can create the equation:

p * (1 + (16 ⅔)/100) = 140

p * (1 + 1/6) = 140

p * 7/6 = 140

p = 140 * 6/7 = $120

Answer: $120
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A dress is marked up 16 2/3% to a final price of $140. What [#permalink] 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] New post   01 Apr 2018, 10:57
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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] New post   01 Apr 2018, 11:13
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liho wrote:
Could anybody please explain in more detail how to convert 16 2/3 % into 1/6?


\(16\frac{2}{3}=\frac{50}{3}\), 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).

Does this make sense?
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] New post   28 Dec 2021, 21:59
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If you remember the percentage -fraction table , this question would be very easy for you.

We know that 1/3 corresponds to 33.33%

Also , taking half on both sides, 1/6 corresponds to 16.66% which is same as 16 2/3 %

Let the original price be x and it is marked up 16 2/3% to a final price of $140.

X + 1/6 X = 140

7X/6 = 140

X =120
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] New post   21 Jul 2013, 14:33
Thank you Bunuel, I completely missed the percent...
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] 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] 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:
Show Spoiler
120


My concern:
Show 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)



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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A dress is marked up 16 2/3% to a final price of $140. What [#permalink] New post   17 Jun 2020, 14:26
16 2/3 % marked up = (50/3)*(1/100) increase = 1/6 => Multiplier = 1+1/6 = 7/6.

Let x be the original price of 1 dress.
7/6 x=140
x=(6*140)/7=120
So, 3x=360. (I'm not sure whether the question asked for original price of 1 dress or 3..., or the number "3" was just a typo?! :D)

Answer: $360 (for 3 dresses).
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] New post   05 Oct 2020, 08:21
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Let the original price of the dress be 'x'.

Marked up the price by \(\frac{50}{3}\)% or \(\frac{350}{300}\) which makes it to 140.

=> x * \(\frac{350}{300}\) = 140

=> x = 120

Answer 120
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] New post   09 Oct 2020, 10:05
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Bunuel wrote:
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:
Show Spoiler
120



Solution:

Let the original price of the dress be p. We can create the equation:

p * (1 + (16 ⅔)/100) = 140

p * (1 + 1/6) = 140

p * 7/6 = 140

p = 140 * 6/7 = $120

Answer: $120
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] New post   12 Nov 2020, 21:31
\(X ((100 + \frac{50}{3})/100) = 140.\)

\(X = \frac{140(100)(3)}{(350)}\)

\(X = 2*20*3 = 120\)
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Re: A dress is marked up 16 2/3% to a final price of $140. What [#permalink] New post   25 Apr 2023, 13:24
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