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

Question

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

A. 80
B. 90
C. 100
D. 110
E. 120

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)

Bunuel · Accepted Answer

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.

GMATSPARTAN · Answer

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

jennisa · Answer

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

liho · Answer

Could anybody please explain in more detail how to convert 16 2/3 % into 1/6?

Bunuel · Answer

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?

Mo2men · Answer

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}

ScottTargetTestPrep · Answer

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

MathRevolution · Answer

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

ScottTargetTestPrep · Answer

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

Tonkotsu · Answer

X ((100 + \frac{50}{3})/100) = 140.

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

X = 2*20*3 = 120

CrackverbalGMAT · Answer

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

sspiral2556 · Answer

Official answer is not provided.

Bunuel · Answer

There are several unofficial ones there. Is anything still unclear? Have you reviewed the discussion carefully?

sspiral2556 · Answer

Sorry, I mean there is no technical feedback when you try to enter an answer. All the answer choices don't flash red/green when you hit submit.

The answer is indeed available in the discussion.

Krunaal · Answer

Thanks, fixed OA. You can use "Report a problem" button to report such issues to mods.

AnishPatel · Answer

Markup = 16^2/3% = 1/6.
Final Price = (1 + 1/6) × Original = (7/6) × Original.
so,
Original = Final × (6/7)
Original = 140 × (6/7) = 120
Answer = 120 (E)

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

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