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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:
My concern:
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)
Please explain.
Reference: Chapter 5: FDPs (Manhattan GMAT guide 1: Fractions, Decimals, & Percents)
28 Jun 2013, 08:19
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trushit
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:
My concern:
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)
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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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
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
)
