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# A certain article of clothing was discounted during a spec

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Manager
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A certain article of clothing was discounted during a spec [#permalink]

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28 Feb 2013, 05:31
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Difficulty:

25% (medium)

Question Stats:

67% (01:54) correct 33% (01:04) wrong based on 127 sessions

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A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?

A. 50%
B. 33.33%
C. 25%
D. 16.66%
E. 12.5%
[Reveal] Spoiler: OA

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Last edited by Bunuel on 28 Feb 2013, 06:34, edited 2 times in total.
Edited the question.
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Re: A certain article of clothing was discounted during a spec [#permalink]

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28 Feb 2013, 06:37
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Expert's post
emmak wrote:
A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?

A. 50%
B. 33.33%
C. 25%
D. 16.66%
E. 12.5%

Say the original retail price of the item was $200. The price after the first sale = 3/4 *$200 = $150. The price after the second sale = 1/2 *$200 = \$100.

The percent change from the first sale to the second = (150 - 100) / 150 = 1/3 = 33.33%.

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Re: A certain article of clothing was discounted during a spec [#permalink]

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23 Feb 2017, 10:22
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Expert's post
emmak wrote:
A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?

A. 50%
B. 33.33%
C. 25%
D. 16.66%
E. 12.5%

We can let the article of clothing’s original price = x.

Since it was discounted to 3/4 of its original price, the first discounted price was (3/4)x. Since it was discounted further to 1/2 of its original price, the new discounted price is (1/2)x. If we let n = the percent decrease from the first sale to the second sale, we can create the following equation to determine n:

(3/4)(x)[1 - (n/100)] = (1/2)x

(3/4)[1 - (n/100)] = 1/2

Multiplying the entire equation by 4, we have:

3[1 - (n/100)] = 2

Multiplying the entire equation by 100, we have:

3(100 - n) = 200

300 - 3n = 200

3n = 100

n = 33.33 percent

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Re: A certain article of clothing was discounted during a spec [#permalink]

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28 Feb 2013, 05:40
Suppose original retail price = 100.

1st discount = 76 (100 -34)
2nd discount = 50

76 - 50 = 26.

25 % of 76 is 19 & 50 % is 38. therefore, ans should be between them. Thus, B.
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Re: A certain article of clothing was discounted during a spec [#permalink]

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17 Feb 2017, 05:42
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Re: A certain article of clothing was discounted during a spec [#permalink]

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23 Feb 2017, 10:46
emmak wrote:
A certain article of clothing was discounted during a special sale to 3/4 of its original retail price. When the clothing didn't sell, it was discounted even further to 1/2 of its original retail price during a second sale. By what percent did the price of this article of clothing decrease from the first sale to the second sale?

A. 50%
B. 33.33%
C. 25%
D. 16.66%
E. 12.5%

Let Original retail price be 8

Discounted special price is 6

2nd Discounted special price is 4

Thus, the 2nd discount was 2/6*100 = 33.33%

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Re: A certain article of clothing was discounted during a spec   [#permalink] 23 Feb 2017, 10:46
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