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28 Jun 2017, 02:05
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:27) correct 44% (02:42) wrong based on 66 sessions

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A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now? (A) 100(1 − 0.2)^2 (B) 100 (1 − 0.4) (C) 100(1 − 0.4)^2 (D) 100 (1 − 0.8) (E) 100 (1 − 0.96) _________________ Director Joined: 04 Dec 2015 Posts: 751 Location: India Concentration: Technology, Strategy WE: Information Technology (Consulting) A coat’s original price of$112 was reduced by 20 percent for a sale.  [#permalink]

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Updated on: 29 Jun 2017, 11:53
Bunuel wrote:
A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now? (A) 100(1 − 0.2)^2 (B) 100 (1 − 0.4) (C) 100(1 − 0.4)^2 (D) 100 (1 − 0.8) (E) 100 (1 − 0.96) $$P$$ = Original amount $$= 112$$. Let the first discount be $$r_1$$ and second discount be $$r_2$$. Price after $$2$$ successive discounts $$= (\frac{100 - r_2}{100} ) * (\frac{100 + r_1}{100} ) * P$$ Required Price $$= (\frac{100 - 20}{100}) * (\frac{100 + 20}{100}) * 112$$ Required Price $$= \frac{80}{100} * \frac{120}{100} * 112 = 107.52$$ Difference between original and final price $$= 112 - 107.52 = 4.48$$ Required percent $$= \frac{4.48}{112} * 100 = 4$$%. Lets check options to find $$4$$%. (E) $$100(1 − 0.96) = 100 (0.04) = 4$$%. Answer (E)... Originally posted by sashiim20 on 28 Jun 2017, 02:45. Last edited by sashiim20 on 29 Jun 2017, 11:53, edited 2 times in total. Senior Manager Joined: 28 May 2017 Posts: 283 Concentration: Finance, General Management A coat’s original price of$112 was reduced by 20 percent for a sale.  [#permalink]

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28 Jun 2017, 02:59
1
Bunuel wrote:
A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now? (A) 100(1 − 0.2)^2 (B) 100 (1 − 0.4) (C) 100(1 − 0.4)^2 (D) 100 (1 − 0.8) (E) 100 (1 − 0.96) Price is first reduced by 20%, so price of coat = 0.80 x Coat Price Price is then increased by 20%, so price of coat = 1.2 x 0.80 x Coat Price = 0.96 x Coat Price = 96% of Coat Price Hence Answer E _________________ If you like the post, show appreciation by pressing Kudos button Senior SC Moderator Joined: 22 May 2016 Posts: 2766 A coat’s original price of$112 was reduced by 20 percent for a sale.  [#permalink]

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29 Jun 2017, 11:38
Bunuel wrote:
A coat’s original price of $112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now? (A) 100(1 − 0.2)^2 (B) 100 (1 − 0.4) (C) 100(1 − 0.4)^2 (D) 100 (1 − 0.8) (E) 100 (1 − 0.96) Hmm. I got B. I think I might be confused. Discount = .8 Subsequent price increase = 1.2 (.8) * (1.2) = (.96) (.96) * (112) =$107.52

That matches other answers. But if 100 equals the original, and the original is multiplied by (.96), shouldn't it be Answer B?

100 (1 − 0.4) = (100)(.96), or 96% of original price. In bold above, I multiplied price by .96 and got the correct end figure.

What am I missing?
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Joined: 15 Mar 2015
Posts: 111
Re: A coat’s original price of $112 was reduced by 20 percent for a sale. [#permalink] ### Show Tags 29 Jun 2017, 11:49 1 genxer123 wrote: Bunuel wrote: A coat’s original price of$112 was reduced by 20 percent for a sale. If the sale price was then increased by 20 percent, which of the following, expresses the single percent change, which when applied to the original price of the coat, would result in the same final price of the coat now?

(A) 100(1 − 0.2)^2
(B) 100 (1 − 0.4)
(C) 100(1 − 0.4)^2
(D) 100 (1 − 0.8)
(E) 100 (1 − 0.96)

Hmm. I got B. I think I might be confused.

Discount = .8
Subsequent price increase = 1.2

(.8) * (1.2) = (.96)

(.96) * (112) = $107.52 That matches other answers. But if 100 equals the original, and the original is multiplied by (.96), shouldn't it be Answer B? 100 (1 − 0.4) = (100)(.96), or 96% of original price. In bold above, I multiplied price by .96 and got the correct end figure. What am I missing? They asked for percent change, not percent of original price. Posted from my mobile device Posted from my mobile device _________________ I love being wrong. An incorrect answer offers an extraordinary opportunity to improve. Senior SC Moderator Joined: 22 May 2016 Posts: 2766 Re: A coat’s original price of$112 was reduced by 20 percent for a sale.  [#permalink]

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29 Jun 2017, 12:00
MarkusKarl wrote:
genxer123 wrote:

[107.52] matches other answers. But if 100 equals the original, and the original is multiplied by (.96), shouldn't it be Answer B?

100 (1 − 0.4) = (100)(.96), or 96% of original price. In bold above, I multiplied price by .96 and got the correct end figure.

What am I missing?

They asked for percent change, not percent of original price.

MarkusKarl whose screen name makes me grin, thank you! What a dumb mistake! Lesson learned.
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VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1008
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
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29 Jun 2017, 12:34
drop in the price of coat by 20 % results in a price of 0.8*112 (1-0.2=0.8)
subsequent 20% increase results in a price of 1.2 * 0.8 * 112 (1+0.2=1.2)

the final price is thus 0.96 *112 = 107.48 (i.e 96% of the original price implying a 4% decrease)

Answer to the question would be 100(1-0.96) i.e (E)
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29 Jun 2017, 14:14
112*0.80=89.6
89.6*1.20=107.5
difference is of 4.5 so
{4.5/112}=0.04
ans=e
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16 Sep 2018, 22:08
take x = 100
so 100*4/5*6/5 = 96
so there is 4% change