May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th. Jun 01 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55271

A coat’s original price of $112 was reduced by 20 percent for a sale.
[#permalink]
Show Tags
28 Jun 2017, 02:05
Question Stats:
56% (02:27) correct 44% (02:42) wrong based on 66 sessions
HideShow timer Statistics
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)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



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]
Show Tags
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]
Show Tags
28 Jun 2017, 02:59
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]
Show Tags
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?
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.



Manager
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
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 devicePosted 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]
Show Tags
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.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.



VP
Status: Learning
Joined: 20 Dec 2015
Posts: 1008
Location: India
Concentration: Operations, Marketing
GPA: 3.4
WE: Engineering (Manufacturing)

Re: A coat’s original price of $112 was reduced by 20 percent for a sale.
[#permalink]
Show Tags
29 Jun 2017, 12:30
Imo 112*.8*1.2=.96*112 Required percentage will be 4 percent reduction thus E Sent from my ONE E1003 using GMAT Club Forum mobile app
_________________
Please give kudos if you found my answers useful



Intern
Joined: 01 May 2017
Posts: 28

Re: A coat’s original price of $112 was reduced by 20 percent for a sale.
[#permalink]
Show Tags
29 Jun 2017, 12:34
drop in the price of coat by 20 % results in a price of 0.8*112 (10.2=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(10.96) i.e (E)



Manager
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, 13:19
genxer123 wrote: 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. Dumb indeed. I did the same thing Is it the name or the picture? Posted from my mobile device
_________________
I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.



Intern
Joined: 06 Mar 2016
Posts: 1

Re: A coat’s original price of $112 was reduced by 20 percent for a sale.
[#permalink]
Show Tags
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



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]
Show Tags
29 Jun 2017, 16:44
MarkusKarl wrote: genxer123 wrote: MarkusKarl whose screen name makes me grin, thank you! What a dumb mistake! Lesson learned. Dumb indeed. I did the same thing Is it the name or the picture? MarkusKarl It's both. In a good way! One of my degrees in in political economy, so the name made me grin fondly. Then I saw the picture  I so want a cool picture  and the picture is both not what I was expecting, which made me grin, and cool/adorable, which made me grin. Both name and pic are keepers!
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.



Manager
Joined: 29 Jul 2018
Posts: 114
Concentration: Finance, Statistics

Re: A coat’s original price of $112 was reduced by 20 percent for a sale.
[#permalink]
Show Tags
16 Sep 2018, 22:08
take x = 100 so 100*4/5*6/5 = 96 so there is 4% change




Re: A coat’s original price of $112 was reduced by 20 percent for a sale.
[#permalink]
16 Sep 2018, 22:08






