GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 25 May 2019, 02:06

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A coat’s original price of $112 was reduced by 20 percent for a sale.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55271
A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

Show Tags

New post 28 Jun 2017, 02:05
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

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)

_________________
Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 751
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

Show Tags

New post 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
Senior Manager
avatar
G
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

New post 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
avatar
V
Joined: 22 May 2016
Posts: 2766
A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

Show Tags

New post 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
Manager
User avatar
B
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

New post 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
avatar
V
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

New post 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
VP
User avatar
D
Status: Learning
Joined: 20 Dec 2015
Posts: 1008
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Reviews Badge CAT Tests
Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

Show Tags

New post 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
Intern
avatar
B
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

New post 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)
Manager
Manager
User avatar
B
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

New post 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
Intern
avatar
B
Joined: 06 Mar 2016
Posts: 1
GMAT 1: 670 Q42 V40
Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

Show Tags

New post 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
avatar
V
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

New post 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! 8-)
_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.
Manager
Manager
avatar
B
Joined: 29 Jul 2018
Posts: 114
Concentration: Finance, Statistics
GMAT 1: 620 Q45 V31
GMAT ToolKit User
Re: A coat’s original price of $112 was reduced by 20 percent for a sale.  [#permalink]

Show Tags

New post 16 Sep 2018, 22:08
take x = 100
so 100*4/5*6/5 = 96
so there is 4% change
GMAT Club Bot
Re: A coat’s original price of $112 was reduced by 20 percent for a sale.   [#permalink] 16 Sep 2018, 22:08
Display posts from previous: Sort by

A coat’s original price of $112 was reduced by 20 percent for a sale.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.