NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 01:15 It is currently 25 Apr 2024, 01:15
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Decreasing the original price of an item by 25% and then

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
megafan
Manager
Manager
Joined: 28 May 2009
Posts: 139
Own Kudos [?]: 797 [27]
Given Kudos: 91
Location: United States
Concentration: Strategy, General Management
Schools: Booth PT '18 Stern PT Fall'18
GMAT Date: 03-22-2013
GPA: 3.57
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User
Decreasing the original price of an item by 25% and then [#permalink] New post   04 Mar 2013, 08:13
5
Kudos
22
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

43% (02:04) correct 57% (01:46) wrong based on 387 sessions
Hide Show timer Statistics
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
B
mau5
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3092 [5]
Given Kudos: 141
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   04 Mar 2013, 08:26
3
Kudos
2
Bookmarks
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)



Let the initial price be 100. Initial drop is by 25%. This gives 75. Assume z=100%. Thus, the final price now will be, a 100% decrease on 75 = 0. This is equivalent to a 100% decrease on the initial price of 100. Put z = 100%, only option A matches.

A.
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [5]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   04 Mar 2013, 08:24
2
Kudos
3
Bookmarks
Expert Reply
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800


Suppose original Price is X
decreasing by 25%, new price is X (100-25)/100 = 0.75X
Decreasing the new price by z%, new price will be 0.75X * (100-z)/100

= 0.75*(1-(z/100)) * X
original price is decreased by
X - 0.75*(1-(z/100)) * X
= X ( 0.25 + Z*(0.75/100))
= X * 0.25 ( 1 + (3z/100))

So, answer will be A
hope it helps!
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92904
Own Kudos [?]: 618874 [2]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   04 Mar 2013, 12:00
2
Kudos
Expert Reply
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800


Similar question to practice from OG: increasing-the-original-price-of-an-article-by-15-percent-127086.html

Hope it helps.
User avatar
vikrantgulia
Manager
Manager
Joined: 18 Oct 2013
Posts: 62
Own Kudos [?]: 266 [0]
Given Kudos: 36
Location: India
Concentration: Technology, Finance
Schools: Duke '16 Schulich '15 Neeley '15 Erasmus '16 HKUST '16 Johnson '16 HSG '15 Marshall '16 Kelley '16 Insead '14 McDonough '16 Tepper '16 IE April'15
GMAT 1: 580 Q48 V21
GMAT 2: 530 Q49 V13
GMAT 3: 590 Q49 V21
WE:Information Technology (Computer Software)
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   10 Nov 2013, 11:42
Let z=50%

so equivalent change must be 62.5% .So answer is A
User avatar
S
SVaidyaraman
Director
Director
Joined: 17 Dec 2012
Posts: 589
Own Kudos [?]: 1519 [1]
Given Kudos: 20
Location: India
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   10 Nov 2013, 17:07
1
Bookmarks
Expert Reply
Bunuel wrote:
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800


Similar question to practice from OG: increasing-the-original-price-of-an-article-by-15-percent-127086.html

Hope it helps.



An easy approach is to assume a convenient value for z.

1. Let it be 20%
2. The value is first reduced by 25%. So it becomes 75%
3. The above value is then reduced by 20%. So it becomes 60%
4. So the equivalent reduction is 40%

Choice A gives the same equivalent percentage i.e., 0.25(1 + 3*20/100) = 0.25 (1+0.6) = 0.4 = 40%.

If you want to confirm and have the time, you can test for 1 more value of z.
avatar
Moumila
Intern
Intern
Joined: 04 May 2015
Posts: 2
Own Kudos [?]: 2 [2]
Given Kudos: 0
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   18 May 2015, 05:13
2
Kudos
For two successive increase/decrease , say a% and b%
the total effective increase/decrease will be a+b+ab/100

So here the total decrease will be = -25 -z +25z/100 (for price decrease the sign will be -ve)
= -[25 + 75z/100]
= -[.25+ .75z/100] % (converting to Percentage decrease)
= - .25[1+3z/100] % (-ve sign implies decrease in price)


So the total percentage decrease is .25[1+3z/100] ----- option A
User avatar
S
HARRY113
Manager
Manager
Joined: 06 Aug 2015
Posts: 55
Own Kudos [?]: 54 [0]
Given Kudos: 83
Concentration: General Management, Entrepreneurship
Schools: LBS '22 INSEAD Jan'21 Intake IMD '21 Cambridge '22 Said '22
GMAT Date: 10-30-2016
GRE 1: Q160 V135
GPA: 3.34
WE:Programming (Computer Software)
Send PM
GMAT ToolKit User Reviews Badge
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   11 Jul 2016, 10:22
Simple!

If A is decreased by x% =>
outcome = A (1 - (x/100) ).

use this approach to solve this.

You will end at option A.
User avatar
G
Madhavi1990
Senior Manager
Senior Manager
Joined: 15 Jan 2017
Posts: 259
Own Kudos [?]: 85 [0]
Given Kudos: 932
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   10 Dec 2017, 11:10
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) 0.25(1+3z/100)

(B) 0.25(1+z/100)

(C) 0.25(1−3z/100)

(D) 0.75(1−z/100)

(E) 0.75(1+3z/100)

Done by POE. So 75 +z/100(75) = 75 [1 + z/100] approx 1/3rd and a little more

So only A fits 0.25 *3z/100 +1 as closest to 1/3rd plus one. Rest do not add up.

Kudos if the answer was useful :)
User avatar
L
stne
SVP
SVP
Joined: 27 May 2012
Posts: 1680
Own Kudos [?]: 1422 [0]
Given Kudos: 632
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   15 Apr 2018, 08:09
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800


can anybody help, are we looking for the percentage decrease or are we looking the amount of decrease ?
Let initial amount be 100 after 25% discount we get 75 then z% discount will give \(\frac{(100-z)}{100}*75\) = \(\frac{100-z}{4}*3\)

So equivalent discount is
100 -\(\frac{300+3z}{4}\)
\(\frac{100+3z}{4}\)

Well as option A after simplification states \(\frac{100+3z}{400}\)

So why this difference ?

( Guaranteed Kudos for anyone who can help with this, thank you)
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14822
Own Kudos [?]: 64907 [1]
Given Kudos: 426
Location: Pune, India
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   16 Apr 2018, 05:33
1
Kudos
Expert Reply
stne wrote:
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800


can anybody help, are we looking for the percentage decrease or are we looking the amount of decrease ?
Let initial amount be 100 after 25% discount we get 75 then z% discount will give \(\frac{(100-z)}{100}*75\) = \(\frac{100-z}{4}*3\)

So equivalent discount is
100 -\(\frac{300+3z}{4}\)
\(\frac{100+3z}{4}\)

Well as option A after simplification states \(\frac{100+3z}{400}\)

So why this difference ?

( Guaranteed Kudos for anyone who can help with this, thank you)


Responding to a pm:

You can easily figure this out by taking numbers instead of variables to understand the concept here:

Say there are 2 discounts - 25% and 20%
Question: What is the overall discount? (it will be in percentage terms only since no actual numbers are provided)

If you assume $100 and then arrive at $75 and then at 80/100 * $75 = $60

Then using the logic used by you above, you say this is $100 - $60 = $40

This 40 is your (100 + 3z)/4

But note that the answer cannot be 40. The overall discount will be in terms of percentage. We say that the discount is 40 per cent i.e. 40/100 i.e. 40%.

So it will be (100 + 3z)/400
User avatar
L
stne
SVP
SVP
Joined: 27 May 2012
Posts: 1680
Own Kudos [?]: 1422 [0]
Given Kudos: 632
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   16 Apr 2018, 06:20
VeritasPrepKarishma wrote:
stne wrote:
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800


can anybody help, are we looking for the percentage decrease or are we looking the amount of decrease ?
Let initial amount be 100 after 25% discount we get 75 then z% discount will give \(\frac{(100-z)}{100}*75\) = \(\frac{100-z}{4}*3\)

So equivalent discount is
100 -\(\frac{300+3z}{4}\)
\(\frac{100+3z}{4}\)

Well as option A after simplification states \(\frac{100+3z}{400}\)

So why this difference ?

( Guaranteed Kudos for anyone who can help with this, thank you)


Responding to a pm:

You can easily figure this out by taking numbers instead of variables to understand the concept here:

Say there are 2 discounts - 25% and 20%
Question: What is the overall discount? (it will be in percentage terms only since no actual numbers are provided)

If you assume $100 and then arrive at $75 and then at 80/100 * $75 = $60

Then using the logic used by you above, you say this is $100 - $60 = $40

This 40 is your (100 + 3z)/4

But note that the answer cannot be 40. The overall discount will be in terms of percentage. We say that the discount is 40 per cent i.e. 40/100 i.e. 40%.

So it will be (100 + 3z)/400


Thank you , for clearing this up, Karishma. Without your guidance it would really have been difficult to understand this. Your awesomeness simply dazzles!
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6272 [1]
Given Kudos: 1646
Send PM
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   17 Apr 2018, 16:10
1
Kudos
Expert Reply
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)


We can let the original price be 100 and z be 20. Thus the final price is:

100(75/100)(1 - 20/100) = 75(80/100) = 60

We see that the price has reduced by 40%.

Now let’s analyze the answer choices:

A) 0.25(1 + 3z/100)

0.25(1 + 3(20)/100) = 0.25(1.6) = 0.4 = 40%

We see that choice A could be the correct answer. We also see that in choices B, C and E couldn’t possibly be the correct answer. Let’s see if choice D also yield 40% (if it doesn’t, then choice A MUST be the correct answer; if it does, then we have to use another number for z).

D) 0.75(1 - z/100)

0.75(1 - 20/100) = 0.75(0.8) = 0.6 ≠ 40%

Answer: A
avatar
B
vp1989
Intern
Intern
Joined: 07 Aug 2018
Posts: 4
Own Kudos [?]: 29 [0]
Given Kudos: 21
Location: India
WE:General Management (Manufacturing)
Send PM
GMAT ToolKit User
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   09 Aug 2020, 10:28
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800


One simple approach is to use the formula of equivalent percentage.
If one discount is A% and subsequent discount is B%, then equivalent discount is
\(Eq. Dis. percent= A+B -\frac{AB}{100}\)
So, \(Eq. dis. percent= 25+z-\frac{25z}{100}\)
\( =25+\frac{75z}{100}\)
\( =25(1+\frac{3z}{100})\)
Since the question is asking final value then,
\(Final value =\frac{25}{100}(1+\frac{3z}{100})\)
\(Final value =0.25(1+\frac{3z}{100})\)............ hence (A)
User avatar
S
samarpan.g28
Manager
Manager
Joined: 08 Dec 2023
Posts: 202
Own Kudos [?]: 29 [0]
Given Kudos: 1164
Location: India
Concentration: Strategy, Operations
Schools: HEC Montreal ISB IIM Rotman HEC INSEAD Jan'25 intake
GPA: 4
WE:Engineering (Tech)
Send PM
Decreasing the original price of an item by 25% and then [#permalink] New post   03 Mar 2024, 22:28
 
megafan wrote:
Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by

(A) \(0.25(1 + \frac{3z}{100})\)

(B) \(0.25(1 + \frac{z}{100})\)

(C) \(0.25(1 - \frac{3z}{100})\)

(D) \(0.75(1 - \frac{z}{100})\)

(E) \(0.75(1 + \frac{3z}{100})\)

Source: Gmat Hacks 1800

­I believe, that assuming an initial selling price and a value of z will help to find the answer faster. I was thinking of an alternate approach by using the consecutive discount method, and this seems easier. I assumed the selling price as 100 and z as 100, and found a value there. Then put the same in options and (A) was a match.­ However, if we use the later method then overall discount becomes 25+z -25z/100 = 25(1+3z/100). So overall decrease will be by 25/100 * (1+3z/100) = 0.25(1+3z/100). Option (A) is correct.
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5343
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: Decreasing the original price of an item by 25% and then [#permalink] New post   03 Mar 2024, 22:50
megafan
Asked: Decreasing the original price of an item by 25% and then decreasing the new price by z% is equivalent to decreasing the original price by
Let the original price of an item be x.
Decreasing the original price of an item by 25% results in price = .75x
Then decreasing the new price by z% results in price = .75x(1-z/100)

Let the price be decreased by y in total
\(.75x(1-\frac{z}{100}) = x(1 - y)\)
\(1-y = .75(1-\frac{z}{100})\)
\(y = 1 - .75(1-\frac{z}{100}) = .25 + \frac{.75z}{100} = .25(1+\frac{3z}{100})\)

IMO A
­
GMAT Club Bot
gmatclubot
Re: Decreasing the original price of an item by 25% and then [#permalink]
03 Mar 2024, 22:50
Moderators:
Bunuel
Math Expert
92901 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions