Find all School-related info fast with the new School-Specific MBA Forum

It is currently 29 Aug 2014, 02:11

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A retail item is offered at a discount of p percent (where p

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
User avatar
Joined: 07 Feb 2011
Posts: 89
Followers: 0

Kudos [?]: 13 [2] , given: 43

A retail item is offered at a discount of p percent (where p [#permalink] New post 27 Mar 2013, 14:41
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (04:34) correct 38% (01:39) wrong based on 159 sessions
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

A. p+5/1.05
B. p/1.05 +5
C. 1.05p-5
D. p-5/1.05
E. 1.05(p – 5)
[Reveal] Spoiler: OA

_________________

We appreciate your kudos'

Expert Post
3 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627
Followers: 41

Kudos [?]: 560 [3] , given: 135

Premium Member
Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 27 Mar 2013, 20:23
3
This post received
KUDOS
Expert's post
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

p+5/1.05
p/1.05 +5
1.05p-5
p-5/1.05
1.05(p – 5)


Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

5 KUDOS received
Intern
Intern
avatar
Joined: 22 Jan 2010
Posts: 25
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)
Followers: 0

Kudos [?]: 11 [5] , given: 3

Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 27 Mar 2013, 21:51
5
This post received
KUDOS
Let x be the price of the item.
Final price after discount and sales tax = x * (1 - p/100) * 1.05

Let q be the percent discount which would result in the same final price.
Then,
x * (1 - p/100) * 1.05 = x * (1 - q/100)
=> 1.05 - 1.05p/100 = 1 - q/100
=> q/100 = 1.05p/100 - .05
=> q = 1.05p - 5

Hence , option C is correct.
---------------------------------------
Appreciate your KUDOS.
_________________

Please press +1 KUDOS if you like my post.

1 KUDOS received
Manager
Manager
User avatar
Joined: 07 Feb 2011
Posts: 89
Followers: 0

Kudos [?]: 13 [1] , given: 43

Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 28 Mar 2013, 04:24
1
This post received
KUDOS
So I initially approached it the way you all did but messed up the math as I tried to convert the 1.05 into a fraction over 100 on both sides.

Instead to stay within 2:30 I plugged and chugged
Original Price: 100
Discount: 10
Discounted Price: 90

Sales tax on 90 is 4.5. Final price is 94.5

To achieve this price without tax you need a discount of 5.5

The answer choices are nice too for plugging and chugging

p+5/1.05 too big approximately 15/1
p/1.05 +5 too big again
1.05p-5 10.5-5=4.5 exactly
p-5/1.05 5/1.05...slightly smaller than 5 but not by much. Not nearly as big as the denominator bring the value to half way between 4 and 5
1.05(p – 5) More than 5. In fact 5.25

Answer is C
_________________

We appreciate your kudos'

Manager
Manager
avatar
Joined: 30 May 2013
Posts: 193
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 26 [0], given: 72

GMAT ToolKit User
Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 21 Sep 2013, 21:43
mau5 wrote:
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

p+5/1.05
p/1.05 +5
1.05p-5
p-5/1.05
1.05(p – 5)


Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.


Hi,

Please help me with understanding the question?
.
What does the second part of the question states " If the state sales tax were not assessed......"

My understanding is that for text ''if the sales tax were not assessed" mean tax is not charged that means the discounted purchase price would be

Discounted purchase price = 80 i.e. with out the 5% of tax in the discounted purchase price

Please help me.

Thanks in Advance,
Rrsnathan.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22146
Followers: 3412

Kudos [?]: 24976 [1] , given: 2698

Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 23 Sep 2013, 01:50
1
This post received
KUDOS
Expert's post
rrsnathan wrote:
mau5 wrote:
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

p+5/1.05
p/1.05 +5
1.05p-5
p-5/1.05
1.05(p – 5)


Assume p = 20 % and original price = 100. Thus, the discounted purchase price = 80 and the sales tax assessed on this is 5 % = 84. Thus, a 16 % discount on the original retail price would result in the same price. Only option C gives 16 % for p = 20.

C.


Hi,

Please help me with understanding the question?
.
What does the second part of the question states " If the state sales tax were not assessed......"

My understanding is that for text ''if the sales tax were not assessed" mean tax is not charged that means the discounted purchase price would be

Discounted purchase price = 80 i.e. with out the 5% of tax in the discounted purchase price

Please help me.

Thanks in Advance,
Rrsnathan.


Original price = $100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = $84.

The question asks: if the tax were not assessed, what percent discount from the original price ($100) would result in the same final price of $84. The answer is 16%.

Does this make sense?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Manager
Manager
avatar
Joined: 25 Sep 2012
Posts: 204
Followers: 0

Kudos [?]: 57 [1] , given: 135

GMAT ToolKit User CAT Tests
Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 23 Sep 2013, 04:14
1
This post received
KUDOS
manimgoindowndown wrote:
So I initially approached it the way you all did but messed up the math as I tried to convert the 1.05 into a fraction over 100 on both sides.

Instead to stay within 2:30 I plugged and chugged
Original Price: 100
Discount: 10
Discounted Price: 90

Sales tax on 90 is 4.5. Final price is 94.5

To achieve this price without tax you need a discount of 5.5

The answer choices are nice too for plugging and chugging

p+5/1.05 too big approximately 15/1
p/1.05 +5 too big again
1.05p-5 10.5-5=4.5 exactly
p-5/1.05 5/1.05...slightly smaller than 5 but not by much. Not nearly as big as the denominator bring the value to half way between 4 and 5
1.05(p – 5) More than 5. In fact 5.25

Answer is C

Just a small tip...When plugging in always try the easier option first. A and B involve divsion wheresa B and E involve only multiplication
Director
Director
avatar
Joined: 17 Apr 2013
Posts: 514
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT Date: 11-30-2013
GPA: 3.3
Followers: 3

Kudos [?]: 26 [0], given: 239

CAT Tests
Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 28 Oct 2013, 14:53
Original price = $100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = $84.

The question asks: if the tax were not assessed, what percent discount from the original price ($100) would result in the same final price of $84. The answer is 16%.

Does this make sense?

Bunuel,

How have you arrived at this-
Discount = p = 20%.
_________________

Like my post Send me a Kudos :) It is a Good manner.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22146
Followers: 3412

Kudos [?]: 24976 [0], given: 2698

Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 29 Oct 2013, 23:53
Expert's post
honchos wrote:
Original price = $100.
Discount = p = 20%.
Tax = 5%.

Final price = 100*0.8*1.05 = $84.

The question asks: if the tax were not assessed, what percent discount from the original price ($100) would result in the same final price of $84. The answer is 16%.

Does this make sense?

Bunuel,

How have you arrived at this-
Discount = p = 20%.


I assumed it, plugged smart numbers.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1627
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 155 [0], given: 254

GMAT ToolKit User
Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 24 Dec 2013, 11:20
manimgoindowndown wrote:
A retail item is offered at a discount of p percent (where p > 10), with a 5% state sales tax assessed on the discounted purchase price. If the state sales tax were not assessed, what percent discount from the item’s original retail price, in terms of p, would result in the same final price?

A. p+5/1.05
B. p/1.05 +5
C. 1.05p-5
D. p-5/1.05
E. 1.05(p – 5)


Backsolving would be the best approach here using Smart Numbers
Original price = 100
p = 20%
Tax = 5%

Then reduced price after tax $84
So then we need 16% before taxes

Therefore,
Target 16
Input P = 20

Now, it would help if the answer choices are stated clearly as fractions but anyway the approach is clear

Hope it helps
Cheers!
J :)
Manager
Manager
avatar
Joined: 25 Apr 2014
Posts: 92
Followers: 0

Kudos [?]: 11 [0], given: 1187

Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 21 Jul 2014, 11:31
Bunuel,

What do they mean by "If the state sales tax were not assessed" ? I took the final price as 80 thinking we need not include the sales tax to it !
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22146
Followers: 3412

Kudos [?]: 24976 [0], given: 2698

Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 21 Jul 2014, 11:42
Expert's post
maggie27 wrote:
Bunuel,

What do they mean by "If the state sales tax were not assessed" ? I took the final price as 80 thinking we need not include the sales tax to it !


Original price = $100.
Final price = $84.

The question basically asks about the actual discount on the item, which is 16%.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 25 Apr 2014
Posts: 92
Followers: 0

Kudos [?]: 11 [0], given: 1187

Re: A retail item is offered at a discount of p percent (where p [#permalink] New post 21 Jul 2014, 11:53
Bunuel wrote:
maggie27 wrote:
Bunuel,

What do they mean by "If the state sales tax were not assessed" ? I took the final price as 80 thinking we need not include the sales tax to it !


Original price = $100.
Final price = $84.

The question basically asks about the actual discount on the item, which is 16%.



But my doubt is how do we decide that "final price" is 84 which with the applied sales tax or jus 80 which is without sales tax?
What if the "If the state sales tax were not assessed" part is omitted?
Re: A retail item is offered at a discount of p percent (where p   [#permalink] 21 Jul 2014, 11:53
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic The price of an item is discounted 10 percent on day 1 of emmak 2 11 Mar 2013, 22:43
1 Experts publish their posts in the topic If an item is purchased for x percent less than its retail megafan 3 31 Jan 2013, 21:43
Experts publish their posts in the topic P inlander 8 01 Oct 2011, 19:25
A discount retailer... raghavs 2 28 Feb 2010, 09:28
A merchant sells an item at a 20 percent discount, but still mbassmbass04 5 28 Jul 2005, 05:04
Display posts from previous: Sort by

A retail item is offered at a discount of p percent (where p

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.