Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 07 Feb 2011
Posts: 95

A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
27 Mar 2013, 15:41
Question Stats:
63% (02:14) correct 37% (01:33) wrong based on 516 sessions
HideShow timer Statistics
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. 1.05p5 D. p5/1.05 E. 1.05(p – 5)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
We appreciate your kudos'




Intern
Joined: 22 Jan 2010
Posts: 24
Location: India
Concentration: Finance, Technology
GPA: 3.5
WE: Programming (Telecommunications)

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
27 Mar 2013, 22:51
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.




Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 614

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
27 Mar 2013, 21:23
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 1.05p5 p5/1.05 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 notDeep Dive Inequality
Hit and Trial for Integral Solutions



Manager
Joined: 07 Feb 2011
Posts: 95

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
28 Mar 2013, 05:24
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 1.05p5 10.55=4.5 exactly p5/1.05 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
Joined: 30 May 2013
Posts: 164
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
21 Sep 2013, 22:43
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 1.05p5 p5/1.05 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.



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
23 Sep 2013, 02:50
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 1.05p5 p5/1.05 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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Current Student
Joined: 25 Sep 2012
Posts: 263
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34

A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
Updated on: 03 Oct 2014, 00:35
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 1.05p5 10.55=4.5 exactly p5/1.05 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,B and D involve divsion whereas C and E involve only multiplication.
Originally posted by b2bt on 23 Sep 2013, 05:14.
Last edited by b2bt on 03 Oct 2014, 00:35, edited 1 time in total.



Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 520
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
28 Oct 2013, 15:53
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. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
30 Oct 2013, 00:53



SVP
Joined: 06 Sep 2013
Posts: 1820
Concentration: Finance

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
24 Dec 2013, 12:20
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. 1.05p5 D. p5/1.05 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
Joined: 25 Apr 2014
Posts: 126

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
21 Jul 2014, 12:31
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 !



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
21 Jul 2014, 12:42



Manager
Joined: 25 Apr 2014
Posts: 126

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
21 Jul 2014, 12:53
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?



Intern
Joined: 05 Feb 2014
Posts: 15
Location: India
Concentration: Human Resources, General Management
GPA: 3.33

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
18 Jun 2015, 02:47
Bunuel wrote: 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. Hi Bunnuel, if 5% on 80 is assessed as sales tax then it should be 804 right? why is it 80+4?



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
18 Jun 2015, 03:28



Senior Manager
Joined: 03 Apr 2013
Posts: 284
Location: India
Concentration: Marketing, Finance
GPA: 3

A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
11 Jul 2016, 06:19
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. 1.05p5 D. p5/1.05 E. 1.05(p – 5) When we usually talk about taxes being applicable..they are applicable on both the Marked Price and the Discounted Price. The question should state that state sales tax is assessed on what and on what its not...ambiguous wording..
_________________
Spread some love..Like = +1 Kudos



Intern
Joined: 13 Jun 2016
Posts: 19

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
23 Nov 2016, 20:41
Understand the right answer is to plug in smart numbers. But could someone please show step by step on how to solve this algebraically? I can't seem to be able to get the right answer. Any help much appreciated ! Bunuel



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1196
Location: India
WE: Engineering (Other)

A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
13 Apr 2018, 16:40
Bunuel niks18 chetan2uQuote: 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?
Quote: 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 Let us say original price is 100 since i am dealing with %tages and discounts. I can have all sort of combinations from : 100 * 1.07 * 1.05 to 100*1.02*1.05 In a PS problem, do I not need an unique value to proceed from here?
_________________
It's the journey that brings us happiness not the destination.



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1213
Location: India
GPA: 3.82

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
14 Apr 2018, 18:55
adkikani wrote: Bunuel niks18 chetan2uQuote: 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?
Quote: 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 Let us say original price is 100 since i am dealing with %tages and discounts. I can have all sort of combinations from : 100 * 1.07 * 1.05 to 100*1.02*1.05In a PS problem, do I not need an unique value to proceed from here? Hi adkikaniCan you clarify what the highlighted number signify here and how you are proceeding with respect to the question. If you are assuming any value then you should stick with that value and solve the question. If for example you have assumed p as 7% or 2% (which is not possible in this case), then you should use any one of this value and solve the question. then check the option using the assumed values of p



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1213
Location: India
GPA: 3.82

Re: A retail item is offered at a discount of p percent (where p
[#permalink]
Show Tags
14 Apr 2018, 19:03
xnthic wrote: Understand the right answer is to plug in smart numbers. But could someone please show step by step on how to solve this algebraically? I can't seem to be able to get the right answer. Any help much appreciated ! BunuelHi xnthicLet the original price be 100, after discount of p% the price will be \(100p\). Now sales tax of 5% is added to this price. Hence final price will be \((100p)*1.05\)(1) Now the second part of the question says that sales tax is not assessed, but the final price is same as (1). so let the new discount be \(y\), Hence new price will be \(100y\), this is same as (1), so we have \(100y=(100p)*1.05 =>100y=1051.05p\) therefore, \(y=1.05p5\)




Re: A retail item is offered at a discount of p percent (where p &nbs
[#permalink]
14 Apr 2018, 19:03



Go to page
1 2
Next
[ 22 posts ]



