Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 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

Intern
Joined: 02 Jul 2013
Posts: 19

Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
Updated on: 14 Oct 2013, 06:55
Question Stats:
70% (02:18) correct 30% (02:36) wrong based on 577 sessions
HideShow timer Statistics
Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z? A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by bulletpoint on 14 Oct 2013, 06:24.
Last edited by Bunuel on 14 Oct 2013, 06:55, edited 1 time in total.
Moved to PS forum.




Math Expert
Joined: 02 Sep 2009
Posts: 56307

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
14 Oct 2013, 06:58
bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?
A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (100*0.95)*1.05 < 100. y = (100*1.05)*0.95 < 100. z = 100. So, we have that x=y<z. Answer: B.
_________________




Senior Manager
Joined: 04 Jul 2014
Posts: 294
Location: India
GMAT 1: 640 Q47 V31 GMAT 2: 640 Q44 V34 GMAT 3: 710 Q49 V37
GPA: 3.58
WE: Analyst (Accounting)

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
24 Nov 2014, 03:18
Hi Bunuel, I tried this on a spreadsheet. I took a common number (100) and did 2 sets of operations for 2 options: option 1 (Store Y) added X% and subtracted Y% from the result of the first operation option 2 (Store X) subtracted Y% and added X% from the result of the first operation Attachment:
Capture.PNG [ 1.74 KiB  Viewed 36365 times ]
I always got the same answer. Is this a property that we can by heart?
_________________
Cheers!! JAIf you like my post, let me know. Give me a kudos!



Math Expert
Joined: 02 Sep 2009
Posts: 56307

Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
24 Nov 2014, 06:44
joseph0alexander wrote: Hi Bunuel, I tried this on a spreadsheet. I took a common number (100) and did 2 sets of operations for 2 options: option 1 (Store Y) added X% and subtracted Y% from the result of the first operation option 2 (Store X) subtracted Y% and added X% from the result of the first operation Attachment: Capture.PNG I always got the same answer. Is this a property that we can by heart? Yes, increasing a quantity by x% and then decreasing the result by y% is the same as decreasing by y% and then increasing the result by x%: \([p*(1 + \frac{x}{100})]*(1  \frac{y}{100}) = [p*(1 \frac{y}{100})]*(1 + \frac{x}{100})\)
_________________



Intern
Joined: 04 Sep 2012
Posts: 13
Location: United States
Concentration: Finance, Technology
GPA: 3
WE: Securities Sales and Trading (Other)

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
28 Jul 2015, 16:30
Thought process: We're dealing with percents. Increase and decrease. Strategy: Pick numbers and plow through the calculations. Choose 100 or another easy round number.
See that x=y<z CHOOSE B
ON TO THE NEXT



Intern
Joined: 20 May 2013
Posts: 1

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
29 Sep 2016, 03:02
Bunuel Can you please explain if this is correct  If we used the formula instead of successive discounts ie A + B + AB/100 (where A and B are successive discounts/percentages applied to the same quantity) then the ans for final list price value is: X: (5) + 5 25/100 (X) => X is the list price Y: 5  5 25/100 (Y) => Y is the list price But seems like the final list price value is different using this formula. Is it incorrect to use it here?



Intern
Joined: 19 Jan 2016
Posts: 36

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
09 Oct 2016, 08:03
Hi Bunnel,
I tried solving this question by taking the value of the product as 100. A 5% decrease results 95 (discounted price) after we add the tax to this value it is equal to 99.3. If the sales tax is added and then discounted its 101.5. Can you please explain what am i missing here ?



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3625

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
09 Oct 2016, 08:50
nikitamitra wrote: Bunuel Can you please explain if this is correct  If we used the formula instead of successive discounts ie A + B + AB/100 (where A and B are successive discounts/percentages applied to the same quantity) then the ans for final list price value is: X: (5) + 5 25/100 (X) => X is the list price Y: 5  5 25/100 (Y) => Y is the list price But seems like the final list price value is different using this formula. Is it incorrect to use it here? Yes, using the formula also we will get the same result. Note that List price of the product is same. So, Try taking the value of each product 'a' and then substutitute in your formula. You will get the result. anuj11 wrote: Hi Bunnel,
I tried solving this question by taking the value of the product as 100. A 5% decrease results 95 (discounted price) after we add the tax to this value it is equal to 99.3. If the sales tax is added and then discounted its 101.5. Can you please explain what am i missing here ? You are making a calculation mistake. List price 100. Case 1 : 5% increase then 5% discount. = 105 * 0.95 Case 2 : 5% discount the n 5% increase = 95 *1.05 Both will be equal.
_________________
My GMAT Story: From V21 to V40My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeBlog: Subscribe to Question of the Day BlogGMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here. New! Best Reply Functionality on GMAT Club!Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.



Intern
Joined: 15 Nov 2015
Posts: 2

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
04 Jun 2017, 20:29
Bunuel wrote: bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?
A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (100*0.95)*1.05 < 100. y = (100*1.05)*0.95 < 100. z = 100. So, we have that x=y<z. Answer: B. Hi, I understand that Y<Z, but could you please explain why X equals to Y<Z?



Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
04 Jun 2017, 22:43
nielsenn wrote: Bunuel wrote: bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?
A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (100*0.95)*1.05 < 100. y = (100*1.05)*0.95 < 100. z = 100. So, we have that x=y<z. Answer: B. Hi, I understand that Y<Z, but could you please explain why X equals to Y<Z? Hi x=y<z simply means that x and y are equal to each other, and both are less than z.



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2822

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
06 Jun 2017, 16:46
bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?
A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x We are given that Stores X and Y are located in a state with a 5 percent sales tax, and both sell an item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. We are also given that Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. Let’s determine the prices, x, y, and z and let the original price of the item = 100. Price at Store X: (100)(0.95)(1.05) = $99.75 Price at Store Y: (100)(1.05)(0.95) = $99.75 Price at Store Z: $100 Thus, x = y < z Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 14 Jul 2017
Posts: 21

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
02 Mar 2018, 00:09
Hi
Cant we use the %change formula = x + y + (xy/100) to calculate two successive % change instead of calculating the discount and tax seperately??
Posted from my mobile device



Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
02 Mar 2018, 00:15
RashmiT wrote: Hi
Cant we use the %change formula = x + y + (xy/100) to calculate two successive % change instead of calculating the discount and tax seperately??
Posted from my mobile device Hi Yes we can do that. Discount of 5% would mean 5% change, while tax of 5% would mean +5% change. So, for Store X, it would be = 5 + 5 + (5)*5/100 =  2.5% change overall and for Store Y, it would be = +5 5 + 5*(5)/100 = 2.5% change overall So the final values for Stores X and Y would be same



Intern
Joined: 09 Apr 2018
Posts: 20

Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
14 Sep 2018, 04:45
While this questions is straight, I made a very silly mistake, in a hurry missed that, for y discount is applied to (List Price + Sales Tax), I still feel there is some contradiction in the question stem.
Stem says  1. Stores X, Y, and Z each sell a certain item that has a given list price. 2. X&Y give 5 percent discount off list price. Now this List Price is a given price for ALL X, Y & Z. This clearly means that if LP is a given value (say 100), the Value of Discount on LP is 5% LP in X & Y (=$5), and $0 in Z.
In such a case, The S.Ps of all are X: (100  5)*1.05 = $99.75 Y: (100*1.05) (5% of LP) = 105  5 = $100 Z: $100 So, x < y = z Of course this is incorrect given the OA, but I strongly feel there is some contradiction (though minimal) in the question stem. Is it that I am thinking too much or missing something here? Perhaps the question shouldn't have mentioned off list price for the Discount Applied by X and Y.



Intern
Joined: 06 Jun 2018
Posts: 44
Location: India
GMAT 1: 640 Q47 V30 GMAT 2: 540 Q42 V22
GPA: 3.7

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
20 Oct 2018, 04:42
Bunuel, abhimahna chetan2u  I have got answer correct by considering list price as 100 however where is it mentioned that list price are same ? If list price of x and y is different then B can not be answer and even we do not in that case z will be less or more than x and y.



Math Expert
Joined: 02 Aug 2009
Posts: 7763

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
20 Oct 2018, 06:47
NAvinash wrote: Bunuel, abhimahna chetan2u  I have got answer correct by considering list price as 100 however where is it mentioned that list price are same ? If list price of x and y is different then B can not be answer and even we do not in that case z will be less or more than x and y. Hi it is given a certain item that has a list price.. This points to same item and same price.. Otherwise it would a certain item that has a list price for each place/that has a different list price or something to that effect
_________________



Intern
Joined: 04 Apr 2017
Posts: 24

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
21 Dec 2018, 06:21
Bunuel wrote: bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?
A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Say the price of the item is 100. Then: x = (100*0.95)*1.05 < 100. y = (100*1.05)*0.95 < 100. z = 100. So, we have that x=y<z. Answer: B. Can you please clarify how you easily know that (100*0.95)*1.05 is < 100 without calculations? Is it by logic? I spent sometime in calculations to reach it?



CEO
Joined: 12 Sep 2015
Posts: 3857
Location: Canada

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
19 Mar 2019, 07:09
bulletpoint wrote: Stores X, Y, and Z each sell a certain item that has a given list price. Stores X and Y are located in a state with a 5 percent sales tax, and both sell the item at a 5 percent discount off list price, while Store Z is located in a state with no sales tax and gives no discounts. Store X applies its discounts first and then charges sales tax on the discounted price, while Store Y adds the tax first and then applies the discount to the price with tax. If x and y are the prices, with tax and discount, charged by Stores X and Y, respectively, and z is the price charged by Store Z, which of the following statements correctly describes the relationship among x, y, and z?
A. x=y=z B. x=y<z C. x<y<z D. x<z<y E. y<z<x Let $100 = the list price for all 3 stores Store X $100 plus 5% sales tax = $105 $105 minus 5% discount = (0.95)($105) = $99.75Aside: a 5% discount means the buyer is paying 95% of the cost (thus 95% of $105) Store Y $100 minus 5% discount = $95 $95 plus 5% sales tax = (1.05)($95) = $99.75Store Z $100We can see that $99.75 = $99.75 < $100In other words, x = y < zAnswer: B Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Manager
Joined: 09 Mar 2018
Posts: 56
Location: India

Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
Show Tags
27 Mar 2019, 04:10
for 2 successive decrease and increase in %ages the best formula is
\(X+Y+\frac{XY}{100}\)
the sign may vary if it is an increase or decrease.
let the original price be 100 then,
plugging in values(for store X) : \(5  5 + \frac{(5)(5)}{100}\)
which gives : 0.25% change overall
similar will be the case for store Y .
hence we can conclude X=Y<Z




Re: Stores X, Y, and Z each sell a certain item that has a given
[#permalink]
27 Mar 2019, 04:10






