Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 12:20

### 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

# Stores X, Y, and Z each sell a certain item that has a given

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

### Hide Tags

Intern
Joined: 02 Jul 2013
Posts: 19
Schools: LBS MIF '15
Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

### Show Tags

Updated on: 14 Oct 2013, 06:55
7
45
00:00

Difficulty:

55% (hard)

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

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.
##### Most Helpful Expert Reply
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
15
10
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.
_________________
##### General Discussion
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
2
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!!

JA
If 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
5
3
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
GMAT 1: 710 Q45 V42
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
1
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 V40
My MBA Journey: My 10 years long MBA Dream
My 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 place

GMAT 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 free
Check 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 _________________ # Jeffrey Miller Head of GMAT Instruction Jeff@TargetTestPrep.com 122 Reviews 5-star 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 1 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
Schools: IIMA PGPX"20 (D)
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
1
Top Contributor
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) =$99.75
Aside: 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) =$99.75

Store Z
$100 We can see that$99.75 = $99.75 <$100
In other words, x = y < z

Answer: B

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Manager
Joined: 09 Mar 2018
Posts: 56
Location: India
Schools: CBS Deferred "24
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
Display posts from previous: Sort by

# Stores X, Y, and Z each sell a certain item that has a given

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

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