It is currently 18 Mar 2018, 06:36

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

14 Oct 2013, 06:24
4
KUDOS
28
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

72% (01:01) correct 28% (01:23) wrong based on 697 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
[Reveal] Spoiler: OA

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: 44290
Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

Show Tags

14 Oct 2013, 06:58
7
KUDOS
Expert's post
11
This post was
BOOKMARKED
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.

_________________
Current Student
Joined: 04 Jul 2014
Posts: 306
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
KUDOS
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 17364 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: 44290
Stores X, Y, and Z each sell a certain item that has a given [#permalink]

Show Tags

24 Nov 2014, 06:44
1
KUDOS
Expert's post
5
This post was
BOOKMARKED
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%:

$$[p*(1 + \frac{x}{100})]*(1 - \frac{y}{100}) = [p*(1 -\frac{y}{100})]*(1 + \frac{x}{100})$$
_________________
Current Student
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?
Manager
Joined: 19 Jan 2016
Posts: 51
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: 3232
Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink]

Show Tags

09 Oct 2016, 08:50
1
KUDOS
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.
_________________

How I improved from V21 to V40! ?

How to use this forum in THE BEST way?

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.

Hi, I understand that Y<Z, but could you please explain why X equals to Y<Z?
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 889
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.

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
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2116
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

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 14 Jul 2017
Posts: 6
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
DS Forum Moderator
Joined: 22 Aug 2013
Posts: 889
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
KUDOS
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
Re: Stores X, Y, and Z each sell a certain item that has a given   [#permalink] 02 Mar 2018, 00:15
Display posts from previous: Sort by

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

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