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Intern  Joined: 02 Jul 2013
Posts: 18
Schools: LBS MIF '15
Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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48 00:00

Difficulty:   45% (medium)

Question Stats: 70% (02:21) correct 30% (02:36) wrong based on 667 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 60480
Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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15
12
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.

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

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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 49104 times ]

I always got the same answer. Is this a property that we can by heart?
Math Expert V
Joined: 02 Sep 2009
Posts: 60480
Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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8
5
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%:

$$[p*(1 + \frac{x}{100})]*(1 - \frac{y}{100}) = [p*(1 -\frac{y}{100})]*(1 + \frac{x}{100})$$
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Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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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]

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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  B
Joined: 19 Jan 2016
Posts: 34
Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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

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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.
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Intern  Joined: 15 Nov 2015
Posts: 2
Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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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?
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Joined: 22 Aug 2013
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Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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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.
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Affiliations: Target Test Prep
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Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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1
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 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  B Joined: 14 Jul 2017 Posts: 25 Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 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 P Joined: 22 Aug 2013 Posts: 1403 Location: India Re: Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 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  B Joined: 09 Apr 2018 Posts: 20 Stores X, Y, and Z each sell a certain item that has a given [#permalink] ### Show Tags 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.
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Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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

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

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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.

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

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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

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

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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
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GMAT 1: 600 Q46 V27 Re: Stores X, Y, and Z each sell a certain item that has a given  [#permalink]

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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

This question is literally a 500 level question. But the way GMAC words it makes it a 600-700 level question. This is absolute brilliance.

If you are comfortable with percentages then you know the sequence does not matter. 5% increase followed by 5% decrease or the other way round will give the exact same result. You can try it.

B is the perfect choice.

Glad I got it right during the test. !
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