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

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.
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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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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

I always got the same answer. Is this a property that we can by heart?

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

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?

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 ?

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.



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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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.

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
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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

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.

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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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?

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

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

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. !