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GMAT PREP EXAM 1 PS QUESTION (Stores x, y, and z...)

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GMAT PREP EXAM 1 PS QUESTION (Stores x, y, and z...)

by beatgmatny1 » Tue Feb 18, 2014 4:26 pm
I couldn't find a good explanation for question below. This question is from GMAT PREP EXAM 1. What is the appropriate method to solve this question. I tried to test numbers for this question and it was time consuming. Eventually, I had to guess and move-on during the exam. If we were to test numbers, what would be ideal numbers to test? Also, can I assume the list price to be the same for all the three stores?

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
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by [email protected] » Tue Feb 18, 2014 4:55 pm
Hi beatgmatny1,

This question can be beaten by TESTing Values or by understanding the "math" behind the question (without doing too much of it).

Here's how to TEST Values:

The first sentence tells us that all 3 stores sell an item at a given list price; this implies that the list price is that same for all 3 stores (the words "a given list price" tips us off to that). As an aside, this question would be IMPOSSIBLE to answer if all 3 stores sold the item at a different list price (since we aren't given any information about the list price at any store, beyond that first sentence).

Here's what the stores do:
X = list price -5% discount + 5% tax
Y = list price + 5% tax - 5% discount
Z = list price w/no tax and no discount

We're asked to put these prices "in order"

TESTing 100 as the list price makes the math pretty easy:

X = 100 - 5% discount = 95 + 5% tax = 95 + 4.75 = 99.75
Y = 100 + 5% tax = 105 -5% discount = 105 - 5.25 = 99.75
Z = 100

So, Z is biggest and X and Y are the same.

Final Answer: B

Then there's the "math pattern" behind this question. I'm going to rewrite the above information in a slightly different way:

X = 100(.95)(1.05) ----> Discount first, tax second
Y = 100(1.05)(.95) ----> Tax first, discount second
Z = 100

You'll notice and X and Y will have the same result, since multiplying the same numbers in a different order will lead to the same result! You would probably still need to calculate one of them to figure out that X and Y are less than Z. You might also realize that 5% of 95 is less than 5% of 100, so X MUST end up being less than 100. Either way, you'll end up with the same answer as above.

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by Patrick_GMATFix » Tue Feb 18, 2014 9:48 pm
the order in which percentage changes are applied doesn't make a diffence. Adding 5%, then discounting 5% is akin to multiplying by (1.05)*(0.95).

Adding 5% = multiplying by 1.05. Discounting by 5% = multiplying by 0.95. the order in which the changes occur makes no difference since (1.05)*(0.95) = (0.95)*(1.05). As a result, x=y.

To compare x and y to z, just think logically: after adding 5%, you end with a bigger number. Subtracting 5% of a bigger number will mean discounting by a greater amount than the amount you previously added. So the final amount will be smaller than the original amount. This means that x=y < z. Answer is B.
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by GMATGuruNY » Wed Feb 19, 2014 3:58 am
beatgmatny1 wrote:I couldn't find a good explanation for question below. This question is from GMAT PREP EXAM 1. What is the appropriate method to solve this question. I tried to test numbers for this question and it was time consuming. Eventually, I had to guess and move-on during the exam. If we were to test numbers, what would be ideal numbers to test? Also, can I assume the list price to be the same for all the three stores?

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
5% = 5/100 = 1/20.
Since 5% must be taken twice, plug in a value that can easily be divided twice by 20.

Let the list price = 20*20 = 400.

Store X: 5% discount applied first, then 5% tax added
Discounted price = 400 - 5% of 400 = 380.
Price with tax = 380 + 5% of 380 = 399.

Store Y: 5% tax added first, then 5% discount applied
Price with tax = 400 + 5% of 400 = 420.
Discounted price = 420 - 5% of 420 = 399.

Store Z: No discount or tax
List price = 400.

Since X=399, Y=399, and Z=400, X=Y<Z.

The correct answer is B.
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by beatgmatny1 » Wed Feb 26, 2014 12:54 pm
Thank you for the detailed explanations.

Rich - is there a better to test numbers on DS questions in general? I tend to take long time to test numbers esp. when it involves variables and inequality signs. I can eventually get these questions right but during the practice tests, I do take quite a bit of time to test numbers (~3mins). Are a specific set of numbers you would advise to pick?

Thanks alot!
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by [email protected] » Wed Feb 26, 2014 7:39 pm
Hi beatgmatny1,

When TESTing Values, I tend to look for numbers that would fit the given scenario (for example, if we're told X < 0, then any negative would work, but simple negatives such as -1, -2, -3 will probably make whatever math we have to do easier). In special situations, certain numbers tend to be easier to use than others. Here, we're dealing with percents, so 100 is a good choice.

Pacing issues are usually due to inexperience, so you need to put some time in and practice this tactic. Over time, you'll improve and speed up.

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