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# Stores L and M each sell a certain product at a different

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Stores L and M each sell a certain product at a different [#permalink]

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31 Aug 2010, 22:31
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Stores L and M each sell a certain product at a different regular price. If both stores discount their regular price of the product, is the discount price at Store M less than the discount price at Store L ?

(1) At Store L the discount price is 10 percent less than the regular price; at Store M the discount price is 15 percent less than the regular price.
(2) At Store L the discount price is $5 less than the regular store price; at Store M the discount price is$6 less than the regular price.
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Re: OG12 #63 Stores L and M each sell a certain product [#permalink]

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Stores L and M each sell a certain product at a different regular price. If both stores discount their regular price of the product, is the discount price at Store M less than the discount price at Store L ?

Let the regular price of a certain product at store L be $$x$$ and the regular price of a certain product at store L be $$y$$.

If the rates of discounts were $$s$$ and $$t$$ then the prices would become: $$x(1-s)$$) and $$y(1-t)$$. Question: is $$x(1-s)>y(1-t)$$.

(1) At Store L the discount price is 10 percent less than the regular price; at Store M the discount price is 15 percent less than the regular price --> $$s=0.1$$ and $$t=0.15$$ --> no info about the initial prices - $$x$$ and $$y$$, hence not sufficient.

(2) At Store L the discount price is $5 less than the regular store price; at Store M the discount price is$6 less than the regular price --> $$x(1-s)=x-5$$ and $$y(1-t)=y-6$$. Not sufficient.

(1)+(2) As from (1) $$s=0.1$$ and from (2) $$x(1-s)=x-5$$ then $$0.9x=x-5$$, $$x=50$$ and similarly as from (1) $$t=0.15$$ and from (2) $$y(1-t)=y-6$$ then $$0.85y=y-6$$, $$y=40$$ --> we have all information needed. Sufficient. ($$x(1-s)=45>34=y(1-t)$$).

Answer: C.
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(1)
Product Price @ L= 100
After Discount = 90
Product Price @ M= 100
After Discount = 85
M's Price after Discount < L's price after discount.

Product Price @ L= 50
After Discount = 45
Product Price @ M= 100
After Discount = 85
L's Price after Discount < M's price after discount.

Not Sufficient.

(2)
Product Price @ L= 100
After Discount = 95
Product Price @ M= 100
After Discount = 94
M's Price after Discount < L's price after discount.

Product Price @ L= 50
After Discount = 45
Product Price @ M= 100
After Discount = 94
L's Price after Discount < M's price after discount.

Not Sufficient.

Combing both;
5 = 0.1L; L=50; After discount: 45
6 = 0.15M; M=40; After discount: 34
M's price after discount < L's price after discount.

Sufficient.

Ans: "C"
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Re: Stores L and M each sell a certain product at a different [#permalink]

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10 May 2016, 07:52
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gtr022001 wrote:
Stores L and M each sell a certain product at a different regular price. If both stores discount their regular price of the product, is the discount price at Store M less than the discount price at Store L ?

(1) At Store L the discount price is 10 percent less than the regular price; at Store M the discount price is 15 percent less than the regular price.
(2) At Store L the discount price is $5 less than the regular store price; at Store M the discount price is$6 less than the regular price.

Solution:

We are given that stores L and M sell a certain product at different regular prices. We are also given that both of these stores discount the regular price of the product. We must determine whether the discount price at Store M is less than the discount price at Store L.

Statement One Alone:

At store L the discount price is 10 percent less than the regular price; at store M the discount price is 15 percent less than the regular price.

Even though we know the percent discount at each store, without actually knowing the regular price of the product at each store, we can’t determine the discount price of the product in each store. Thus, we can’t compare their discount prices. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

At store L the discount price is $5 less than the regular store price; at store M the discount price is$6 less than the regular price.

Even though we know the amount of discount at each store, without actually knowing the regular price of the product at each store, we still can’t determine the discount price of the product in each store. Thus, we can’t compare their discount prices. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we have the following information:

a) At store L the percent discount is 10% and the amount of discount is $5. b) At store M the percent discount is 15% and the amount of discount is$6.

Now if we let p = the regular price of the product at store L and q = the regular price of the product at store M. Then:
a) 0.10p = 5
b) 0.15q = 6

Thus p = 5/.10 = $50 and q = 6/.15 =$40. Furthermore, the discount price of the product at store L is 50 – 5 = $45 and the discount price of the same product at store M is 40 – 6 =$34. Thus, we know that the discount price at store M is indeed less than the discount price at store L.

The answer is C.
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Re: OG12 #63 Stores L and M each sell a certain product [#permalink]

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01 Sep 2010, 11:39
+1 for you Bunuel, originally i thought the regular price cld not be determined, so i picked E. But it looks like with the eqn you've setup, you were able to solve for the reg price, very nice...
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Re: OG12 #63 Stores L and M each sell a certain product [#permalink]

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22 Oct 2011, 15:46
Great explanation from Bunuel. Thank you.
The explanation from OG is very succint. Your explanation definitely helped.
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Re: OG12 #63 Stores L and M each sell a certain product [#permalink]

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25 Dec 2011, 17:17
Bunuel wrote:
Stores L and M each sell a certain product at a different regular price. If both stores discount their regular price of the product, is the discount price at Store M less than the discount price at Store L ?

Let the regular price of a certain product at store L be $$x$$ and the regular price of a certain product at store L be $$y$$.

You mean the regular price of the product at store M is y right?
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30 Apr 2015, 07:55
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Re: Stores L and M each sell a certain product at a different [#permalink]

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10 May 2016, 04:24
Hello from the GMAT Club BumpBot!

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Re: Stores L and M each sell a certain product at a different   [#permalink] 10 May 2016, 04:24
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