Stores L and M each sell a certain product at a different regular pric

Let the regular price at store L is 100L & at store M is 100M
1) Discounted price at L = 90L
Discounted price at store M = 85M
But still we don't the respective value of L & M --->Insufficient

2) Discounted price at L = 100L - 5
Discounted price at M = 100M - 6
But still we don't the respective value of L & M --->Insufficient

1+2) 10L = 5 & 15M = 6
We can get the respective value of L & M --->Sufficient
Answer C

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 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...

(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"

Great explanation from Bunuel. Thank you.
The explanation from OG is very succint. Your explanation definitely helped.

SOLUTION

Stores Land 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.

Each statement is clearly insufficient to answer the question.

When we consider the statements together we have that 10% of regular price at store L corresponds to $5 and 15% of regular price at store M corresponds to $6. We can find regular prices, and discounted prices, thus answer the question. Sufficient.

Answer: C.
_________________

1) If Store L's cost is 10000000000000$ and store M's cost is 10$, after the discounts Store L would be more expensive. If the case is vice versa, store M would be more expensive.

2) Again, If Store L's cost is 10000000000000$ and store M's cost is 10$, after the deductions Store L would be more expensive. If the case is vice versa, store M would be more expensive.

Both statements together.
A 10% discount = 5$ in store L. A 15 % discount = 6$ in store M.
So the prices before discount and the discounted prices for both stores can be found.

Hence answer is C.

discount at store M < discount at store L ?

statement 1

L-0.10L=0.90L
M-0.15M=0.85M

no value can't answer insufficient

statement 2

L-5
M-6 again insufficient

combining both

L-5=0.90L
M-6=0.85 M 2 equations 2 unknowns sufficient

0.15M = 6 >>> M=6/.15 = 40 therefore 40-6 = 34

0.1L = 5 >>> L=5/.1 = 50 therefore 50-5 = 45

34<45

sufficient answer is C

Statment 1 gives us the % difference between regular and discounted prices for each store. But clearly not sufficient information to find out difference in discounted prices.

Statment 2 gives us the absolute difference between regular and discounted prices for each store. But clearly not sufficient information to find out difference in discounted prices.

However combining statement 1 and 2,we know that 10% corresponds to $5 for store 1 and 15% corresponds to $6 for store 2. With this we can find out regular price and therefore the discounted prices for each. Hence sufficient.

Ans C

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.
_________________

Target question: Is the DISCOUNT price at Store M less than the DISCOUNT price at Store L ?

Statement 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.
We don't know the REGULAR PRICES at each store, so we can't determine the DISCOUNTED PRICES.
For example, consider these two conflicting cases:
Case a: REGULAR price at store L = $10, and REGULAR price at store M = $100. So, the DISCOUNT price at store L = $9, and the DISCOUNT price at store M = $85. In this case, the DISCOUNT price at store L is LESS THAN the DISCOUNT price at store M
Case b: REGULAR price at store L = $100, and REGULAR price at store M = $10. So, the DISCOUNT price at store L = $90, and the DISCOUNT price at store M = $8.50. In this case, the DISCOUNT price at store L is GREATER THAN the DISCOUNT price at store M
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 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
Once again, since we don't know the REGULAR PRICES at each store, we can't determine the DISCOUNTED PRICES.
For example, consider these two conflicting cases:
Case a: REGULAR price at store L = $7, and REGULAR price at store M = $10. So, the DISCOUNT price at store L = $2, and the DISCOUNT price at store M = $4. In this case, the DISCOUNT price at store L is LESS THAN the DISCOUNT price at store M
Case b: REGULAR price at store L = $100, and REGULAR price at store M = $10. So, the DISCOUNT price at store L = $95, and the DISCOUNT price at store M = $4. In this case, the DISCOUNT price at store L is GREATER THAN the DISCOUNT price at store M
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
At this point, we should recognize that we can use both statements to determine the regular prices at each store, which means we also can determine the discount prices at each store. So, we can answer the target question with certainty (without actually performing the calculation)

Answer: C

ASIDE: for "fun" let's actually perform the necessary calculations.
Combining the statement, we know that, at store L, a 10% discount is equal to $5
In other words, 10% of the regular price = $5
Or, we can write: (0.1)(regular price) = $5
So, the regular price = $50, which means the DISCOUNT price at store L = $45

Likewise, at store M, a 15% discount is equal to $6
In other words, 15% of the regular price = $6
Or, we can write: (0.15)(regular price) = $6
So, the regular price = $40, which means the DISCOUNT price at store M = $34

At this point, we can see that the DISCOUNT price at store L is GREATER THAN the DISCOUNT price at store M
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:

Cheers,
Brent

Let original Price at Store L be X$ and at Store M be Y$.
Stmt 1:-
Price after Discount @L = 0.9X
Price after Discount @M = 0.85Y
Not suff because we dont know the value of X and Y

Stmt 2:-
Price after Discount @L = X-5
Price after Discount @M = Y-6
Not suff because we dont know the value of X and Y

Stmt 1 & 2:-
Equating the discounted price of Store L & M we get the respective values of X and Y
X= 50$
Y= 40$

Ans: C

Let the regular price of store L =X
The regular price of store M = Y
Is the discount price of L less than M;

(1) Discount store L is 10%, so the discounted price is = 0.90X
Discount store M is 10%, so the discounted price is = 0.90Y

WE DON'T KNOW THE VALUE OF X AND Y INSUFFICIENT.

(2) DISCOUNTED PRICE OF L = X-5
DISCOUNTED PRICE OF M = Y-6

AGAIN, WE DON'T KNOW THE VALUE OF X AND Y INSUFFICIENT.


FOR BOTH (2) AND (1)

0.90X = X-5
X = 50
SO, THE DISCOUNTED PRICE OF L = 50*0.90 = $50

0.85Y = Y - 6
Y = 40

SO, THE DISCOUNTED PRICE OF M = 40*0.85 = $36

SO, DISCOUNT PRICE OF M LESS THAN M.

ANSWER C.

Each statement alone is insufficient. We don't know the original price of each item and therefore we don't know if the 10% Store L discount is greater than the 15% Store M discount.

Combined, we can conclude:

$5 = 10% Store L
$50 = 100% Store L

$6 = 15%
$40 = 100% Store M

Store M has the lower discount price. Answer is C.
_________________

Answer: Option C

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Given: Stores L and M each sell a certain product at a different regular price.

Asked: 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.
Let the regular price at Store L be x and at Store M be y.
Discounted price at Store L = (100%-10%)x = .9x
Discounted price at Store M = (100%-15%)y = .85y
Since absolute values of regular prices x &y are not known
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.
Let the regular price at Store L be x and at Store M be y.
Discounted price at Store L = x - $5
Discounted price at Store M = y - $6
Since absolute values of regular prices x &y are not known
NOT SUFFICIENT

(1) + (2)
(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.
Let the regular price at Store L be x and at Store M be y.
(100%-10%)x = .9x = x - $5; x = $50
(100%-15%)y = .85y = y - $6; .15y = $6; y = $6/.15 = $40
Discounted price at Store L = .9x = $45
Discounted price at Store M = .85y = $34
Discounted price at Store L > Discounted price at Store M
SUFFICIENT

IMO C