Data Sufficiency

vikkimba17 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.

Hi vikkimba17,

We need to compare the discounted prices at stores L and M.

Let's take each statement one by one.

S1: 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.

Say the regular price at store L = $x and the regular price at store M = $y

The discounted price at store L = $90% of x = 0.9x

The discounted price at store M = $85% of y = 0.85y

Since we do not have the value of x and y, we cannot compare. 0.9x can be equal to, less than, or more than 0.85y. Not sufficient.

S2: 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.

Discounted price at store L = x - 5

Discounted price at store M = y - 6

We do not have the values of x and y to compare.

S1 and S2:

From S1 and S2, we get

0.90x = x - 5 => x = 50 => Discounted price at store L = $45

0.85y = y - 6 => y = 40 => Discounted price at store M = $42

So, the discounted price at store M = $42 is less than the discounted price at store L = $45. The answer is YES. A unique answer.

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Barcelona | Manila | Melbourne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

vikkimba17 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.

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: C

Cheers,
Brent

vikkimba17 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.

We are given that Stores L and M sell a certain product at different regular prices. We are also given that both 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 percentage 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.

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. Statement two alone is not sufficient to answer the question.

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.

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 = 5/0.10 = $50 and q = 6/0.15 = $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 less than the discount price at Store L.

Answer: C