Gmat_mission wrote: ↑

Wed Sep 29, 2021 8:02 am

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.

Answer: C

Source: Official Guide

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