BrentGMATPrepNow wrote:
GMATinsight wrote:
At a certain clothing store, customers who buy 2 shirts pay the regular price for the first shirt and a discounted price for the second shirt. The store makes the same profit from the sale of 2 shirts that it makes from the sale of 1 shirt at the regular price. For a customer who buys 2 shirts, what is the discounted price of the second shirt?
(1) The regular price of each of the 2 shirts the customer buys at the clothing store is $16.
(2) The cost to the clothing store of each of the 2 shirts the customer buys is $12.
Given: At a certain clothing store, customers who buy 2 shirts pay the regular price for the first shirt and a discounted price for the second shirt. The store makes the same profit from the sale of 2 shirts that it makes from the sale of 1 shirt at the regular price. IMPORTANT: How is it possible that the store makes the
same profit from the sale of TWO shirts that it makes from the sale of ONE shirt at the regular price?
This occurs only when there is
no profit on the discounted shirt.
In other words, the
price of the discounted shirt = the amount of the store paid for the shirt Target question: For a customer who buys 2 shirts, what is the discounted price of the second shirt? Statement 1: The regular price of each of the 2 shirts the customer buys at the clothing store is $16. There are several different scenarios that satisfy statement 1. Here are two:
Case a: The store BOUGHT each shirt for $10, and assigned a regular price of $16 to each shirt. The discounted price of one shirt is $10. Notice that the total profit for the sale of both shirts = ($16 + $16) - ($10 + $16) =
$6, and the total profit for the sale the NON-DISCOUNTED shirt = $16 - $10 =
$6. So all of the given conditions are satisfied. In this case, the answer to the target question is
the discounted price of the second shirt is $10Case b: The store BOUGHT each shirt for $11, and assigned a regular price of $16 to each shirt. The discounted price of one shirt is $11. Notice that the total profit for the sale of both shirts = ($16 + $16) - ($11 + $16) =
$5, and the total profit for the sale the NON-DISCOUNTED shirt = $16 - $11 =
$5. In this case, the answer to the target question is
the discounted price of the second shirt is $11Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The cost to the clothing store of each of the 2 shirts the customer buys is $12.We already concluded that
price of the discounted shirt = the amount of the store paid for the shirt So, if the store paid $12 for each shirt, then
the discounted price of the second shirt must be $12Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
I am unable to understand if we have a reason to assume that both the shirts have same regular price (and hence CP2 = DP2)..
As per Statement 2:
CP1 = 12; CP2 = 12
Let, SP1(Regular selling price for shirt#1) = 20
SP2(Regular selling price for shirt#2) = 25
DP2(Discounted Selling price for shirt#2) = 17
Profit 1 = SP1 - CP1 = 20 - 12 = 8
Profit 2 = DP2 - CP2 = 17 - 12 = 5
Profit from selling shirt#2 at regular price = 25 - 12 = 13
Profit 1 + Profit 2 = Profit from selling shirt#2 at regular price = 13
However, there could be multiple values for SP1 & SP2 and corresponding DP2, thereby, making statement2 alone insufficient.
Could you please guide me for the fault in interpretation?