Data Sufficiency | OG 2021, 700 level

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Data Sufficiency | OG 2021, 700 level

by DAM1997 » Sat Nov 28, 2020 12:00 am
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.

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DAM1997 wrote:
Sat Nov 28, 2020 12:00 am
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 $10
Case 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 $11
Since 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 $12
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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