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At a certain clothing store, customers who buy 2 shirts pay the regular price for the first shirt and a discounted price

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by Vincen » Tue Jan 19, 2021 9:35 am

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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.

Answer: B

Source: Official Guide
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Source: — Data Sufficiency |

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Re: At a certain clothing store, customers who buy 2 shirts pay the regular price for the first shirt and a discounted p

by Brent@GMATPrepNow » Thu Jan 28, 2021 6:22 am
Vincen wrote: ↑
Tue Jan 19, 2021 9:35 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.

Answer: B

Source: Official Guide
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
Brent Hanneson - Creator of GMATPrepNow.com
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Re: At a certain clothing store, customers who buy 2 shirts pay the regular price for the first shirt and a discounted p

by swerve » Thu Jan 28, 2021 5:54 pm
Vincen wrote: ↑
Tue Jan 19, 2021 9:35 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.

Answer: B

Source: Official Guide
\(CP\) of each shirt\(= m\)
\(SP\) of \(1\) shirt\(= x\)
Discounted \(SP\) of \(2\)nd shirt \(= y\) (or \(a\%\cdot x\))

\(ATS\), Profit from sale of \(1\) shirt \(=\) Profit from sale of \(2\) shirts

Therefore, \((x-m) = (x+y) - 2m\)

Simplify, \(y = m\)

So, we need \(CP (m)\) to get the value of \(y\)

Statement 1: given value of \(x\). Insufficient \(\Large{\color{red}\chi}\)

Statement 2: given value of \(m\). Sufficient \(\Large{\color{green}\checkmark}\)

Therefore, B
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