The step-by-step video solution is attached here

Answer: Option B

Link to Other new OG2021 problems can be found in Signature


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Let the regular price of each shirt be $r, let the discounted price be $d and the cost be $c.

From the question stem, Profit from the sale of 2 shirts = Profit from the sale of 1 shirt

Breaking down the question stem, we can say

r – c + d – c = r – c. Simplifying, we have d = c.
So, to find out the discounted price of the shirt i.e. d, we need the value of c.

Statement I alone is insufficient since this gives the value of r. Answer options A and D can be eliminated. Possible answer options are B, C or E.

Statement II alone is sufficient since it gives the value of c. Answer option C and E can be eliminated.

The correct answer option is B.
Hope that helps!
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CP of each shirt= m
SP of 1 shirt= x
Discounted SP of 2nd shirt = y (or a%*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

S1- given value of x
Insufficient

S2- given value of m
sufficient.

Ans B

Lots of confusing solution above

Let's see what we have mentioned in question.
For simplification, given
cost price of 1 shirt =c
selling price of 1 shirt =s
discount(in Rs)=x

To find=S-X



thus customer buy 2 shirts at price=s+(s-x)

Thus Profit from selling 1 shirt= profit from 2 shirts in which 1 sold at discounted price
Profit= Selling price - cost price

S-C= S+(S-X)-2C
C=S-X

Hence we need just cost price of a shirt.

Thus option B is enough to get the answer.

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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A great question indeed.

So, the catch here is that the profit in selling either 1 or 2 shirt is the same. So the 2nd item is sold with no profit at all as the profit is made by selling one item itself.

1. Statement 1 gives the details about the Selling price which is not sufficient to get the discounted price.
2. Statement 2 says that the cost price of the shirt is $12 which is in fact equal to the selling price of 2nd shirt. So, we have the discounted price as $12. Sufficient

Answer is Option B

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?

I am unable to understand if we have a reason to assume that both the shirts have same regular price (and hence CP2 = DP2)..


You're absolutely right. There does seem to be some ambiguity in the question.
I'm assuming that the test-makers feel that the following information indicates that both shirts have the same regular price: 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.
I guess the fact that they don't distinguish one shirt from the other (e.g., the more expensive shirt, the undiscounted shirt, etc) suggests that shirts have the same regular price.

To remove all ambiguity, they could have added a few extra words.
As it stands, I think you've made a good point.
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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.
Asked: For a customer who buys 2 shirts, what is the discounted price of the second shirt?
The discounted price for the second shirt is the cost price of the shirt since there is no profit for the second shirt.

(1) The regular price of each of the 2 shirts the customer buys at the clothing store is $16.
NOT SUFFICIENT

(2) The cost to the clothing store of each of the 2 shirts the customer buys is $12.
The discounted price for the second shirt = Cost price of the second shirt = $6
SUFFICIENT

IMO B
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Profit=Price-cost

If they make the same profit from selling 1 or 2, the Profit of the second is 0
0=Price-cost
Price=cost

Alternative B give us the cost, therefore the price
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Let regular price of shirt = \(P_r\)
Discount offered on the second shirt = d
Cost of shirt = c
Price of discounted shirt = \(P_r - d\)

Now, \(P_r - c + P_r - d - c = P_r - c\)
\(P_r - d = c\) = Discounted Price of second shirt.

St. 1
Nothing about cost given.
INSUFFICIENT.

St. 2
c = = \(P_r - d\) = 12

SUFFICIENT.

Answer B.
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This question can be solved without variables and just via logic.

Question says:
One shirt is sold at regular prize, while another is sold at discounted prize.
Profit when 1 shirt is sold at regular prize = Profit when 1 shirt is sold at regular prize and another is sold at discounted prize.

What can be inferred here?
Take random numbers:

$3 = $3 + what?
0. Right?

So profit from shirt 2 will be 0, meaning shirt 2 was sold at cost prize.

If the Profit from selling A is same as the Profit from Selling both A and B, it means B was sold at cost.
Hence all we need to know is the Cost of Shirt B

Prompt gives us that the second shirt must be sold for the cost price of a shirt.

(2) gives us the cost price.

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