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I think it would have been (E) if the question had asked to calculate the amount of profit generated, then your reasoning would have been correct that we dont know the exact number of premium and regular quantity sold/unsold.
But since the question only asks if he generates a profit, i think A would be sufficient
SomethingSomw
We can't really answer this question based on the information provided in the 2 options, so the answer should be E.

Initially, we are told that premium and regular quality shirts are purchased at 'various prices'. For simplicity sake lets assume all premium cost a and all regular cost b. and lets assume that the number of these shirts is x and y respectively. Next, we know that the average price of these shirts combined is 40$. => Cost Price of shirts for Fairview Department Store = 40(x+y)
About the selling price, we know that a,b both now have a markup of 50% so the selling price (aka original retail price) is 3a/2 and 3b/2.
This is all the things we know from the question, now we'll look at the options.

(1) 80% of the shirts were sold at the original retail price.
Here it would seem that technically the SP for 80% of the shirts should be 80% of 40(3/2)(x+y) from our previous understanding of Cost Price, but we dont know what share of premium vs regular shirts have been sold, neither do we know what is the price difference of the 2 types of shirts. We can't tell how much money could have been made as profit here. Nor can we tell how much of the Cost Price we would still have to offset from the remain 20% shirts to tell if we made a profit.
=> INSUFFICIENT

(2) Markdown price is 12$ per shirt.
Here, we still don't know how much profit we would have made while selling at the original retail price, and neither do we know how much of a loss are we incurring by selling shirts at 12$ across the board.
=>INSUFFICIENT

(1) + (2)
Even considering the 2 together, we would still not know the profit made over the first 80% of the shirts or the loss incurred on the remain of the 20% of the shirts coz we don't know the original retail price
=> INSUFFICIENT

Therefore, E is correct
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Lets look at an example case here for option (1).
Assume that the premium shirt costs 100$ and regular shirt costs 20$. also lets assume 70% of the shirts are regular. (assume 7x is number of shirts) This means that if 80% of the shirts are sold, worst case scenario would be that 70% sold were regular and 10% sold were premium.
=> taking the 50% markup.
The profit from regular shirts is (7x)(1/2)(20) = 70x
The profit from premium shirts is (1x)(1/2)(100) = 50x.
Bringing the total profit to 120x.

Now, we still need to sell the 20% remaining shirts which are all premium, and which would have costed the Store CP = (2x)(100) = 200x.

So to even get to a breakeven on this, store needs to make another (200x-120x)$ more = 80x$ in sale from the remaining 20% shirts. IF the selling price after markdown is any less than 40$, the total SP of the remaining 20x shirts would be <80x. In this case it would mean loss.

We essentially know nothing about any of the parameters from the question so it is possible still to incur a loss like in the example above. Can't gaurantee a profit.
Advait01
I think it would have been (E) if the question had asked to calculate the amount of profit generated, then your reasoning would have been correct that we dont know the exact number of premium and regular quantity sold/unsold.
But since the question only asks if he generates a profit, i think A would be sufficient

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This is a tricky question. There are no constraints given regarding the value for regular and premium shirts so that should already give a green flag for possible option E.

When we look at it deeper it further strengthens the pre thinking of E as 80% of clothes sold at 1.5x might comprise of ALL regular dresses.
If regular were for 10 bucks and premium were for 2000 bucks, and lets take total goods to be 100. 80 for regular and 20 for premium.
Now all 80 goes into selling for 1.5*10 = 15
SP = 15*80 = 1200
SP for remaining 20 we arent sure of at all!
If SP of premium were 1500 each (marked down) then,
1500*20 = 30000. We clearly see that there is an offset in favour of CP with a massive gap of 500 bucks for every 20 goods of premium. Clear LOSS.
On the other hand, you already came up with the positive scenario for profit.
Two cases.
INSUFFICIENT.

Statement 2:
Marked price given but how much % is the marked down value, and what percentage good is regular and premium. Nothing we know of!
INSUFFICIENT.

Combining the two:
Again no percentage of either of the goods that we have and we dont have a magical constraint scenario where Profit exceeds 40n each time like we saw the extreme cases or any other case always can have 2 results.
INSUFFICIENT.

Answer: Option E
Advait01
(1) Even if 80% of the shirts were sold at the original retail price, the difference between their buying price and selling price is 0, So the rest 20% which were sold at 50% higher would generate a profit
Sufficient

(2) We dont know how many were unsold and what was the exact price of buying or selling
Insufficient

Therefore, (A)
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Yeah it seems i had considered that the marked down price would be same as the original purchase price,
Thx for the correction
Adit_
This is a tricky question. There are no constraints given regarding the value for regular and premium shirts so that should already give a green flag for possible option E.

When we look at it deeper it further strengthens the pre thinking of E as 80% of clothes sold at 1.5x might comprise of ALL regular dresses.
If regular were for 10 bucks and premium were for 2000 bucks, and lets take total goods to be 100. 80 for regular and 20 for premium.
Now all 80 goes into selling for 1.5*10 = 15
SP = 15*80 = 1200
SP for remaining 20 we arent sure of at all!
If SP of premium were 1500 each (marked down) then,
1500*20 = 30000. We clearly see that there is an offset in favour of CP with a massive gap of 500 bucks for every 20 goods of premium. Clear LOSS.
On the other hand, you already came up with the positive scenario for profit.
Two cases.
INSUFFICIENT.

Statement 2:
Marked price given but how much % is the marked down value, and what percentage good is regular and premium. Nothing we know of!
INSUFFICIENT.

Combining the two:
Again no percentage of either of the goods that we have and we dont have a magical constraint scenario where Profit exceeds 40n each time like we saw the extreme cases or any other case always can have 2 results.
INSUFFICIENT.

Answer: Option E

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