A store sold 60 percent of the hats from a shipment of hats at a

Hello, GMATophobe. I'm not sure where I went wrong in my calculation based on your figures. Could you please help me check?

For the first case, the revenue is 3 * 60 = 180
The cost is 2 * 60 = 120
So, the profit for the first case is 180 - 120 = 60

For the second case, the revenue is 1 * 28 = 28
The cost is 2 * 28 = 56
So, the profit for the second case is 56 - 28 = -28

So, the total gross profit is 60 - 28 = 32
Therefore, the percentage of the total cost is 32 / 200 = 0.16 = 16%

Why isn't it 4%? Where did I go wrong in my calculation?

In the reply, I saw that if we calculate the gross profit for each batch, we need to include the third batch's loss of -24.

But why, according to your method, is there no need to calculate the gross profit for the third batch? In my method, we would need to account for the third batch's gross profit.

I look forward to your reply, and thank you so much!

Let the shipment = 100 hats
Since the price for each hat is initially 1/2 greater than the cost and later reduced by 2/3, let the cost for each hat = the product of the two denominators = 2*3 = 6
Total cost for the 100 hats = (100 hats)($6 per hat) = 600

A store sold 60 percent of the hats at a selling price that was 50 percent greater than the store's cost for each hat.
At a selling price of $9 per hat -- 50% greater than the $6 cost -- the revenue for the first 60 hats = (60 hats)($9 per hat) = 540

The store reduced the selling price by 66 2/3 percent and sold 70 percent of the remaining hats at the reduced selling price.
70% of the 40 remaining hats = 28 hats
At a selling price of $3 per hat -- 2/3 less than the initial $9 price -- the revenue for the next 28 hats = (28 hats)($3 per hat) = 84

Profit = total revenue - total cost = (540+84) - 600 = 24

The store's gross profit from the sale of the hats was what percent of the store's cost for the hats from the shipment?
\(\frac{Profit}{Cost} = \frac{24}{600} = \frac{4}{100} =\) 4%

I also think it's 14%. I followed gmatophobia method to calculate, assuming there are 100 hats in total, with a cost of 2 $ per hat, so the selling price for the first case is 3 $.

So, for the first case, the revenue is 3 * 60 = 180
The cost is 2 * 60 = 120
So, the profit for the first case is 180 - 120 = 60

For the second case, the revenue is 1 * 28 = 28
The cost is 2 * 28 = 56

So, the profit for the second case is 56 - 28 = -28
So, the total gross profit is 60 - 28 = 32

Therefore, the percentage of the total cost is 32 / 200 = 0.16 = 16%

Why isn't it 4%? Where did I go wrong in my calculation?

In the reply, I saw that if we calculate the gross profit for each batch, we need to include the third batch's loss of -24.
But why, according to your method, is there no need to calculate the gross profit for the third batch? In my method, we would need to account for the third batch's gross profit.

I’ve looked at it many times and couldn’t find any errors. I’d like to ask the experts to point out where I went wrong! Thank you!

Bunuel Krunaal Could I please ask both experts to guide me on where the error occurred? Thank you so much! :please:

The key misstep lies in this batch-wise profit calculation approach, as it does not directly account for the overall gross profit across the shipment.

Gross profit is not the sum of the profits from individual batches; instead, it is the difference between total revenue and total cost across the entire shipment.

In your calculation:

1. You found the profit for the first and second sales correctly but missed incorporating the overall structure of gross profit as a single calculation.
2. Unsold hats were excluded, but their costs were already accounted for in the total cost. This led to a misalignment between total revenue and total cost.

This led to an overestimation.

Gross profit is the total revenue from all sales minus the total cost of all hats. It must always be calculated holistically

Gross Profit = Total Revenue - Total Cost

Now, first adding revenue you calculated for two batches = 180 + 28 = 208
Total cost of the shipment = 200
Gross Profit = 208 - 200 = 8

8/200 = 4%

Hope it helps.

Thank you, Krunaal.
It turns out that in my calculation, I only included the revenue from the first and second batches but overlooked the loss from the third batch, which caused a mismatch between the total revenue and total cost.
Now I finally understand the definition of gross profit. Your explanation is very clear—thank you so much!

Hi experts. JeffTargetTestPrep Bunuel KarishmaB
Going through all the replies in this post, I still have a small doubt:

Why is gross profit taken as total revenue - total cost across all shipments and not as just revenue - cost (across shipments sold)? Is this because of how "gross profit" defined? If yes, please expand on what "gross profit" actually means. I googled the exact definition of "gross profit" and found this:
It says cost of goods sold, so why are we taking the cost of goods that actually weren't sold?
In my head, I assumed gross profit as profit, which we define as "revenue from goods sold" - "cost of the goods sold". By this definition, the cost should only consider the "goods that are sold".

Let me try to answer your doubt too,

The definition you found is correct:
COGS typically refers to the total cost of producing or procuring all the goods available for sale, not just the goods that are sold. This is because the cost of goods in inventory (whether sold or unsold) is considered part of the store's operational cost for the shipment.
In this specific question, we are dealing with total shipment costs rather than a dynamic inventory accounting where unsold goods can be carried forward. Since the problem states that no other hats from the shipment were sold, the cost of the hats in the shipment is fully accounted for, regardless of how many were sold.
In short, COGS refers to the total cost of acquiring or producing the goods that were available for sale, regardless of how many were sold.

Let me know if this helps put things in perspective, or if you need more clarification.

You are given in the question: ... If the store did not sell any other hats form the shipment,...

It means the remaining hats were unsold and hence a loss was taken on them. That needs to be taken into consideration in the calculation of gross profit.
When something is to be sold later, we do not consider its cost price in our current calculations then. But if something remains unsold, that is a loss and its cost price needs to be adjusted in gross profit.

Thanks Krunaal and KarishmaB
It makes sense now. One last follow up - whoever wants to pitch in on this, say we were not to take the cost of unsold goods into account, how would the question be phrased differently in that case? My goal is to learn how I can differentiate between the two cases.
Had the last line directly been " the store's gross profit from the sale of the hats from the shipment was what percent of the store's cost for the hats from the shipment?"
instead of " If the store did not sell any other hats form the shipment, then the store's gross profit from the sale of the hats from the shipment was what percent of the store's cost for the hats from the shipment?"
Would we then just take the cost of the goods sold into account and not the unsold goods?

That's a good question, and the distinction indeed lies in the specific phrasing - the current phrasing in the question explicitly includes the entire shipment cost in the calculation because the focus is on the gross profit for the entire shipment, not just the sold portion. If the question wanted to exclude the cost of unsold goods and focus only on the sold hats, it would need to be reworded. For instance:"The store's gross profit from the hats it sold was what percent of the cost of those hats?" or, "What percent of the revenue from the hats sold represents the gross profit from those hats?" Such wording restricts the scope to only the hats sold and implies we should focus solely on the cost of the sold hats

Classic shopkeep problem. Just make X your cost and see how much in excess of X you land:

This question can be easier in calculation if we take Total hats as 100 and cost per hat as 10.
60% hats sold at 50% greater= 60*15=900
40 hats are left
70% of 40 hats are sold at 66.6% OFF which means 33% of the cost it was initially which is 15(Very tricky to understand this as 66% off, many times we read it as cost is reduced from 100% to 66.6% (that's the trap set in this question)

(70/100)*40*(100/3)*15=28*5=140

Total profit= (1000-(900+140))=40
Total cost=100*10
Profit %= 40/1000= 4/100= 4%

Hope it is clear