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A store sold 60 percent of the hats from a shipment of hats at a 11 Jan 2025, 10:13
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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
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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?
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A store sold 60 percent of the hats from a shipment of hats at a 30 Jan 2025, 13:45
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Classic shopkeep problem. Just make X your cost and see how much in excess of X you land:
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A store sold 60 percent of the hats from a shipment of hats at a 01 Aug 2025, 13:00
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Total cost of shipment be - x

60% Of the shipment would cost - 3/5x
Revenue from 60% of shipment would be 3/5x*3/2 = 9/10x

70% of remaining 40% of shipment would cost - 14/50x
Revenue from it would be - 7/50x (3/2* 1/3 = 1/2 - Note that 66 2/3 = 1/3)

Total revenue - 9/10x+7/50x = 52/50x, Profit = 52/50x - x = 2/50x

Profit % = 2/50 x divided by x *100 = 4%
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A store sold 60 percent of the hats from a shipment of hats at a 15 Dec 2025, 11:21
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Hi Bunuel I totally understand the solution and I got it correct too because solving for the other way led me to 16% which is not one of the answer choice - my question is why are we taking the 12 unsold hats to have made a loss? maybe they are in the inventory and we can still sell them later? (we get 12 if we assume the shipment consists of 100 hats, 88 are sold and 12 remain unsold)
The question asks what was the profit from the sale of the hats from the shipment with respect to the cost for hats from the shipment - how do I understand from this that I need to consider [profit from 100 hats/cost for 100 hats] vs [profit from the 88 hats sold/cost incurred for the 88 hats sold] ?
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A store sold 60 percent of the hats from a shipment of hats at a selling price that was 50 percent greater than the store's cost for each hat. Then the store reduced the selling price by 66 2/3 percent and sold 70 percent of the remaining hats at the reduced selling price. 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?

A) 1%
B) 4%
C) 9%
D) 13%
E) 25%
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A store sold 60 percent of the hats from a shipment of hats at a 15 Dec 2025, 23:29
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Dragon805
Hi Bunuel I totally understand the solution and I got it correct too because solving for the other way led me to 16% which is not one of the answer choice - my question is why are we taking the 12 unsold hats to have made a loss? maybe they are in the inventory and we can still sell them later? (we get 12 if we assume the shipment consists of 100 hats, 88 are sold and 12 remain unsold)
The question asks what was the profit from the sale of the hats from the shipment with respect to the cost for hats from the shipment - how do I understand from this that I need to consider [profit from 100 hats/cost for 100 hats] vs [profit from the 88 hats sold/cost incurred for the 88 hats sold] ?

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Notice we are not being asked for the profit from the shipment.

Yes, the 12 unsold hats are inventory, and we are not treating them as a loss or a profit here.

The question only asks this: take the profit made on the hats that were actually sold, then take the cost of the whole shipment, and compute the ratio of the first number to the second.
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A store sold 60 percent of the hats from a shipment of hats at a 09 Jan 2026, 07:18
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0.6q*1.5p = .9pq
.28q*.5p= .140
Total 1.04pq so 4% profit
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A store sold 60 percent of the hats from a shipment of hats at a 31 Mar 2026, 22:50
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Hi, you dindt account for the unsold hats and still got the correct ans. How?

gmatophobia


Choosing the right numbers is very crucial to solve this question.

Let's assume that the number of hats in the shipment = 100

A store sold 60 percent of the hats from a shipment of hats at a selling price that was 50 percent greater than the store's cost for each hat

Number of hats sold = 60

Also given - The initial selling price of the hats = \(\frac{3}{2}\) * times the store's cost for each hat.

Let's assume the stores cost for each hat = $2
Cost price of 100 hats = $2 * 100 = $200

The initial selling price of the hats = \(\frac{3}{2} * 2 = $3\)

Hats remaining = \(100 - 60 = 40\)

Then the store reduced the selling price by 66 2/3 percent and sold 70 percent of the remaining hats at the reduced selling price.

\(66 \frac{2}{3}\)% \(= \frac{2}{3}\)

New selling price = \(\frac{1}{3}\)rd * old selling price

New selling price = \(\frac{1}{3}\)rd * 3 = $1

Number of hats sold = \(\frac{70}{100} * 40 = 28\)

Total Revenue = (60 * 3) + (28 * 1)= 208

Profit = $(208-200) = $8

Profit % = \(\frac{8}{200} * 100 = 4\)%

Option B
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A store sold 60 percent of the hats from a shipment of hats at a 31 Mar 2026, 23:02
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ok guys i've figured out the problem with people getting 16%.

If you are calculating the GP batchwise ie. 60*1.5x -60*x and 28*0.5x-28*x. Then, you need to account for the loss on the 12 unsold hats ie. 12*x then take the net GP and divide by 100x.

If you are however, doing SP-CP overall, then you can just do SP (60*1.5x+28*0.5x) - CP (30*x)/CP (30*x).

I solved by taking CP=30, SP=45.
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