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A store sold 60 percent of the hats from a shipment of hats at a 08 Jan 2025, 11:17
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Hi. How did you come to the conclusion that 66 2/3 percent is equal to 2/3? Where did the 66 go? When I was doing it I thought it was 66 * 2/3 %, which in my mind would equal 44%. Thank you.
gmatophobia
rakman123
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%

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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SOFIA19
Hi. How did you come to the conclusion that 66 2/3 percent is equal to 2/3? Where did the 66 go? When I was doing it I thought it was 66 * 2/3 %, which in my mind would equal 44%. Thank you.
gmatophobia
rakman123
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%

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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66 2/3 percent translates to 66 + 2/3 percent => 66 + 0.66667 percent => 66.66667 percent => 66.66667 * 1/100 => 0.6666667 => 2/3

Usually you will find multiplication denoted by a * or brackets. For eg. 2*3 = 6 or 2(3) = 6. Hope this helps.
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A store sold 60 percent of the hats from a shipment of hats at a 09 Jan 2025, 20:15
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THANK YOU!! I thought I was losing my mind with everyone breezing past this obvious error. Bunuel and the others blow right by it. This question is unambiguously wrong. Gross profit, by definition, is as you define. We are looking at profit with respect to hats sold-- NOT total hats. Gross profit is $16, and total cost of ALL hats, sold and unsold, is $100. Therefore 16% is correct. Good lord what a nightmare.
EthanTheTutor
Gross profit is defined as Revenue - COGS (cost of goods sold).

The correct answer here is 16%, given the universal definition of gross profit. I haven't seen a lot of questions on the GMAT that are unambiguously incorrect, but this one is.
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A store sold 60 percent of the hats from a shipment of hats at a 10 Jan 2025, 10:22
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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! :)
gmatophobia
rakman123
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%

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 10 Jan 2025, 12:23
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rakman123
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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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%

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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!
johnm2
THANK YOU!! I thought I was losing my mind with everyone breezing past this obvious error. Bunuel and the others blow right by it. This question is unambiguously wrong. Gross profit, by definition, is as you define. We are looking at profit with respect to hats sold-- NOT total hats. Gross profit is $16, and total cost of ALL hats, sold and unsold, is $100. Therefore 16% is correct. Good lord what a nightmare.
EthanTheTutor
Gross profit is defined as Revenue - COGS (cost of goods sold).

The correct answer here is 16%, given the universal definition of gross profit. I haven't seen a lot of questions on the GMAT that are unambiguously incorrect, but this one is.
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A store sold 60 percent of the hats from a shipment of hats at a 10 Jan 2025, 19:56
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Bunuel Krunaal Could I please ask both experts to guide me on where the error occurred? Thank you so much! :cry::please:
hattie
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!
johnm2
THANK YOU!! I thought I was losing my mind with everyone breezing past this obvious error. Bunuel and the others blow right by it. This question is unambiguously wrong. Gross profit, by definition, is as you define. We are looking at profit with respect to hats sold-- NOT total hats. Gross profit is $16, and total cost of ALL hats, sold and unsold, is $100. Therefore 16% is correct. Good lord what a nightmare.
EthanTheTutor
Gross profit is defined as Revenue - COGS (cost of goods sold).

The correct answer here is 16%, given the universal definition of gross profit. I haven't seen a lot of questions on the GMAT that are unambiguously incorrect, but this one is.
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A store sold 60 percent of the hats from a shipment of hats at a 11 Jan 2025, 02:29
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Bunuel Krunaal Could I please ask both experts to guide me on where the error occurred? Thank you so much! :cry::please:
hattie
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!
Show more
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.
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A store sold 60 percent of the hats from a shipment of hats at a 11 Jan 2025, 03:32
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Thank you, Krunaal.:angel:
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!

Krunaal
hattie
Bunuel Krunaal Could I please ask both experts to guide me on where the error occurred? Thank you so much! :cry::please:
hattie
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!
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.
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Hi experts. JeffTargetTestPrep Bunuel KarishmaB
Going through all the replies in this post, I still have a small doubt:
Quote:
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?
Show more

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:
Quote:
Gross profit is the direct profit left over after deducting the cost of goods sold, or cost of sales, from sales revenue
Show more
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".
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Let me try to answer your doubt too,

The definition you found is correct:
Quote:
Gross profit = Revenue - Cost of Goods Sold (COGS)
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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.
siddhantvarma
Hi experts. JeffTargetTestPrep Bunuel KarishmaB
Going through all the replies in this post, I still have a small doubt:
Quote:
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?

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:
Quote:
Gross profit is the direct profit left over after deducting the cost of goods sold, or cost of sales, from sales revenue
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".
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siddhantvarma
Hi experts. JeffTargetTestPrep Bunuel KarishmaB
Going through all the replies in this post, I still have a small doubt:
Quote:
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?

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:
Quote:
Gross profit is the direct profit left over after deducting the cost of goods sold, or cost of sales, from sales revenue
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".
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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.
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A store sold 60 percent of the hats from a shipment of hats at a 11 Jan 2025, 09:21
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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 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
siddhantvarma
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 14 Apr 2025, 08:09
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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

rakman123
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 06 Jun 2025, 05:21
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KarishmaB is 66*2/3 = 2/3?
KarishmaB
rakman123
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%
­Method 1: Assuming Values

Say there were 100 hats and each was bought for $6 (LCM of 2 and 3 so that we can easily increase it by 50% and reduce by 2/3rd). Total cost price = $600

60 hats were sold for selling price that was 50% more i.e. $9 each
Revenue = 60*9 = 540

70% of the remaining 40 hats i.e. 28 hats were sold for selling price that for 2/3rd less than 9 i.e. at $3
Revenue = 28*3 = $84

Total Profit = 540 + 84 - 600 = $24

Percentage of profit = 24/600 * 100 = 4%

Answer (B)

Method 2: Use weighted averages

60 hats were sold at 50% profit.
70% of 40 hats i.e. 28 hats were sold at "increase of 50% and then reduction of 66.67%". We know how to handle successive percentage changes using multiplication factors. It will be (3/2) * (1/3) = 1/2. Hence this is 50% loss.
Rest of the 12 hats are sold at 100% loss

Avg profit = \(\frac{(60*50 + 28*(-50)+12*(-100))}{100} = 4\)


Concept Videos of weighted averages:
https://www.youtube.com/watch?v=_GOAU7moZ2Q
Post on successive percentage changes:
https://anaprep.com/arithmetic-successi ... e-changes/­
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A store sold 60 percent of the hats from a shipment of hats at a 06 Jun 2025, 05:45
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shubhim20
KarishmaB is 66*2/3 = 2/3?
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Explained here - https://gmatclub.com/forum/a-store-sold ... l#p3512215

Request you to kindly invest some time and go through the previous discussion on thread.
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A store sold 60 percent of the hats from a shipment of hats at a 08 Jun 2025, 23:01
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Don't forget the % sign.

66(2/3) % = 2/3

Percent to Fraction equivalents. Check here: https://youtu.be/HxnsYI1Rws8

shubhim20
KarishmaB is 66*2/3 = 2/3?
KarishmaB
rakman123
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%
­Method 1: Assuming Values

Say there were 100 hats and each was bought for $6 (LCM of 2 and 3 so that we can easily increase it by 50% and reduce by 2/3rd). Total cost price = $600

60 hats were sold for selling price that was 50% more i.e. $9 each
Revenue = 60*9 = 540

70% of the remaining 40 hats i.e. 28 hats were sold for selling price that for 2/3rd less than 9 i.e. at $3
Revenue = 28*3 = $84

Total Profit = 540 + 84 - 600 = $24

Percentage of profit = 24/600 * 100 = 4%

Answer (B)

Method 2: Use weighted averages

60 hats were sold at 50% profit.
70% of 40 hats i.e. 28 hats were sold at "increase of 50% and then reduction of 66.67%". We know how to handle successive percentage changes using multiplication factors. It will be (3/2) * (1/3) = 1/2. Hence this is 50% loss.
Rest of the 12 hats are sold at 100% loss

Avg profit = \(\frac{(60*50 + 28*(-50)+12*(-100))}{100} = 4\)


Concept Videos of weighted averages:
https://www.youtube.com/watch?v=_GOAU7moZ2Q
Post on successive percentage changes:
https://anaprep.com/arithmetic-successi ... e-changes/­
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A store sold 60 percent of the hats from a shipment of hats at a 15 Jul 2025, 06:21
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Would you please tell why we have taken here the whole 100 hats yo get profit because store didn't sell all hats. He sold only 88 hats?
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rakman123
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%

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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