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

Given: 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.

Asked: 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?

Let the cost of the hats from the shipment be x.

Let the total hats be 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.
60 hats sold at selling price of 1.5x.

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.
40*70% = 28% of hats were sold at 1.5x(100% - 662/3)% = .5x

Total selling price = 1.5x *60 + .5x *28 = 90x + 14x = 104x
Total cost price = 100x
Gross profit = 104x - 100x = 4x

Gross Profit as percent of the store's cost for the hats from the shipment = 4x/100x *100% = 4%

IMO B

Hi Bunuel JeffTargetTestPrep Kinshook gmatophobia,
Can you help me understand where I am going wrong in my logic.

I asssumed there are 100 hats in the shipment. The CP = 100 for each hat.

Now 60 percent are sold at 1.5 times the CP. SP = 150. So profit on 60 hats = 60*50 = 3000
The SP is then reduced by 2/3rd. New SP = 150*1/3 = 50
Loss per hat = 150 - 100 = 50
So loss for 28 hats (70 percent of remaining) = 28*50 = (1400)

So I got total Profit as 3000 - 1400 = 1600

So \(\frac{1600}{100*100}*100\)

But I'm really far from the required answer.

Any help is appreciated.

You have not included the loss incurred due to non sale of 12 hats (30% of remaining).
This will incur a loss of 12*100 or 1200.

Total profit now is 1600-1200 or 400.
% =100 * 400/(100*100) = 4

Thank you, I got it. I thought the question only asked about the hats that were sold. I had to pay more attention to the highlighted part.

As the question deals with %, take the amounts as 100. Let the CP and also the number of hats purchased be 100.

1). Total money spent = 100*100 = 10,000

2) Money received
(I) 60 hats at 50% profit = 60*150 = 9000
(II) 70% of remaining 40 hats, that is 28 hats, at 66 2/3 % discount.
33 1/3, 66 2/3 and 100 are equivalent to three parts 1/3, 2/3 and 3/3 respectively. Thus a discount of 2/3 the amount means the new SP is 1/3 of initial SP = 150*1/3 = 50. Amount received = 28*50 = 1400
Total = 9000+1400 = 10400

3) Profit = 10400-10000 = 400
Profit % = \(\frac{400}{10000}*100=4\)

B

100 hats lets each hat Cost price (CP) =1 then CP of 100 hats =100
60 hats sp 1.5 (50% greater than Cost) total rev = 60*1.5 = 90
70%of 40( remaining ) = 28
28 sold for after reducing price by 66.67 % ie 1.5-2/3*(1.5)=0.5
revenue from 28 hats = 28*0.5 =14
total revenue = 90 + 14 = 104
cp was 100
so 4 % profit

answer b

Here's a way that avoids plugging in numbers, and the sometimes ugly calculations that can result from that.

Gross profit requires a calculation of revenue - cost.

Cost we only have to calculate once, since that it's simply the cost of the entire shipment. Let that equal c*x, where x is however many hats were purchased..

Revenue we calculate twice, once for each of the two different prices that the hats were sold at.

1) 60% of the hats (again, hats are denoted by x) were sold at 150% the dollar value of the cost, or 1.5c.
Therefore, 6/10(x) * 3/2(c) = 9/10(xc)

2) 70% of the remaining hats (i.e. 40% of the total hats) were sold at a third of the previous price. That price is 1/3 * 3/2(c) = 1/2(c).
So 7/10*(4/10)x * (1/2)c = 7/50(xc)

Now add the two revenues:
9/10(xc) + 7/50(xc) = 45/50(xc) + 7/50(xc) = 52/50(xc) = 26/25(xc)

Finally, gross profit = revenue - cost. Cost, remember, is xc, so:
26/25(xc) - xc = 26/25(xc) - 25/25(xc) = 1/25(xc) = 4/100(xc), or 4% of (xc), i.e. 4% of our cost!

Answer: B

This question is unfair towards anyone with a financial background as it assumes without stating that the unsold inventory from the shipment would be written down and expensed as part of the costs of goods sold for the purposes of this exercise, which is not obvious at all.

In the video below, I breakdown 2 key habits for ones like this:

1) Organize the info into a P*Q = R table, just like many people do on Rate problems (R*T = D)

2) For the Cost, pick the number 100 for the Price and Quantity

Hi there,

Im trying to figure out where I went wrong and would appreciate if you could give me some help.
I have the same steps and calculations as you but start to go wrong when I calculate gross profit immediately for each selling price, 3c/2 and c/2.

Gross profit for 60% of hats = (3c/2-c)*0.6x = 0.3xc
Gross profit for 70% of remainder of hats = (c/2-c)*0.28x = -0.14xc

Total gross profit = 0.3xc -0.14xc = 0.16xc
Gross profit as % of total cost = 0.16xc / xc = 16%.
­

­If you calculate the profit/loss on individual batches of hats, then you should also take into account the third batch of 0.12x hats, which were not sold and thus generated a loss of -0.12cx. Thus, the gross profit equals 0.3xc - 0.14xc - 0.12xc = 0.04xc.

How do we understand that we have to take the total cost which is assumed as 100 and not the cost of the 88 hats which have been sold? we have total sold 60+28 hats right? I took the denominator as 88 -CP considering that we need to find the profits as a percentage of the CP of hats that are sold and not as a percentage of total hats cost price.
Can someone highlight how to differentiate between the two wordings? Thanks

GMATNinja TargetTestPrep Bunuel­

­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/­

­it would be 1.5-2/3*1.5 = 1/2 and not 1/3 at 70% line

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.

Let, total Hats = 100
et cost price for each hat = 100
Total Cost = 100*100 = 10000


First 60 hats sold @150 each, i.e. Revenue = 60*150 = 9000

New Reduced selling price = (1/3)*150 = 50
70% of remaining (40) = 0.7*40 = 28
Revenue here = 50*28 = 1400


Total revenue so far = 9000 + 1400 = 10400
Gross profit = 10400-10000 = 400

Prfit as % of cost = (400/10000)*100 = 4%

Answer:: Option B