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A retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack. If the retailer sold all the shirts it purchased and profited $84 on the sale, how many packs of shirts did it sell?
A. 10
B. 48
C. 56
D. 96
E. 240
OA B.
A retailer buys cases of 24 shirts for $30/case and then
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The key information here is that the retailer sold all the shirts it purchasedAAPL wrote:Veritas Prep
A retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack. If the retailer sold all the shirts it purchased and profited $84 on the sale, how many packs of shirts did it sell?
A. 10
B. 48
C. 56
D. 96
E. 240
This is a huge hint!
For example, we know that the retailer did NOT buy only 1 case of 24 shirts, because 24 shirts will not divide into packs of 5 shirts.
Likewise, we know that the retailer did NOT buy 2 cases of shirts, because 48 shirts will not divide into packs of 5 shirts.
And we know that the retailer did NOT buy 3 cases of shirts, because 72 shirts will not divide into packs of 5 shirts.
Etc.
The first possible scenario is that the retailer bought 5 cases of shirts for a total of 120 shirts.
Let's see what happens with this scenario.
At $30 per case, the retailer PURCHASED the 5 cases for $150 [since 30 x 5 = 150]
120 shirts can be divided into 24 packs of 5 shirts
At $8 per pack, retailer SOLD the 24 packs for $192 [since 8 x 24 = 192]
In this scenario, the retailer's profit = $192 - $150 = $42
This doesn't work, since we're told the profit = $84
IMPORTANT: In the above scenario, the retailer's profit was HALF of what we needed.
So, in order for the retailer's profit to be $84, we must DOUBLE the number of shirt bought and sold.
In the above scenario, the retailer SOLD 24 packs of 5 shirts
So, to meet the required $84 profit, the retailer must SELL 48 packs of 5 shirts
Answer: B
Cheers,
Brent
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Hi All,
We're told that a retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack, the retailer sold ALL of the shirts it purchased and profited $84 on the sale. We're asked for the number of PACKS of shirts that it sold. This question can be approached in a couple of different ways, including by TESTing THE ANSWERS.
To start, there's a great Number Property 'shortcut' built into the question. Since ALL of the shirts were sold - and shirts are bought in cases of 24 - we know that the TOTAL number of shirts must be a multiple of 24. Those shirts are then sold in packs of 5, so that same TOTAL must be a multiple of 5. To find the total, you can find the LCM of 5 and 24 and try the various multiples of that LCM OR you can 'brute' force the multiples of 24 and 5 until you find the match OR you can use the answer choices to your advantage to find the one that would lead to a total that fits those multiples...
Answer A: 10 5-packs = 50 shirts. This is NOT a multiple of 24.
Answer B: 48 5-packs = 240 shirts. This IS a multiple of 24.
240/24 = 10 cases of shirts = (10)($30) = $300 is the COST of these shirts
48 5-packs sold = (48)($8) = $384 in revenue
Profit here = $384 - $300 = $84
This is an exact match for what we were told, so this must be the answer!
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that a retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack, the retailer sold ALL of the shirts it purchased and profited $84 on the sale. We're asked for the number of PACKS of shirts that it sold. This question can be approached in a couple of different ways, including by TESTing THE ANSWERS.
To start, there's a great Number Property 'shortcut' built into the question. Since ALL of the shirts were sold - and shirts are bought in cases of 24 - we know that the TOTAL number of shirts must be a multiple of 24. Those shirts are then sold in packs of 5, so that same TOTAL must be a multiple of 5. To find the total, you can find the LCM of 5 and 24 and try the various multiples of that LCM OR you can 'brute' force the multiples of 24 and 5 until you find the match OR you can use the answer choices to your advantage to find the one that would lead to a total that fits those multiples...
Answer A: 10 5-packs = 50 shirts. This is NOT a multiple of 24.
Answer B: 48 5-packs = 240 shirts. This IS a multiple of 24.
240/24 = 10 cases of shirts = (10)($30) = $300 is the COST of these shirts
48 5-packs sold = (48)($8) = $384 in revenue
Profit here = $384 - $300 = $84
This is an exact match for what we were told, so this must be the answer!
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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The cost per shirt is 30/24 = 5/4.AAPL wrote:Veritas Prep
A retailer buys cases of 24 shirts for $30/case and then resells them in packs of 5 for $8/pack. If the retailer sold all the shirts it purchased and profited $84 on the sale, how many packs of shirts did it sell?
A. 10
B. 48
C. 56
D. 96
E. 240
The revenue per shirt is 8/5.
The profit per shirt is (revenue - cost) = (8/5 - 5/4)
If we let n = the number of shirts sold, we have:
(8/5 - 5/4)n = 84
Multiplying the equation by 20, we have:
(32 - 25)n = 84 x 20
7n = 84 x 20
n = 12 x 20
n = 240
Since each pack has 5 shirts, there are 240/5 = 48 packs of shirts.
Answer: B
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