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 key information here is that
the retailer sold all the shirts it purchased
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
