Problem Solving

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

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

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 cost per shirt is 30/24 = 5/4.

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