A retailer buys cases of 24 shirts for $30/case and then resells them

Question

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

A. 10
B. 48
C. 56
D. 96
E. 240

GMATinsight · Accepted Answer

Buys cases of 24 shirts for $30/case  and  resells them in packs of 5 for $8/pack

Cost price per shirt = 30/24 = $1.25

Selling price per shirt = 8/5 = $1.60

Profit per shirt = 1.60-1.25 = $0.35

Total profit = $84

Total Shirts = 84/0.35 = 240 Shirts

Total packs while selling = 240/5 = 48

Answer: Option B

Luckisnoexcuse · Answer

Let y be no. of cases bought and x be no. of packs sold
24*y = 5*x

8*x - 30*y = 84

y= 5x/24

8x - 25x/4 = 84
7x = 84*4
x = 48
B

shra1raju · Answer

Well the math here in this question is straight forward. I'm confused with the wording of the question.

A retailer buys cases of 24shirts for $30/case

1. How do we know how many cases are bought?

beacuse $30 is not for all the shirts, it is per CASE. How about retailer bought 2 cases. Which would make $60 for 2 cases(24shirts) and $2.5 per shirt.

But all the calculations are made on this assumption that there are 24 shirts and 1 case. Can you please help me understand this bit of the question please.

generis · Answer

shra1raju , I think you may be a little mixed up about the total number of shirts originally bought and/or number of shirts per case . The total number of shirts bought is NOT 24 . Could you explain how you got that idea? The only reason that I can imagine is that the word "OF" does not make sense to you. See below. Total # of shirts is 24 per case times number of cases. True. But that assumption is inferred from this language: "A retailer buys cases of 24 shirts for $30/case..." cases OF 24 shirts = -- cases that have 24 shirts in them OR -- cases in which the contents of each case consist OF 24 shirts True, $30 is for one case. But each case contains 24 shirts. And the "cases of 24" that cost "$30 per case" are the same cases. Why not? How not? This declaration is an assertion, not an explanation. Could you explain? I do not see the logic. If "cases OF 24" is not the problem, then I cannot understand what makes you believe that: 1) total shirts bought is 24; and 2) there are NOT 24 shirts in each case Extend the analysis re "cases of 24 shirts..." Think of "pens come in packages of 10." There are 10 pens in one package. Or "I bought some cartons of 12 eggs for $5.00/carton." Does that language seem to you as if the number of eggs in the carton changes? Or as if I bought only 12 eggs? Or only one carton? No . 2 cases = 48 shirts She did not buy a total of 24 shirts. She bought 24 shirts per case . She bought some # of cases. (Turns out to be 10, see below.) The prompt does not say, "a retailer buys 24 shirts for $30/case." We can backsolve to get the number of cases purchased. Cost per shirt: \frac{$30}{24shirts}=$1.25 per shirt Sell price per shirt: \frac{$8}{5shirts}=$1.60 per shirt Profit per shirt: (SP - C) = ($1.60 - $1.25) = $0.35 Number of shirts sold: \frac{TotalProfit}{ProfitPerShirt}=\frac{$84.00}{$0.35}=240 shirts Number of cases purchased originally - We could divide the total of 240 shirts by 24 shirts per case: she bought 10 cases Total cost: ($30/case * 10 cases) = $300 Total revenue: ($8/pack * 48 packs^) = $384 Total profit: (TR - TC) = ($384 - $300) = $84 Hope this helps. If it does not, please try to rephrase your logic to explain how you inferred what you did?

^48 packs is the answer to the question: "How many packs of shirts did she sell?" She sold 240 shirts. 5 shirts per pack. She sold \frac{240}{5}=48 packs of shirts

BrentGMATPrepNow · Answer

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     
120 shirts can be divided into 24 packs of 5 shirts
At $8 per pack, retailer SOLD the 24 packs for  $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

EMPOWERgmatRichC · Answer

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. Eliminate Answer A.

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

ScottTargetTestPrep · Answer

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

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A retailer buys cases of 24 shirts for $30/case and then resells them

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