shra1raju wrote:

GMATinsight wrote:

Bunuel wrote:

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?

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.

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.

**Quote:**

all the calculations are made on this assumption that there are 24 shirts and 1 case.

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

**Quote:**

beacuse $30 is not for all the shirts, it is per CASE

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.

**Quote:**

that one case does not necessarily have 24 shirts.

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?

**Quote:**

How about retailer bought 2 cases. Which would make $60 for 2 cases(24shirts) and $2.5 per shirt.

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
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