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To raise funds, a racing team sold T-shirts imprinted with

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To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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New post 30 Oct 2013, 09:49
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Question Stats:

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To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of $100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x?

1. The team purchased 200 T-shirts, sold each T-shirt for $12, and made a $900 profit.
2. In addition to the $100 setup fee, the team paid $7 for each T-shirt.
[Reveal] Spoiler: OA

Last edited by guerrero25 on 30 Oct 2013, 16:01, edited 1 time in total.

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Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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guerrero25 wrote:
To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of $100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x?

1. The team purchased 200 T-shirts, sold each T-shirt for $12, and made a $900 profit.
2. In addition to the $100 setup fee, the team paid $7 for each T-shirt.

I do not have the OA with me ;i 'll update as soon as I get . Thanks in Advance .

Dear guerrero25,
This is a very tricky problem, and I'm happy to help. :-)

First of all, here's a refresher on revenue, profit, and cost, if these ideas are rusty for you:
http://magoosh.com/gmat/2013/profit-and ... -the-gmat/

Part of what's hard is that there are two unknowns:
x = amount of discount
n = number of shirts

Statement #1: The team purchased 200 T-shirts, sold each T-shirt for $12, and made a $900 profit.
So, revenue = 200*12 = $2400.
(profit) = (revenue) - (cost)
$900 = $2400 - cost
cost = $1500
Of that cost, $100 was for set up, so the rest is the cost of n shirts, at a rate of (8-(x/100)n), and we know n = 200
$1400 = n*(8-(x/100)n) = 200*(8-(x/100)*200)
OK, this is DS. At this point, we have a single equation for x, which we could solve. This statement will allow us to solve for x.
This statement, alone and by itself, is sufficient.

Statement #2: In addition to the $100 setup fee, the team paid $7 for each T-shirt.
This tells us 7 = (8-(x/100)n)
We have to be very careful not to import information from Statement #1 here. We have a single equation with two unknowns, so we cannot solve. See:
http://magoosh.com/gmat/2012/gmat-quant ... variables/
This statement, alone and by itself, is insufficient.

It seems to me the answer is (A).

Does all this make sense?
Mike :-)
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Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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New post 30 Sep 2014, 06:47
Easy one!!!

Profit =selling price-cost

cost=(8-(x/100)*200) here n=200

selling price=200*12

profit=selling-cost price= 200*12-(8-x/2)=900 ,we have a single equation for x, which we could solve :)
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Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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New post 01 Dec 2015, 13:25
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Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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New post 05 Aug 2017, 09:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: To raise funds, a racing team sold T-shirts imprinted with [#permalink]

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New post 11 Aug 2017, 09:34
guerrero25 wrote:
To raise funds, a racing team sold T-shirts imprinted with the team's logo. The team paid their supplier a one-time setup fee of $100. Because they purchased at least 50 T-shirts, the team qualified for their supplier's quantity discount of x cents per T-shirt and paid (8-(x/100)n) dollars for each of the n T shirts they purchased. What is the value of x?

Fantastic DS Question.

One-time setup fee = $100
Discount per t-shirt = x cents
Price per t-shirt = $ (8 - n(\(\frac{x}{100}\)))
x = ?

Quote:
1. The team purchased 200 T-shirts, sold each T-shirt for $12, and made a $900 profit.
2. In addition to the $100 setup fee, the team paid $7 for each T-shirt.


1) n = 200
SP = $12
=> Total Selling Price = $2400
Profit = $900
=> Cost = 2400 - 900 - 100
=> Cost = $ 1400

1400 = 8 - (\(\frac{x}{100}\))*200
We can solve for x.
Sufficient.

2) 7 = (8 - n(\(\frac{x}{100}\)))
2 variables and 1 equation.
Insufficient.

A is the answer.
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Re: To raise funds, a racing team sold T-shirts imprinted with   [#permalink] 11 Aug 2017, 09:34
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