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:
https://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:
https://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