Solutions

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Question

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 Tshirts, 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?

I. The team purchased 200 T-shirts, sold each T-shirt for $12, and made a $900 profit.

II. In addition to the $100 setup fee, the team paid $7 for each T-shirt.


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Hard

Solution

Option A is the correct answer.


Option Analysis

Let,

x = amount of discount

n = number of shirts

Statement I is sufficient: 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)

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 II is insufficient: In addition to the $100 setup fee, the team paid $7 for each Tshirt.

This tells us 7 = (8-(x/100)n)

We have a single equation with two unknowns, so we cannot solve.


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