## Last year, a certain company began manufacturing…

## Solution:

We are given that the expenses for manufacturing product X were $100,000 plus 5% of the total revenue from all units of product X sold. So if we let E = total expenses for product X, R = revenue per unit of product X, and N = the number of units sold, we can create the following equation:

E = 100,000 + 0.05NR

As we can see from the equation above, NR is the company’s total revenue. Since we are also given that the company made a profit last year, this means that NR > E.

Since E = 100,000 + 0.05(NR), we can substitute 100,000 + 0.05(NR) for E in the inequality NR > E. Thus we have:

NR > 100,000 + 0.05(NR)

0.95(NR) > 100,000

We need to determine whether N > 21,000.

**Statement One Alone: **

The company’s total revenue from the sale of product X last year was greater than $110,000.

We earlier defined the company’s total revenue as NR; statement one tells us that NR > 110,000. However, we do not have enough information to determine N, the total number of units sold. Statement one alone does not provide enough information to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone: **

For each unit of product X sold last year, the company’s revenue was $5.

It follows that R = 5. We can substitute 5 for R into the inequality 0.95(NR) > 100,000.

0.95(5)(N) > 100,000

4.75(N) > 100,000

N > 100,000/4.75

N > 100,000/(475/100)

N > (100,000)(100)/475

N > (100,000)(4)/19

N > 400,000/19

N > 21,052 12/19

Since N is greater than 21,052, we know that the company did sell more than 21,000 units of product X last year. Statement two alone is sufficient to answer the question.

**Answer:** B