# A company makes and sells two products, P and Q…

# Solution:

We are given the following information in regard to products P and Q.

Cost per unit of P = 8 dollars

Revenue per unit of P = 10 dollars

Profit per unit of P = 10 – 8 = 2 dollars

Cost per unit of Q = 9.5 dollars

Revenue per unit of Q = 13 dollars

Profit per unit of Q = 13 – 9.5 = 3.5 dollars

We are also given that 834 units were sold. If we let n = the number of units of P sold and 834 – n = the number of units of Q sold, we can create the following equation:

2(n) + 3.5(834 – n) = total profit

2n + 2919 – 3.5n = total profit

2919 – 1.5n = total profit

Thus, we must determine whether:

2919 – 1.5n > 2,000

Is -1.5n > -919 ?

Is n < 612.67?

Since n is a whole number, if we can determine that n, the number of units of product P that were sold, is at most 612, then we can determine the answer to the question.

**Statement One Alone: **

During the month, more units of P than units of Q were sold.

Since half of 834 is 417, using the information in statement one, we can determine that a minimum of 418 units of P were sold.

We see that a minimum of 418 units of P sold doesn’t guarantee the number of units of P sold is at most 612. For example, the actual number of units of P sold could be 500, and then the total profit would be more than $2000. However, if the actual number of units of P sold were 700, then the total profit would be less than $2000. Thus, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone: **

During the month, at least 100 units of Q were sold.

Using the information in statement two, we can determine that at most 834 – 100 = 734 units of P were sold; that is, a maximum of 734 units of P were sold.

We see that a maximum of 734 units of P sold doesn’t guarantee the number of units of P sold is at most 612. Again the actual number of units of P sold could be either more than 612 or less than 612. Thus, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together: **

Using statements one and two we know that a minimum of 418 and a maximum of 734 units of P were sold. However, this still doesn’t guarantee that the number of units of P sold is at most 612. Thus, statements one and two together are not sufficient to answer the question.

**Answer: E **