Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE DS – A company makes and sells two products, P and Q…

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 

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