Question

A company makes and sells two products, P and Q. The costs per unit of making and selling P and Q are $8.00and$9.50, respectively, and the selling prices per unit of P and Q are $10.00and$13.00, respectively. In one month the company sold a total of 834 units of these products. Was the total profit on these items more than $2,000.00 ?
(1) During the month, more units of P than units of Q were sold.
(2) During the month, at least 100 units of Q were sold.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

• It is given that the profit on each unit of P is $\$10.00–\$8.00=\$2.00$, and the profit on each unit of Q is $\$13.00–\$9.50=\$3.50$. Also, if p and q represent the number of units of Products P and Q made and sold, then it is given that $p+q=834$. Determining if the total profit on these items was more than $\$2,000$ requires determining how many units of at least one of the products were sold.
• This indicates that p > q, but does not give a specific value for p or q, NOT sufficient.
• This indicates that q $\ge 100$, but does not give a specific value for q, NOT sufficient.
• Taking (1) and (2) together, $p>q$ and $q\ge 100$, so $p>100$, but a specific value for p or q cannot be determined.