As a salesperson, Brandon's compensation is structured so that each mo

Let’s let Brandon’s sales for the month of August be S. According to the information given to us, Brandon earns $5,000 if S ≤ 10,000 and $5,000 + 0.1(S - 10,000) if S > 10,000.

Statement One Alone:

Had Brandon sold $10000 more than he did in August, his total compensation for the month would have been equal to 15% of his sales.

If Brandon sold $10,000 more, his sales for the month of August would have been (S + 10,000), which is always greater than or equal to $10,000. Thus, he would have earned $5,000 + 0.1(S + 10,000 - 10,000) = $5,000 + 0.1S. Since we are told that this is equal to 15% of S, we have:

5,000 + 0.1S = 0.15S

This is an equation with a single unknown where the unknowns do not cancel out. Thus, without actually solving this equation, we know that there is a unique solution.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

Had Brandon sold $40000 less than he did in August, his total compensation for the month would have been equal to 10% of his sales.

If S > 50,000, then S - 40,000 > 10,000; thus, he would earn $5,000 + 0.1(S - 40,000 - 10,000) = $5,000 + 0.1(S - 50,000). Since we are told that this is equal to 10% of S, we have:

5,000 + 0.1(S - 50,000) = 0.1S

5,000 + 0.1S - 5,000 = 0.1S

Notice that the unknowns cancel out and we are left with 0 = 0 in this equation. This means that any S with S > 50,000 will satisfy this equation.

For example, let S = 60,000. Had he sold $40,000 less, he would have sold 60,000 - 40,000 = 20,000 and made $5,000 + 0.1(20,000 - 10,000) = $5,000 + 0.1(10,000) = $5,000 + 1,000 = $6,000, which is equal to 10% of S. On the other hand, if S = 70,000, he would earn $5,000 + 0.1(30,000 - 10,000) = $5,000 + $2,000 = $7,000, which is again equal to 10% of S. Thus, we cannot determine a unique value for his sales.

Statement two is not sufficient to answer the question.

Answer: A