jousuf7 wrote:
As a salesperson, Brandon's compensation is structured so that each month he earns a $5000 base salary plus 10% of his total sales above $10000 for the month. What were Brandon's total sales for the month of August?
(1) 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.
(2) 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.
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
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.