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

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As a salesperson, Brandon's compensation is structured so that each mo  [#permalink]

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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.

Originally posted by jousuf7 on 01 Dec 2019, 11:30.
Last edited by Bunuel on 01 Dec 2019, 23:01, edited 1 time in total.
Renamed the topic and edited the question.
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Re: As a salesperson, Brandon's compensation is structured so that each mo  [#permalink]

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New post 01 Dec 2019, 11:44
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from the given: \(B = 5000 + \frac{10}{100}(S-10000)\)

question : find S

from statement (1):
\(B = 5000 + \frac{10}{100}(S + 10000-10000)\) = \(\frac{15}{100}S\)
so \(5000 = \frac{5}{100}S\) and S = 100000 --> sufficient

from statement (2): \(B = 5000 + \frac{10}{100}(S -40000 -10000)\) = \(\frac{10}{100}S\)
so \(5000 + \frac{10}{100}S - 5000\) = \(\frac{10}{100}S\) --> insufficient (because both sides are the same)

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As a salesperson, Brandon's compensation is structured so that each mo  [#permalink]

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New post 03 Dec 2019, 09:29
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.


Given: 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.

Asked: What were Brandon's total sales for the month of August?

Brandon's compensation is given by formula:
C = $5000 + 10%(S-$10,000)
C: Compensation
S: Sales

(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.
Let S' = S + $10000
C = $5000 + 10%(S+$10000-$10000) = 15%S
5%S = $5000
S = $5000/5% = $100,000
SUFFICIENT

(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.
S' = S - $40000
C = $5000 + 10%(S -$40000 - $10,000) = 10%S
S can not be solved
NOT SUFFICIENT

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Re: As a salesperson, Brandon's compensation is structured so that each mo  [#permalink]

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New post 05 Dec 2019, 20:15
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
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Re: As a salesperson, Brandon's compensation is structured so that each mo   [#permalink] 05 Dec 2019, 20:15
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