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Intern  B
Joined: 02 Jan 2019
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As a salesperson, Brandon's compensation is structured so that each mo  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 18% (01:28) correct 82% (01:41) wrong based on 11 sessions

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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.
Director  V
Status: Manager
Joined: 27 Oct 2018
Posts: 745
Location: Egypt
GPA: 3.67
WE: Pharmaceuticals (Health Care)
Re: As a salesperson, Brandon's compensation is structured so that each mo  [#permalink]

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2
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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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 IMO A Target Test Prep Representative V Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 8619 Location: United States (CA) Re: As a salesperson, Brandon's compensation is structured so that each mo [#permalink] ### Show Tags 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.

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