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Martha receives an annual salary of $20,000 plus a commission of 10 pe

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Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000
[Reveal] Spoiler: OA

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Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 25 Jan 2018, 23:48
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


Let \(S\) be the sale when both the salaries are equal

so we have \(20000+10\)%\(*(S-80000)=30000+5\)%\(*S\)

Solving we get \(S=360000\)

Option D
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Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 29 Jan 2018, 10:01
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


We can create the following equation in which n = total sales:

20,000 + 0.1(n - 80,000) = 30,000 + 0.05n

0.1n - 8,000 = 10,000 + 0.05n

0.05n = 18,000

n = 18,000/.05 = 360,000

Answer: C
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Last edited by JeffTargetTestPrep on 29 Jan 2018, 11:02, edited 1 time in total.
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Re: Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 29 Jan 2018, 10:56
JeffTargetTestPrep wrote:
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


We can create the following equation in which n = total sales:

20,000 + 0.1(n - 80,000) = 30,000 + 0.05(n -120,000)

0.1n - 8,000 = 10,000 + 0.05n - 6,000

0.05n = 12,000

n = 12,000/.05 = 1,200,000/5 = 240,000

Answer: C


Hi JeffTargetTestPrep

5% commission is on total sales. So the second equation should be 0.5n

Posted from my mobile device
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Re: Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 29 Jan 2018, 11:02
niks18 wrote:
JeffTargetTestPrep wrote:
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


We can create the following equation in which n = total sales:

20,000 + 0.1(n - 80,000) = 30,000 + 0.05(n -120,000)

0.1n - 8,000 = 10,000 + 0.05n - 6,000

0.05n = 12,000

n = 12,000/.05 = 1,200,000/5 = 240,000

Answer: C


Hi JeffTargetTestPrep

5% commission is on total sales. So the second equation should be 0.5n

Posted from my mobile device


Good call!

My solution has been amended.
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Re: Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 02 Feb 2018, 23:22
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


I understood the equation methodology but If I do it simply by calculating then why is C coming out as an answer?

Let C = 240, 000 be an answer

for Martha = 20,000 + (10/100 ) * (240,000 - 80,000)

= 36,000

for Sandra = 30,000 + (5/100) * (240,000 - 120,000)

= 36,000


THEN WHY IS C wrong? please help
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Re: Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 02 Feb 2018, 23:29
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rocko911 wrote:
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


I understood the equation methodology but If I do it simply by calculating then why is C coming out as an answer?

Let C = 240, 000 be an answer

for Martha = 20,000 + (10/100 ) * (240,000 - 80,000)

= 36,000

for Sandra = 30,000 + (5/100) * (240,000 - 120,000)

= 36,000


THEN WHY IS C wrong? please help


Check the highlighted part: 5% from TOTAL annual sales.

For 240, 000 Sandra gets 30,000 + (5/100)*240,000 = 42,000.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 02 Feb 2018, 23:34
Bunuel wrote:
rocko911 wrote:
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


I understood the equation methodology but If I do it simply by calculating then why is C coming out as an answer?

Let C = 240, 000 be an answer

for Martha = 20,000 + (10/100 ) * (240,000 - 80,000)

= 36,000

for Sandra = 30,000 + (5/100) * (240,000 - 120,000)

= 36,000


THEN WHY IS C wrong? please help


Check the highlighted part: 5% from TOTAL annual sales.

For 240, 000 Sandra gets 30,000 + (5/100)*240,000 = 42,000.


Thanks ...i totally ignored that part...got it now
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Re: Martha receives an annual salary of $20,000 plus a commission of 10 pe [#permalink]

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New post 03 Feb 2018, 06:06
Bunuel wrote:
Martha receives an annual salary of $20,000 plus a commission of 10 percent on sales in excess of $80,000 while Sandra receives an annual salary of $30,000 plus a 5 percent commission on her total annual sales only if they exceed $120,000. Which sales figures would result in equal earnings for both Marta and Sandra?

A. $100,000
B. $150,000
C. $240,000
D. $360,000
E. $400,000


Let \(x\)be the total sales.

\(20,000 + 0.1(x - 80,000) = 30,000 + 0.05x\)

\(0.05x = 18,000\)

\(x = 360,000\)
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Re: Martha receives an annual salary of $20,000 plus a commission of 10 pe   [#permalink] 03 Feb 2018, 06:06
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