In a company of only 20 employees, 10 employees make $80,000

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Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Thu Mar 05, 2015 2:35 pm

In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?
(A) $250,000
(B) $300,000
(C) $350,000
(D) $400,000
(E) $450,000

This question concerns Weighted Averages. For a set of practice problems and a discussion of strategies on this topic, as well as the OA & OE for this particular problem, see:
https://magoosh.com/gmat/2015/gmat-math ... -averages/

Mike

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https://gmat.magoosh.com/

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Source: Beat The GMAT — Problem Solving | Thu Mar 05, 2015 2:35 pm

towerSpider: Master | Next Rank: 500 Posts; Posts: 155; Joined: Mon Dec 13, 2010 11:02 am; Thanked: 3 times

by towerSpider » Fri Mar 06, 2015 2:21 pm

Mike@Magoosh wrote:In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?
(A) $250,000
(B) $300,000
(C) $350,000
(D) $400,000
(E) $450,000

This question concerns Weighted Averages. For a set of practice problems and a discussion of strategies on this topic, as well as the OA & OE for this particular problem, see:
https://magoosh.com/gmat/2015/gmat-math ... -averages/

Mike

175k * 20 = 350 * 10 = 700 * 5 = 3500k
3500k = 10.80k + 6.150k + 4X
Solving for X:
= 800k + 900k + 4X
4X = 1800k
X = 900k/2 = 450,000

People are not prisoners of fate, but prisoners of their own mind.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Mar 09, 2015 11:06 am

Mike@Magoosh wrote:In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?
(A) $250,000
(B) $300,000
(C) $350,000
(D) $400,000
(E) $450,000

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + etc

NOTE: To make things easier, let's drop the thousands and write $80 instead of $80,000
Let x = the annual salary of each highest-paid employee
Plug values into the formula to get: 175 = (10/20)(80) + (6/20)(150) + (4/10)(x)
Simplify: 175 = 40 + 45 + x/5
Simplify: 90 = x/5
Solve: x = 450

So, the annual salary of each highest-paid employee is [spoiler]$450,000[/spoiler]
Answer: E

-----------------------------------------------

For more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Mar 09, 2015 12:01 pm

Mike@Magoosh wrote:In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?
(A) $250,000
(B) $300,000
(C) $350,000
(D) $400,000
(E) $450,000

An alternate approach is to work with the TOTALS.
To make the math easier, drop the last three 0's from each value.

Total for all 20 employees = (number)(average) = (20*175) = 3500.
Total for the first 10 employees = (number)(average) = 10*80 = 800.
Total for the next 6 employees = (number)(average) = 6*150 = 900.
Subtracting the totals in red from the total for all 20 employees, we get:
Total for the last 4 employees = 3500-800-900 = 1800.
Thus:
Average for the last 4 employees = (total)/(number) = 1800/4 = 450.

The correct answer is E.

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Amrabdelnaby: Master | Next Rank: 500 Posts; Posts: 137; Joined: Fri Nov 13, 2015 11:01 amFollowed by: 2 members; Thanked: 1 times

by Amrabdelnaby » Thu Nov 19, 2015 8:32 am

Hi Mike,

Just wanted to check, what is the level of this question?

Thanks

Mike@Magoosh wrote:In a company of only 20 employees, 10 employees make $80,000/yr, 6 employees make $150,000/yr, and the 4 highest-paid employees all make the same amount. If the average annual salary for the 20 employees is $175,000/yr, then what is the annual salary of each highest-paid employee?
(A) $250,000
(B) $300,000
(C) $350,000
(D) $400,000
(E) $450,000

This question concerns Weighted Averages. For a set of practice problems and a discussion of strategies on this topic, as well as the OA & OE for this particular problem, see:
https://magoosh.com/gmat/2015/gmat-math ... -averages/

Mike

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Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Thu Nov 19, 2015 10:31 am

Amrabdelnaby wrote:Hi Mike,

Just wanted to check, what is the level of this question?

Thanks

Dear Amrabdelnaby,
I'm happy to respond.

This question is a somewhat easier question, certainly not a member of that mythological and highly suspicious category called "700+ questions."

My friend, I am going to caution you. Questions about the "level" of various GMAT practice questions will not necessarily help you, nor are these levels particularly well-defined. See this blog:
https://magoosh.com/gmat/2014/is-this-a- ... -question/

I would recommend learning as much as you can from each question, especially those you get wrong the first time. It is the mark of a truly excellent student never to make the same mistake twice.

Does all this make sense?
Mike

Magoosh GMAT Instructor
https://gmat.magoosh.com/

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peter456: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Sep 20, 2015 12:47 am

by peter456 » Sat Nov 21, 2015 9:37 pm

Just an observation:

For the 10 & 6 member employees, the figures given should indicate "average"

For example, 10 employees make an average salary of $80,000/yr, and 6 employees
make an average salary of $150,000/yr....

Otherwise, if 10 employees make $10,000 in a year, that suggests their total salary.

Hope my suggestion makes sense

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by [email protected] » Sun Nov 22, 2015 8:48 am

HI peter456,

The GMAT tends to be a bit more specific with the way that it's writers phrase the questions that you'll face on Test Day - so this type of bias/ambiguity almost never happens on the actual Exam. This question is still a relevant example of a Weighted Average question though, so you should make sure that you're comfortable with the math/concepts involved (since you will see them on Test Day).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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