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A company has 15 managers and 75 associates. The 15 managers have an

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A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 24 Feb 2015, 07:41
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A company has 15 managers and 75 associates. The 15 managers have an average salary of $120,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?

A. $35,000
B. $45,000
C. $55,000
D. $65,000
E. $75,000

Kudos for a correct solution.

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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 24 Feb 2015, 09:35
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Bunuel wrote:
A company has 15 managers and 75 associates. The 15 managers have an average salary of $120,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?

A. $35,000
B. $45,000
C. $55,000
D. $65,000
E. $75,000

Kudos for a correct solution.


these questions can be done in two ways ..
1) average formula:
(15*120000+75*30000)/(15+75)=45000
2) weighted average and ratio method:
the two numbers are in ratio 15:75=1:5.... so the difference of average will be in ratio 5:1..
difference in avg salaries of two groups=120000-30000=90000...
now the average will be closer to higher number,75 , by 1/6 of 90000 =90000*1/6=15000..
so avg = 30000+15000=45000
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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 24 Feb 2015, 10:07
Another method is to get ratios
Say 30000=a and
We know the # of people are in 1:5 ratio
Average=(4a*1+a*5)/6= 9a/6=1.5 a=45000

Answer is B. $45,000
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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 24 Feb 2015, 10:55
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I solved this using average formula :

(15*120,000 + 75 * 30,000) / 90

= 45, 000

Answer B

However, with this approach I needed around 2 minutes. Is there a faster way?
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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 24 Feb 2015, 13:52
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Well, the answer is obviously B , BUT in order to solve the question faster and calculate easier let's try this approach :

AS you know some countries some times eliminate zeros in their currency because of high inflation in their countries , so we can apply this approach in order to solve the problem in a faster way

lets eliminate 3 zero's from the big numbers , so we have 120 $ instead of 120,000 $ and also 30$ instead of 30,000$ :lol: :lol: :lol:

we are told that company has 15 managers with average salary of 120$ .... so total amount of salary will be 15*120= 1800$

Also, we are told that the company has 75 associates with average salary of 30$ .... so total amount of salary for those guys will be 30*75= 2250$

Final stage : for calculating the total average salary we have the sum of two groups of people divided by the total number of people : ( 1800+2250) / (75+15) = 4050/90 OR : we can cancel out

zero from denominator and numerator , so we have : 405/9 = 45 !!!!! by viewing to the answers ONLY option B fits ..... :lol: :lol: :lol: :lol:

Took less than One minute....

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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 24 Feb 2015, 20:18
Answer = B = 45000

Average salary \(= \frac{15*120000 + 75*30000}{15+75} = \frac{15*120000}{90} + \frac{75*30000}{90} = 20000 + 25000 = 45000\)
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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 24 Feb 2015, 23:31
mehrdadtaheri92 wrote:
Well, the answer is obviously B , BUT in order to solve the question faster and calculate easier let's try this approach :

AS you know some countries some times eliminate zeros in their currency because of high inflation in their countries , so we can apply this approach in order to solve the problem in a faster way

lets eliminate 3 zero's from the big numbers , so we have 120 $ instead of 120,000 $ and also 30$ instead of 30,000$ :lol: :lol: :lol:

we are told that company has 15 managers with average salary of 120$ .... so total amount of salary will be 15*120= 1800$

Also, we are told that the company has 75 associates with average salary of 30$ .... so total amount of salary for those guys will be 30*75= 2250$

Final stage : for calculating the total average salary we have the sum of two groups of people divided by the total number of people : ( 1800+2250) / (75+15) = 4050/90 OR : we can cancel out

zero from denominator and numerator , so we have : 405/9 = 45 !!!!! by viewing to the answers ONLY option B fits ..... :lol: :lol: :lol: :lol:

Took less than One minute....

Best Regards,


Hi mehrdadtaheri92,

I like your thinking - that's a clever way to eliminate some of the "excess math" and make the calculations easier. To that end, what would have happened if you had eliminated ALL of the 0s... and used 12 and 3 (instead of 120 and 30)?

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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 28 Feb 2015, 07:36
1
Bunuel wrote:
A company has 15 managers and 75 associates. The 15 managers have an average salary of $120,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?

A. $35,000
B. $45,000
C. $55,000
D. $65,000
E. $75,000

Kudos for a correct solution.


Let us ignore the last 3 zeros since they're common for all terms.
Total salary of 15 managers = 15 * 120 = 1800
Total salary of 75 associates = 75 * 30 = 2250
Total salary of company = 1800 + 2250 = 4050

Average salary of 90 employees = 4050/90
= 45
Let us put back the 3 zeros again
= 45000
Hence option B.

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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 02 Mar 2015, 06:33
Bunuel wrote:
A company has 15 managers and 75 associates. The 15 managers have an average salary of $120,000. The 75 associates have an average salary of $30,000. What is the average salary for the company?

A. $35,000
B. $45,000
C. $55,000
D. $65,000
E. $75,000

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

The 15 managers have an average salary of $120,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $120,000*15 = $1,800,000

The 75 associates have an average salary of $30,000. The sum of their salaries is:
sum = (average)*(number of salaries) = $30,000*75 = $2,250,000

When we add those two sums, we get the total payroll of all 90 employees.
$1,800,000 + $2,250,000 = $4,050,000

So, we have 90 employees, and together they earn $4,050,000, so the average is
average = $4,050,000 ÷90 = $45,000

Answer: B.
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Resources:
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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.


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A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 02 Mar 2015, 14:28
EMPOWERgmatRichC wrote:
mehrdadtaheri92 wrote:
Well, the answer is obviously B , BUT in order to solve the question faster and calculate easier let's try this approach :

AS you know some countries some times eliminate zeros in their currency because of high inflation in their countries , so we can apply this approach in order to solve the problem in a faster way

lets eliminate 3 zero's from the big numbers , so we have 120 $ instead of 120,000 $ and also 30$ instead of 30,000$ :lol: :lol: :lol:

we are told that company has 15 managers with average salary of 120$ .... so total amount of salary will be 15*120= 1800$

Also, we are told that the company has 75 associates with average salary of 30$ .... so total amount of salary for those guys will be 30*75= 2250$

Final stage : for calculating the total average salary we have the sum of two groups of people divided by the total number of people : ( 1800+2250) / (75+15) = 4050/90 OR : we can cancel out

zero from denominator and numerator , so we have : 405/9 = 45 !!!!! by viewing to the answers ONLY option B fits ..... :lol: :lol: :lol: :lol:

Took less than One minute....

Best Regards,


Hi mehrdadtaheri92,

I like your thinking - that's a clever way to eliminate some of the "excess math" and make the calculations easier. To that end, what would have happened if you had eliminated ALL of the 0s... and used 12 and 3 (instead of 120 and 30)?

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


Dear Friend,

You are right of course , But dear friend Notice that eliminating 3 zeros can bring us simplicity enough to solve question fast. :lol: :lol: :lol:

So, I over looked to eliminate zero.... But , you are right my friend, Thanks...
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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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New post 07 Mar 2015, 10:47
LaxAvenger wrote:
I solved this using average formula :

(15*120,000 + 75 * 30,000) / 90

= 45, 000

Answer B

However, with this approach I needed around 2 minutes. Is there a faster way?


hi LaxAvenger ,

Check out the below link. It might help.

http://www.veritasprep.com/blog/2011/03 ... -averages/

Thanks!
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Re: A company has 15 managers and 75 associates. The 15 managers have an [#permalink]

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Re: A company has 15 managers and 75 associates. The 15 managers have an   [#permalink] 28 Dec 2017, 04:11
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