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

Question

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 .

chetan2u · Answer

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

ynaikavde · Answer

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

LaxAvenger · Answer

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?

mehrdadtaheri92 · Answer

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:

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:

Took less than One minute.... Best Regards,

PareshGmat · Answer

Answer = B = 45000

Average salary  = \frac{15*120000 + 75*30000}{15+75} = \frac{15*120000}{90} + \frac{75*30000}{90} = 20000 + 25000 = 45000

EMPOWERgmatRichC · Answer

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

OptimusPrepJanielle · Answer

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. -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

Bunuel · Answer

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.

mehrdadtaheri92 · Answer

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:

So, I over looked to eliminate zero.... But , you are right my friend, Thanks...

sytabish · Answer

hi LaxAvenger , Check out the below link. It might help. https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/03 ... -averages/ Thanks!

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

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