The average salary of 15 people in the shipping department

Question

The average salary of 15 people in the shipping department at a certain firm is $20,000. The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 each. What is the average salary of the remaining employees?

(A) $19,250
(B) $18,500
(C) $18,000
(D) $15,850
(E) $12,300

(A) $19,250
(B) $18,500
(C) $18,000
(D) $15,850
(E) $12,300

This is a relatively easy average problem, but the difficulty occurs with the choice of numbers. Is there a 30-sec approach to this?

GMATSPARTAN · Accepted Answer

5 employees have earned 5000 more than the average
4 employees have earned 4000 less than the average

total difference amount from the average is = 5 * 5000 - 4 * 4000 = $9000 (more than average)

since 9 employees have earned 9000 more than average, this has to be compensated by the remaining 6 members to keep the average at $20000.

so each of the remaining 6 should earn 1500 less than the average, ==> $20000 - $1500 = $18500

Amateur · Answer

total salary... 15*20k=300k
5 emp @ 25k =125k
4 emp @ 16k =64k
remaing 6 emp sal = 300k-125k-64k =111k
average=111k/6 = 18500

PareshGmat · Answer

Total Salary = 15 x 20000

15 x 20000 = 5 x 25000 + 4 x 16000 + 6 x i

6i = 11100
i = 18500 Answer =B

EMPOWERgmatRichC · Answer

Hi All,

The Average Formula is one of a variety of standard formulas that the GMAT will expect you to know and use. Sometimes, Average Formula questions include lots of variables; in this question, we're given lots of numbers to work with and then we're asked to solve for one variable. Here's what it takes to answer the question:

We're told that the average salary of 15 people = $20,000

Sum/15 = $20,000

The Sum of the 15 people = 15($20,000) = $300,000

Then we're told the salary of 5 people = $25,000 each and the salary of 4 of the people = $16,000 each

5($25,000) = $125,000 
4($16,000) = $64,000

Now we know that those 9 people account for a total of $189,000 of salary

The question asks for the average salary of the remaining employees. 
We know that there are 6 employees remaining 
We also know that the remaining money = $300,000 - $189,000 = $111,000

$111,000/6 = $18,500

Final Answer:  B

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

JeffTargetTestPrep · Answer

The total salary of the 15 employees is 15 x 20,000 = 300,000.

The total salary of 5 of the employees is 5 x 25,000 = 125,000.

The total salary of another 4 of the employees is 4 x 16,000 = 64,000.

So, the total salary of the remaining 6 people is 300,000 - (125,000 + 64,000) = 111,000, so the average of the remaining employees is:

111,000/6 = 18,500

Answer: B

Abhishek009 · Answer

15*20000 = 5*25000 + 4*16000 + 6x

Or,  300000 = 125000 + 64000 + 6x

Or, 111000 = 6x

Or, x = 18500 , Answer must be (B)

Probus · Answer

Hi, 
if we know the deviation technique, then such questions can be tackled quickly with min calculation. 
Let us assume that the pay of each of remaining 6 employee is 20,000
Now since 4 employees get less than average and 5 get more than average . So 5*25000-4*16000= 9000.

Since the average of 15 employees remains 20,000 and there is the deviation of 9000. This is the amount then gets divided equally by 6 people so that the average remains 20,000.

20,0000- (9000/6)
18500.

BrentGMATPrepNow · Answer

]The average salary of 15 people in the shipping department at a certain firm is $20,000  
So, (sum of all 15 salaries)/15 = $20,000
Multiply both sides by 15 to get:  sum of all 15 salaries = $300,000

The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 each  
5 x $25,000 = $125,000
4 x $16,000 = $64,000
$125,000 + $64,000 =  $189,000

So, the 9 people accounted for here have a combined salary of  $189,000

What is the average salary of the remaining employees?  
 sum of all 15 salaries = $300,000 
 sum of 9 of the salaries = $189,000

$300,000  -  $189,000  =   $111,000  
So, the remaining 6 people must have a combined salary of   $111,000

Average salary of 6 people =   $111,000  /6 = $18,500

Answer: B

Cheers,
Brent

KarishmaB · Answer

Check this post for how to handle averages using deviation: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/05 ... eviations/ Avg of 15 people is 20k. 5 people have salary of 25k i.e. 5k extra from avg. So we have an excess of 5 * 5k = 25k 4 people have salary of 16k i.e. 4k less than avg. So we have a deficit of 4 * 4k = 16k Overall we have an excess of 25k - 16k = 9k The remaining 6 people need to create a deficit of 9k so they should have an average salary of 9k/6 = 1.5k less than average. Hence the salary of the other 6 people should be 20k - 1.5k = $18,500

ArnauG · Answer

To find the average salary of the remaining employees, we need to subtract the salaries of the 5 employees earning $25,000 each and the salaries of the 4 employees earning $16,000 each from the total average salary of $20,000.

Total salary of the 5 employees earning $25,000 each: 5 * $25,000 = $125,000
Total salary of the 4 employees earning $16,000 each: 4 * $16,000 = $64,000

Total salary of all 15 employees: $20,000 * 15 = $300,000

Total salary of the remaining employees: $300,000 - $125,000 - $64,000 = $111,000

To find the average salary of the remaining employees, we divide the total salary of the remaining employees by the number of remaining employees: $111,000 / (15 - 5 - 4) = $111,000 / 6 = $18,500

Therefore, the average salary of the remaining employees is $18,500.

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The average salary of 15 people in the shipping department

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The average salary of 15 people in the shipping department

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