On July 1 of last year, total employees at company E was dec

On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent of that before July 1 last year?
A. 90%
B. 99%
C. 100%
D. 101%
E. 110%

# of employees before July 1 - \(x\);
# of employees after July 1 - \(0.9x\);

Average salary before July 1 - \(y\);
Average salary after July 1 - \(1.1y\);

Total salary before July 1 - \(xy\);
Total salary after July 1 - \(1.1*0.9*xy=0.99xy\) --> \(\frac{0.99xy}{xy}*100=99%\).

Answer B.
_________________

4. Percents and Iterest

[*]Theory
Math: Number Theory - Percents
Percentages, Interest and More
[list][*]Questions
Compound Interest Problems
DS Questions
PS Questions

For more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread


Hope it helps.
_________________

Question with percentages and answer also in percentages. The first and only thing I want to do is assume values.

Initial total no of emp = 100 (assumed value)
Initial total salary = 100 (assumed value)
Initial average = $1/emp (100/100 = 1)
New total no of emp = 90 (10% decrease)
New average salary = $1.1/emp (10% increase)
New total salary = 90*1.1 = 99
So new total salary is 99% of initial total salary.
Answer (B)
_________________

Bunuel, I would disagree with you here ....the question said that there was no decrease in the salary of other employees but you wrote 1.1Y ...shouldnt it still be Y after the change ?

"the average employee salary was 10% more after the decrease in the number of employees than before the decrease."
_________________

TotalSalarynew = Empnew X AverageSalnew
TotalSalarynew = 9/10 Empold X 11/10 AverageSalold
TotalSalarynew = 99/100 TotalSalaryold

Choose some nice values that satisfy the given information.

BEFORE July 1
Let's say that there were 10 employees
And let's say the average salary was $10.
TOTAL payroll = (10)($10) =$100

Number of employees decreases by 10%
Average salary increases by 10%
So....

AFTER July 1
There are 9 employees
Average salary is $11.
TOTAL payroll = (9)($11) =$99

The total of the combined salaries of all the employees at Company E after July 1 last year was what percent of that before July 1 last year?

99/100 = [spoiler]99%[/spoiler]

Answer: B

If we try to solve this question by assuming values, it becomes fairly easy.

Let initial total employees on July 1= 100
Let the initial salary = $100
Average = $1


New number of employees after 10% decrease = 90
New average salary after 10% increase= $1.1

New salary = 90*1.1 = 99
Which is 99% of the initial salary

Correct choice: B

Draw a chart -

The answer will clearly be \(\frac{9900}{10000}*100 =\) \(99\)%

Hence answer will be (B)
_________________

Number of employee (before= X) (after= 0.9X)
Total Salary (before= Sb) (after= Sa)

Average Salary (before =Sb/X)
Average Salary (after = Sa/0.9X)

Average Salary is increased 10%
So, 1.1*Sb/X =Sa/0.9X
Now, 0.99Sb=Sa
Therefore, Sb is 99% of Sa

Answer=99%

We can start by defining a few variables.

n = the number of employees at Company E last year before July 1

x = the average salary of each employee at company E last year before July 1

We are given that on July 1 of last year, the total number of employees at Company E was decreased by 10 percent. Thus, we can represent the remaining number of employees as 0.9n.

We are also given that the average (arithmetic mean) employee salary was 10 percent more after the decrease in number of employees than before the decrease. We can represent this new average salary as 1.1x.

We must determine what percent the total of the combined salaries of all of the employees at Company E after July 1 last year is of that before July 1 last year.

The combined salaries of the employees before July 1 is nx and the combined salaries of the employees after July 1 is 0.9n * 1.1x = 0.99nx. We can create the following expression:

(salaries after July 1)/(salaries before July 1) * 100%

(0.99nx)/(nx) * 100%

0.99 * 100% = 99%

Answer: B
_________________

VeritasKarishma Bunuel can you confirm the purpose of the statement "Without any change in the salaries of the remaining employees,"?
In my opinion, it means without any other change in the salaries of the remaining employees.

Kindly validate the same.

My approach to this questions is as follows:

Given that the problem is asking us to find the ratio of the sum of two salaries which aren't defined in the problem we can start by defining some variables:

(1) Sum of salaries before the increase = Y
(2) Sum of the salaries after the increase = Z
(3) Number of employees BEFORE the increase = X

We are told in the question stem that the number of employees were reduced by 10%, so that means we will have (1-10/100)x employees remaining, or 9x/10.

Next we are told that the average salary AFTER the decrease is equal to 10% more of the original average. So we can set up the following question:

Y/(9x/10) = 11/10(Z/X), and simplying this further we have 10Y/9X = 11Z/10X. If you're stuck at this point you just need to realize that average salary is equal to $Sum of Total Salary / # of Employees.

Finally the question asks us for what percent of the July 1st salary sum of that BEFORE the decrease, or in other words we need to divide the July 1st Salaries by the BEFORE July 1st Salaries, which according to our variables are Y/Z.

So utilizing 10Y/9x = 11Z/10x we can conclude that Y/Z = 99/100, so 99% is the answer.

Just pick easy numbers and use the average equation to solve for the total.

Average = Total / Number, so Total = (Average)(Number)

Start = 100 employees
End = 90 employees (10% decrease)

Start = Average 90 salary
End = Average 99 salary (10% increase)

Total End / Total Start = (90 x 99) / (100 x 90) = 99/100 = .99 = 99%

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________