Problem Solving

BTGmoderatorLU wrote:Source: GMAT Prep

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%

The OA is B

Since we have to deal with percent values and absolute value in the sight, we can assume convenient values, 100.

Total no. of employees (Before) = 100 (assumed value)
Total salary (Before) = 100 (assumed value)
Average salary (Before) = 100/100 = $1 per employee

Total no. of employees (After) = 100 - 10% of 100 = 90; given 10% decrease
Total salary (After) = 1 + 10% of 1 = $1.1 per employee; given 10% increase
Average salary (After) = 90*1.1 = $99

So, the total salary after the change is (99/100)*10% = 99% of the salary (before).

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: GMAT Prep

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%

The OA is B

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 an 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