Question

Each employec of Company \(\mathrm{X}\) is a member of precisely 1 of 3 shifts of employees. Among the 60 members of the first shift, 20 percent participate in the pension program; among the 50 members of the second shift, 40 percent participate in the pension program; and among the 40 members of the third shift, 10 percent participate in the pension program. What percent of the workers at Company X participate in the pension program? $$\begin{array}{l} 20 \% \\ 24 \% \\ 36 \% \\ 37.5 \% \\ 70 \% \end{array}$$

Short answer

24%

Step-by-step solution

- Determine the Total Number of Employees in Each Shift

Identify the number of employees in each shift:1st shift: 60 employees2nd shift: 50 employees3rd shift: 40 employees

- Calculate the Total Number of Employees in the Company

Add the numbers of employees from each shift:Total employees = 60 + 50 + 40

- Find the Number of Participants in the Pension Program for Each Shift

Calculate the number of participants in the pension program for each shift using the given percentages:1st shift: 20% of 60 = 0.20 * 602nd shift: 40% of 50 = 0.40 * 503rd shift: 10% of 40 = 0.10 * 40

- Calculate the Total Number of Participants in the Pension Program

Add the number of participants from each shift:Total participants = (0.20 * 60) + (0.40 * 50) + (0.10 * 40)

- Determine the Percentage of Total Participants in the Pension Program

Divide the total number of participants by the total number of employees and multiply by 100 to get the percentage:Percentage of workers in pension program = \(\frac{\text{Total participants}}{\text{Total employees}} \times 100\)

Key concepts

pension program calculation

To find out how many employees participate in the pension program, you first need to know the details of each shift.
Company X has three shifts: 60 employees in the first, 50 in the second, and 40 in the third.
The participation rates are given for each shift: 20% for the first shift, 40% for the second, and 10% for the third.
By knowing these rates, you're able to calculate the number of participants in each shift.
Multiply the total employees in each shift by the respective percentage of participants. For example, 20% of 60 in the first shift gives 12 participants.
After calculating for each shift, sum them up to find the total number of participants across all shifts.

percentage calculation

Understanding how to calculate percentages is crucial.
A percentage represents a part of a whole, calculated as a fraction of 100.
In our problem, we use percentages to find how many employees in each shift participate in the pension program.
To find 20% of 60 employees in the first shift, use the formula: \ \[ \text{Percentage} = \frac{20}{100} * 60 \ \]
That gives 12 participating employees.
Repeat the same process for the other shifts: 40% of 50 in the second shift is 20, and 10% of 40 in the third shift is 4.
Add them together to get the total participants in the pension program.

step-by-step math solution

Breaking down problems into smaller steps helps in understanding and solving them correctly.
Let's go through the solution step-by-step:

• First, know the number of employees in each shift: 60, 50, and 40.
• Next, add these to get the total number of employees: \[ 60 + 50 + 40 = 150 \ \]
• Calculate participants using given percentages:
  • First shift: \[ 0.20 * 60 = 12 \ \]
  • Second shift: \[ 0.40 * 50 = 20 \ \]
  • Third shift: \[ 0.10 * 40 = 4 \ \]
• Add participants from all shifts: \[ 12 + 20 + 4 = 36 \ \]
• Finally, find the overall participation percentage: \[ \frac{36}{150} * 100 \ \]
This gives \[ 24 \ \]% of total employees participating in the pension program.

GMAT preparation

The GMAT tests your ability to solve various math problems accurately and efficiently.
Key to this is your understanding of fundamental concepts such as percentages and breaking down complex problems into manageable steps.
Practice with problems similar to this pension program calculation exercise.
Focus on understanding each step and the logic behind the solution.
Familiarize yourself with common questions and practice regularly to build confidence.
Remember to review your solutions and learn from mistakes to improve continuously.