The phrase “of the employees in Engineering” signals nested percents: the next percentage uses Engineering, not the whole company, as its base. Picture 100 employees, find the Software Engineer group, and split everyone into Software Engineers and everyone else. Use Desmos to apply each remote-work rate to its own group. The trap is treating a rate for one group as a rate for all employees.
Hints
- Hint 1
Picture 100 employees so a count out of 100 is also a percentage of the company. The 58% gives you the Engineering group. Which group should you take 45% of to find the Software Engineers?
- Hint 2
A complement is everyone outside a group. Here, not Software Engineers includes people outside Engineering and people in Engineering with other jobs. Which group should you subtract from all 100 employees?
- Hint 3
Remote workers come from both groups. Apply the 10% rate to Software Engineers and the 5% rate to everyone else. After adding those parts, what must you subtract to find employees who do not work remotely full-time?
Step-by-step
Split 100 employees into two groups
Step 1Find the Engineering group
Because the problem gives only percentages, picture 100 employees. A count out of 100 will also be a percent of the company. Type in Desmos. It shows , so 58 of your imagined employees are in Engineering.
- Step 2
Find the Software Engineers
The is of Engineering, so use the 58 Engineering employees, not all 100. Type ; Desmos shows . That represents of all employees. A fractional employee is fine in this imagined group of 100.
- Step 3
Find everyone else
The not-Software-Engineer group includes employees outside Engineering and Engineering employees with other jobs. Type ; Desmos shows . Subtracting the entire Engineering group instead would leave out those other Engineering employees.
- Step 4
Find the full-time remote share
The two groups cover everyone without overlap, so apply each remote rate to its own group, then add the results. Type . Desmos shows , meaning of all employees work remotely full-time.
- Step 5
Find the employees who do not work remotely
The question asks for the complement: employees who do not work remotely full-time. Type ; Desmos shows . So approximately of all employees do not work remotely full-time. Choice D.