A company starts with 8000 workers. The number of workers increases by 5 percent at the end of the first year, by 10 percent at the end of the second year, and by 20 percent at the end of the third year. How many workers does the company have in the fourth year?

Introduction / Context:
This problem tests understanding of successive percentage increases, which is essentially an application of compound growth. Instead of a single percentage applied once, different rates are applied at the end of each year. Recognizing that each year's increase is calculated on the latest value is essential when dealing with populations, investments, salaries and other growing quantities.

Given Data / Assumptions:

• Initial number of workers = 8000.
• Increase at end of first year = 5 percent.
• Increase at end of second year = 10 percent.
• Increase at end of third year = 20 percent.
• We are asked for the number of workers at the start of the fourth year, after all three increases.

Concept / Approach:
For successive percentage changes, we multiply the starting value by each growth factor in sequence. A 5 percent increase corresponds to multiplying by 1.05, a 10 percent increase to multiplying by 1.10, and a 20 percent increase to multiplying by 1.20. The final number is obtained by 8000 * 1.05 * 1.10 * 1.20.

Step-by-Step Solution:
Step 1: After first year, workers = 8000 * 1.05 = 8400.Step 2: After second year, workers = 8400 * 1.10 = 9240.Step 3: After third year, workers = 9240 * 1.20 = 11088.Step 4: Thus, at the beginning of the fourth year the company has 11088 workers.

Verification / Alternative check:
We can do the combined multiplication in one step: 8000 * 1.05 * 1.10 * 1.20 = 8000 * (1.05 * 1.10 * 1.20) = 8000 * 1.386 = 11088. This matches the stepwise calculation, confirming consistency. Both methods rely on the idea that each yearly percentage increase applies to the most up to date number of workers.

Why Other Options Are Wrong:
Option 10188 or 10080 would correspond to using simple addition of percentages or incorrect rounding rather than compounding. Option 11008 is close but does not match the correct compound product of the three factors. Option 11808 is too high and would require larger percentage increases than those given.

Common Pitfalls:

• Adding the percentages first (5 + 10 + 20) and applying a single 35 percent increase to 8000, which is incorrect.
• Applying each percentage change to the original 8000 instead of the progressively updated worker count.
• Rounding intermediate results too aggressively and causing noticeable errors in the final value.

Final Answer:
The number of workers in the fourth year is 11088.