To solve this problem, we can use a Venn diagram to represent the preferences of the staff members. Let's break down the given information step by step:

Step 1: Total number of staff members
According to the question, there are 2000 staff members in total.

Step 2: Coffee, tea, and cocoa preferences
48% of the staff preferred coffee, 54% preferred tea, and 64% preferred cocoa.

Step 3: Overlapping preferences
28% of the staff members used both coffee and tea, 32% used both tea and cocoa, and 30% used both coffee and cocoa.

Step 4: Staff members who prefer none of the three options
Only 6% of the staff members did not prefer any of the three options.

Step 5: Finding the number of staff members who prefer only coffee
To find the number of staff members who prefer only coffee, we need to subtract the staff members who prefer both coffee and tea, both tea and cocoa, and both coffee and cocoa from the total number of staff members who prefer coffee.

Let's calculate:

Total staff members = 2000

Staff members who prefer coffee = 48% of 2000 = 0.48 * 2000 = 960

Staff members who prefer both coffee and tea = 28% of 2000 = 0.28 * 2000 = 560

Staff members who prefer both coffee and cocoa = 30% of 2000 = 0.30 * 2000 = 600

Staff members who prefer both tea and cocoa = 32% of 2000 = 0.32 * 2000 = 640

Staff members who prefer none of the three options = 6% of 2000 = 0.06 * 2000 = 120

Staff members who prefer only coffee = Staff members who prefer coffee - Staff members who prefer both coffee and tea - Staff members who prefer both coffee and cocoa
= 960 - 560 - 600 = 160

Therefore, the number of staff members who prefer only coffee is 160, which corresponds to option C.

To solve this problem, we can use the concept of set theory and Venn diagrams. Let's break down the information given step by step and find the number of staff members who prefer only coffee.

Given Information:
- Total number of staff members = 2000
- Percentage of staff members who prefer coffee = 48%
- Percentage of staff members who prefer tea = 54%
- Percentage of staff members who prefer cocoa = 64%
- Percentage of staff members who use both coffee and tea = 28%
- Percentage of staff members who use both tea and cocoa = 32%
- Percentage of staff members who use both coffee and cocoa = 30%
- Percentage of staff members who use none of these = 6%

Step 1: Calculate the number of staff members who prefer each beverage.
- Number of staff members who prefer coffee = (48/100) * 2000 = 960
- Number of staff members who prefer tea = (54/100) * 2000 = 1080
- Number of staff members who prefer cocoa = (64/100) * 2000 = 1280

Step 2: Calculate the number of staff members who use combinations of beverages.
- Number of staff members who use both coffee and tea = (28/100) * 2000 = 560
- Number of staff members who use both tea and cocoa = (32/100) * 2000 = 640
- Number of staff members who use both coffee and cocoa = (30/100) * 2000 = 600

Step 3: Calculate the number of staff members who do not prefer any of the beverages.
- Number of staff members who use none of these = (6/100) * 2000 = 120

Step 4: Use the principle of inclusion and exclusion to find the number of staff members who prefer only coffee.
- Number of staff members who prefer only coffee = Number of staff members who prefer coffee - Number of staff members who use both coffee and tea - Number of staff members who use both coffee and cocoa + Number of staff members who use all three beverages
- Number of staff members who prefer only coffee = 960 - 560 - 600 + 120 = 160

Therefore, the number of staff members who prefer only coffee is 160. Hence, the correct answer is option C.