Question

What BEST can be concluded about the value of x?

• A. 0, 1 or 2
• B. 2 only
• C. 1 only
• D. 0 or 1 only
• E. 1 or 2 only
• A. Cannot be determined uniquely from the given information
• B. 25
• C. 26
• D. 27
• J. 28

Answer 1

The Correct Option is B

Step 1: Apply the inclusion-exclusion principle. The total number of candidates is 41.

Applying the inclusion-exclusion principle:

41 = (Data Analysis) + (Database Handling) + (Coding) − (Data Analysis and Database Handling) − (Data Analysis and Coding) − (Database Handling and Coding) + (Data Analysis, Database Handling, and Coding)

Substitute values from the table:

41 = 12 + 5 + 7 − 2 − 3 − 6 + x.

Step 2: Simplify the equation. Simplify the right side:

41 = 13 + x = => x = 41 − 13 = 5.

Step 3: Analyze constraints. The problem allows x to have multiple values. Testing other scenarios, x can also satisfy conditions when 0 ≤ x ≤ 2.

Final Answer: (1).

Answer 2

Step 1: Formulate the inclusion-exclusion equation. The total applicant count is 41. Applying the inclusion-exclusion principle:

Total Applicants = (Single Field Expertise) + (Two Fields Expertise) + (All Three Fields) + (No Field Expertise).

Based on the data: - Single Field Expertise = 12 + 5 + 7 − (2 + 3 + 6 + x), - Two Fields Expertise = (2 + 3 + 6) − x, - All Three Fields = x.

Step 2: Determine the number of applicants with at least one area of expertise. Insert the values into the inclusion-exclusion equation:

41 = 12 + 5 + 7 − (2 + 3 + 6 + x) + (2 + 3 + 6) − x + x + (No expertise).

Simplify:

41 = (12 + 5 + 7) − (2 + 3 + 6) + (2 + 3 + 6) − x + (No expertise).

41 = 24 + (No expertise).

Step 3: Calculate the number of applicants with no expertise.

No expertise = 41 − 24 = 25.

Final Answer: 25.