Multiple choice

Directions: Read the following scenario and answer the question that follows. 41 applicants have been shortlisted for interviews for some data analyst positions. Some of the applicants have advanced expertise in one or more fields among the following: data analysis, database handling and coding. The numbers of applicants with different advanced expertise are given in the 2 × 8 table below. The number of applicants with advanced expertise in all three fields is given as x in the table, where x is a non-negative integer. Field Data Analysis Database Handing Coding Data Analysis and Database Handing Database Handling and Coding Data Analysis and Coding All three Number of Candidates with Advanced Expertise 12 5 7 2 3 6 x What BEST can be concluded about the value of x?

  1. 0, 1 or 2

  2. 2 only

  3. 1 only

  4. 0 or 1 only

  5. 1 or 2 only
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

To find the value of x, we use the principle of inclusion-exclusion for three sets, which is Total equals the sum of individual sets minus the sum of pairwise intersections plus the intersection of all three sets. Substituting the provided values gives the equation 41 equals 12 plus 5 plus 7 minus 2 minus 3 minus 6 plus x, simplifying to 41 equals 24 plus x, which leads to x equaling 2. Furthermore, since x must be less than or equal to the pairwise intersections, and the smallest pairwise intersection is 2, the only valid integer value is 2.

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