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.
What BEST can be concluded about the value of x?
- 0, 1 or 2
- 2 only
- 1 only
- 0 or 1 only
- 1 or 2 only
The Correct Option is B
Solution and Explanation
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).
How many applicants DID NOT have advanced expertise in any of the three given fields?
- Cannot be determined uniquely from the given information
- 25
- 26
- 27
- 28
The Correct Option is C
Solution and Explanation
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.
Top Questions on Data Interpretation
- Eight employees of an organization have been rated on a scale of 1 to 50 for their performance. All ratings are integers. The overall average rating of the eight employees is 30. While the five employees with the highest ratings average 38, the five employees with the lowest ratings average 25. Which of the following, about the ratings obtained by the eight employees, is DEFINITELY FALSE?
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Data Interpretation
The plots below depict and compare the average monthly incomes (in Rs. ’000) of males and females in ten cities of India in the years 2005 and 2015. The ten cities, marked A-J in the records, are of different population sizes. For a fair comparison, to adjust for inflation, incomes for both the periods are scaled to 2025 prices. Each red dot represents the average monthly income of females in a particular city in a particular year, while each blue dot represents the average monthly income of males in a particular city in a particular year. The gender gap for a city, for a particular year, is defined as the absolute value of the average monthly income of males, minus the average monthly income of females, in that year.
- XAT - 2025
- Quantitative Ability and Data Interpretation
- Data Interpretation
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- General Aptitude
- Data Interpretation
- Read the scenario and answer the question:
The upper hinge of a dataset is the median of all the values to the right of the median of the dataset in an ascending arrangement, while the lower hinge of the dataset is the median of all the values to the left of the median of the dataset in the same arrangement.
For example, consider the dataset 4, 3, 2, 6, 4, 2, 7. When arranged in the ascending order, it becomes 2, 2, 3, 4, 4, 6, 7. The median is 4 (the bold value), and hence the upper hinge is the median of 4, 6, 7, i.e., 6. Similarly, the lower hinge is 2.
A student has surveyed thirteen of her teachers, and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as A and B, where A < B. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all the thirteen values:
Minimum: 2
Lower Hinge: 6.5
Median: 12
Upper Hinge: 21
Maximum: 29- XAT - 2024
- Quantitative Ability and Data Interpretation
- Data Interpretation
- Want to practice more? Try solving extra ecology questions todayView All Questions