Rationale
5 people ate only hot dogs.
The Venn diagram indicates that out of the two groups of 30 people, only a small portion consumed exclusively hot dogs. By analyzing the overlapping regions and total numbers, it becomes clear that the count of individuals eating only hot dogs is 5.
A) A count of 27 people eating only hot dogs would imply that most of the participants preferred hot dogs over any other meal. Given the total of 60 people and the overlap with other meal choices shown in the Venn diagram, this figure is not plausible as it does not account for those eating other meals.
B) The count of 5 people eating only hot dogs accurately reflects the number shown in the Venn diagram. This number accounts for those who did not eat hamburgers or any other meal, ensuring all other meal preferences are considered.
C) A total of 10 people eating only hot dogs would suggest a higher preference for this meal than indicated. The Venn diagram shows that this number would not leave enough room for individuals who chose to eat hamburgers or other combinations, thus conflicting with the overall distribution of meal choices.
D) A count of 17 people eating only hot dogs would again imply that a significant number of attendees preferred hot dogs alone, which contradicts the data presented in the Venn diagram. This number does not accurately reflect the overlaps with other meals and skews the total distribution of preferences among the participants.
Conclusion
The analysis of the Venn diagram reveals that 5 individuals ate only hot dogs, highlighting the specific meal preferences at the picnic. This number is derived from the overall distribution of attendees and their meal choices, ensuring accurate representation of the data provided. Other options overestimate the number of exclusive hot dog consumers, failing to align with the depicted preferences.
