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Study the given diagram carefully and answer the question that follows. The numbers in different sections indicate the number of persons/objects. How many such officers exist that are also scientists but not professors?
5
4
9
12
12
Identify the intersection region common ONLY to the 'Officers' and 'Scientists' circles that does not overlap with the 'Professors' circle.
Identify the intersection region common ONLY to the 'Officers' and 'Scientists' circles that does not overlap with the 'Professors' circle.
Analyze the Sets
We need the count of people who belong to the 'Officers' set AND the 'Scientists' set, but NOT the 'Professors' set.
Locate the Region
Looking at the intersection of the Scientists circle (top-left) and the Officers circle (bottom), the shared area contains two numbers: 4 and 5.
Apply Exclusions
The number 4 is in the center, meaning it belongs to all three sets (Scientists, Professors, and Officers). Therefore, it must be excluded. The number 5 is strictly inside the intersection of Scientists and Officers, but outside the Professors circle.
A: 12 is the number of exclusive scientists, not the intersection. B: 16 is incorrect as it combines unrelated sections. C: 4 is the intersection of all three sets, including professors, so it is excluded.
D is correct because the region representing Officers and Scientists excluding Professors is the intersection part containing 5.
In Venn diagram problems, always look for the region that is shared by the required sets but does not overlap with the set mentioned as 'not' included.
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