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Study the given diagram carefully and answer the questions. The numbers in different sections indicate the number of persons. How many persons are both poor and uneducated but not famous? (NOTE: You have to take the given data to be true even if they seem to be at variance from commonly known facts.)
5
10
15
20
10
Look for the intersection region that is inside the 'Poor' and 'Uneducated' circles but outside the 'Famous' circle.
Look for the intersection region that is inside the 'Poor' and 'Uneducated' circles but outside the 'Famous' circle.
Identify the relevant sets
The question asks for people who are 'Poor' and 'Uneducated', excluding 'Famous'.
Locate the intersection
Look at the Venn diagram intersection where the 'Poor' circle and 'Uneducated' circle overlap. This region contains two values: 10 (the central intersection of all three) and 5 (the intersection of only Poor and Uneducated).
Filter and conclude
The value 10 is inside the 'Famous' circle, so we exclude it. The value 5 represents the count of persons who are strictly in the intersection of 'Poor' and 'Uneducated' circles but outside the 'Famous' circle.
A: 8 is the count for 'Famous' and 'Uneducated' excluding 'Poor'. C: 12 is the count for 'Famous' and 'Poor' excluding 'Uneducated'. D: 30 represents only the 'Poor' individuals (excluding other categories).
B is correct because the region representing the intersection of 'Poor' and 'Uneducated' that lies outside the 'Famous' circle is uniquely marked with the number 5.
In Venn diagram questions, always start by checking the intersection of the two conditions specified first, then look for exclusions.
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