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Examoogle • User • info@examoogle.com • EE-2024-8821
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In a group of 80 people, 50 speak English and 30 speak Hindi. If 10 speak both, how many speak only English?
40
20
30
50
40
Subtract the intersection directly from the total set of the specific language. No need to use the full union formula for this question.
Total people = 80, People who speak English (E) = 50, People who speak Hindi (H) = 30, People who speak both (E \cap H) = 10
Only E=n(E)−n(E∩H)
Subtract the intersection directly from the total set of the specific language. No need to use the full union formula for this question.
Many students mistake the total number of people (80) as the value needed for the set of only English speakers, or accidentally add the intersection instead of subtracting it.
Define the sets
Let n(E) represent the number of people who speak English and n(E∩H) represent those who speak both.
n(E)=50,n(E∩H)=10
Apply the subtraction logic
To find those who speak ONLY English, we must remove the group that also speaks Hindi from the total English speakers.
Only E=50−10
Calculate the final result
Subtracting the intersection from the total English speakers gives the number of people who speak English exclusively.
50−10=40
A is correct because the number of people who speak only English is calculated by subtracting the 10 bilingual speakers from the 50 English speakers, resulting in 40.
This concept is foundational for Data Interpretation (DI) sets, where Venn diagrams are frequently used to categorize survey data involving overlapping groups.