Practice Questions
Test your logical visual skills with these set-based Venn diagram questions.
In a class of 60, 35 students like Math and 30 like English. 20 students like both. How many like Only English?
Total who like English = 30. Subtract those who also like Math (20). Only English = $30 - 20 = 10$.
Which of the following represents the relationship between 'Furniture, Tables, and Chairs'?
Tables and Chairs are both distinct types of Furniture. So, they are two separate circles inside the larger 'Furniture' circle.
In a group, 40% play cricket, 50% play football and 10% play both. What percentage of people play neither?
Percent playing C or F = $40 + 50 - 10 = 80\%$. Neither = $100\% - 80\% = 20\%$.
A survey of 100 people found 25 like Tea, 40 like Coffee, and 15 like both. How many like Tea but NOT Coffee?
Tea but not Coffee = $n(\text{Tea}) - n(\text{Tea and Coffee}) = 25 - 15 = 10$.
In a class of 200 students, 100 passed Maths, 90 passed Science, 80 passed English, 40 passed Maths & Science, 30 passed Science & English, 20 passed Maths & English, and 10 passed all three. How many failed in all subjects?
$n(M∪S∪E) = 100+90+80-40-30-20+10 = 190$. Failed = $200 - 190 = 10$.
In a survey, 65% like Product A, 55% like Product B, and 25% like both. Find the percentage who like only one product.
Only A = $65-25 = 40\%$. Only B = $55-25 = 30\%$. Only one = $40+30 = 70\%$.
In a competition, 150 students participated in at least one of three events. If 40 participated in all three and the pairwise intersections each have 70, find how many participated in exactly two events.
Each pairwise = 70 includes the 40 from all three. Exactly two per pair = $70-40 = 30$. Three pairs total = $30×3 = 90$.
In a group, everyone likes at least one of three games: Cricket (70), Football (60), Hockey (50). 30 like C&F, 25 like F&H, 20 like C&H, 10 like all three. Find how many like only Hockey.
Only Hockey = $50 - 25 - 20 + 10 = 15$.
In a group of 150, 80 like tea, 70 like coffee, and 30 like both. How many like neither?
$n(T∪C) = 80+70-30 = 120$. Neither = $150-120 = 30$.
In a class of 100 students, 40 play cricket, 30 play football, 20 play both. How many play at least one sport?
$n(C∪F) = 40+30-20 = 50$.
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