Practice Questions
Lane B — Logic & decisions
Study step 17 of 26
40 MCQs ready
Syllogism and sets background helps.
Next topic in path →Concept Explanation
Venn diagrams show how sets overlap. Placement exams use them in three main ways: pick the diagram that fits three words (relation questions), read numbered regions in a three-set figure, and solve 2-set or 3-set counts with union and intersection.
Question types (same as IndiaBIX / PrepInsta LR)
- Best relation: Furniture–Chairs–Tables (disjoint inside a parent), Tiger–Carnivore–Elephant (subset + separate), Tomato–Vegetable–Fruit (overlap).
- Region numbers: Regions 1–7 for only-A, only-B, only-C, pairwise-only overlaps, and all three.
- Counting: at least one = sum of singles + both-only + … ; for two sets: total in A or B = A + B − both.
Region key used in practice
| Region | Meaning |
|---|---|
| 1 | Only set A (left) |
| 2 | Only set B (right) |
| 3 | Only set C (bottom) |
| 4 | A and B only |
| 5 | A and C only |
| 6 | B and C only |
| 7 | All three |
Example diagram
TeaCoffeeWine1234567
How to solve fast
- For relation items, decide pairwise: subset, disjoint, or overlap — then match the picture.
- For region counts, list which region numbers belong to the words in the question before adding.
- For 2-set word problems, draw a quick two-circle sketch and label only-A, both, only-B.
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Q1 EasyWhich diagram best represents the relation among Furniture, Chairs, and Tables?ExplanationChairs and tables are both furniture but no chair is a table — two disjoint sets inside a parent set.
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Q2 EasyWhich diagram best represents Elephant, Carnivorous animals, and Tiger?ExplanationTiger is carnivorous; elephant is unrelated to that category in the diagram.
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Q3 EasyWhich diagram best represents School, Classroom, and Blackboard? (Every blackboard is in a classroom; every classroom is in a school.)ExplanationNested containment: blackboard ⊂ classroom ⊂ school.
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Q4 EasyWhich diagram best represents Dogs, Animals, and Cats? (Both dogs and cats are animals; no dog is a cat.)ExplanationTwo disjoint species circles inside the animals set.
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Q5 EasyWhich diagram best represents Copper, Metal, and Wood?ExplanationCopper is a metal; wood is non-metal and separate.
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Q6 EasyWhich diagram best represents India, Asia, and Delhi?ExplanationDelhi ⊂ India ⊂ Asia.
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Q7 EasyWhich diagram best represents Bus, Vehicle, and Bicycle?ExplanationBus and bicycle are different kinds of vehicles; disjoint inside vehicle.
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Q8 EasyWhich diagram best represents Square, Rectangle, and Circle? (Every square is a rectangle.)ExplanationSquares inside rectangles; circles share no region with rectangles.
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Q9 EasyWhich diagram best represents Pen, Stationery, and Furniture?ExplanationPen is stationery; furniture is unrelated.
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Q10 EasyWhich diagram best represents Mango, Fruit, and Apple?ExplanationMango and apple are distinct fruits inside the fruit category.
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Q11 EasyStudy the diagram (regions 1–7). Numbers show how many people fall in each region.
How many take only tea?ExplanationRegion 1 is tea only = 15. -
Q12 EasyUsing the same tea–coffee–wine diagram:
How many take both tea and coffee but not wine?ExplanationTea ∩ coffee only is region 4 = 8. -
Q13 EasyUsing the same diagram:
How many take all three beverages?ExplanationCenter region 7 = 5. -
Q14 EasyUsing the same diagram:
How many take at least one of tea, coffee, or wine?ExplanationSum of all seven regions = 77. -
Q15 EasyUsing the same diagram:
How many take only coffee?ExplanationRegion 2 = 12. -
Q16 EasyStudents play cricket, football, and/or kabaddi. Regions are numbered as shown.
How many play all three games?ExplanationRegion 7 = 4. -
Q17 EasySame diagram:
How many play only kabaddi?ExplanationRegion 3 = 22. -
Q18 EasySame diagram:
How many play at least one game?ExplanationSum all regions = 84. -
Q19 EasyRefer to the same circle–square–triangle figure:
Which region shows people who are engineers only (not lawyers or environmentalists)?ExplanationP lies in the circle away from square and triangle overlaps. -
Q20 Easy50 people read newspaper A, 30 read B, and 10 read both. How many read only A?ExplanationOnly A = 50 − 10 = 40.
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Q21 EasyIn a survey, 40 like tea, 35 like coffee, 18 like both. How many like at least one?Explanation40 + 35 − 18 = 57.
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Q22 EasyWhich region code gives B only in the standard 1–7 three-set diagram?ExplanationBy convention here, region 2 is only the right set (B).
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Q23 Easy80 employees: 50 know Java, 40 know Python, 25 know both. How many know only Python?ExplanationOnly Python = 40 − 25 = 15.
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Q24 MediumWhich diagram best represents Vegetables, Tomato, and Fruits? (Tomato is both a vegetable and a fruit in exam logic.)ExplanationTomato sits in the overlap of vegetables and fruits; neither set contains the other wholly.
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Q25 MediumWhich diagram best represents Women, Mothers, and Engineers? (Some engineers are women; mothers are women but not all women are mothers.)ExplanationMothers lie inside women; engineers overlap women but are not a subset of mothers.
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Q26 MediumWhich diagram best represents Teachers, Females, and Doctors? (Some doctors are female; some teachers are female; not all females are teachers or doctors.)ExplanationThree groups can pairwise overlap (female teachers, female doctors) without nesting.
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Q27 MediumWhich diagram best represents Spiders, Arachnids, and Insects? (Spiders are arachnids, not insects.)ExplanationSpiders ⊂ arachnids; insects are a separate class.
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Q28 MediumUsing the same diagram:
How many take tea and wine but not coffee?ExplanationTea ∩ wine only is region 5 = 10. -
Q29 MediumUsing the same diagram:
How many take wine (any wine drinker)?ExplanationWine regions: only wine (3) + tea∩wine (5) + coffee∩wine (6) + all three (7) = 42. -
Q30 MediumUsing the same diagram:
How many take coffee and wine but not tea?ExplanationRegion 6 = 7.
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Q31 MediumUsing the same diagram:
Total tea drinkers (tea in any form)?ExplanationTea appears in regions 1, 4, 5, 7 → 38. -
Q32 MediumSame sports diagram:
How many play cricket and football but not kabaddi?ExplanationCricket ∩ football only = region 4 = 9. -
Q33 MediumSame diagram:
Total football players?ExplanationFootball in regions 2, 4, 6, 7. -
Q34 MediumSame diagram:
How many play cricket and kabaddi but not football?ExplanationRegion 5 = 11. -
Q35 MediumIn the figure, circle = engineers, square = lawyers, triangle = environmentalists. Which region S best fits lawyers who are also environmentalists?ExplanationS marks the overlap of square (lawyers) and triangle (environmentalists).
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Q36 MediumIn a class of 60 students, 35 play cricket, 25 play football, and 12 play both. How many play neither?ExplanationAt least one sport: 35 + 25 − 12 = 48; neither = 60 − 48 = 12.
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Q37 Medium100 students: 55 in maths club, 45 in science club, 20 in both. How many in exactly one club?ExplanationOnly maths 35 + only science 25 = 60.
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Q38 MediumRegion key: 1 = only A, 2 = only B, 3 = only C, 4 = A∩B only, 5 = A∩C only, 6 = B∩C only, 7 = A∩B∩C. If region 4 has 6 people and region 7 has 4, how many are in A∩B (including triple overlap)?ExplanationA∩B = region 4 + region 7 = 6 + 4 = 10.
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Q39 MediumWhich diagram best represents Weekend, Sunday, and Monday? (Sunday is a weekend day; Monday is not.)ExplanationSunday lies inside weekend; Monday is a separate day outside the weekend set.
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Q40 HardWhich diagram best represents Gold, Ornaments, and Silver? (Some ornaments are gold; some are silver; gold and silver are different metals.)ExplanationGold and silver overlap the ornament set separately; neither metal contains the other.