Venn Diagrams for CUET General Aptitude

AnswerC · A small circle inside a larger circle, and a third circle apart from both

1. Every mother is a woman, but not every woman is a mother: the Mothers circle lies inside the Women circle.

2. No man is a woman (and so no man is a mother): the Men circle is separate from both.

3. The picture needed is a small circle inside a larger one, with a third circle apart from both.

AnswerD · Three circles, each inside the next

1. Every city in Kerala is a city in India, and every city in India is a city in Asia.

2. Each class is wholly inside the next: Kerala inside India inside Asia.

3. The picture is three circles, each inside the next.

AnswerB · Two separate circles inside a larger circle

1. Every bus is a vehicle and every bicycle is a vehicle: both circles go inside Vehicles.

2. Nothing is both a bus and a bicycle: those two circles do not meet.

3. So two separate circles sit inside a larger circle.

AnswerA · Three circles, each overlapping the other two

1. Some teachers are parents and some are not, so Teachers and Parents overlap.

2. Some teachers are graduates and some parents are graduates, and neither class is wholly inside Graduates: each pair overlaps.

3. Some people are all three (a teacher who is a parent and a graduate).

4. So the picture is three circles, each overlapping the other two.

AnswerD · Two separate circles, each overlapping a third circle

1. No boy is a girl: Boys and Girls are separate circles.

2. Some boys are students and some are not (a boy who has left school): Boys overlaps Students. The same is true of Girls.

3. So the picture is two separate circles, each overlapping a third circle.

AnswerA · A small circle inside a larger circle, and a third circle apart from both

1. Iron is a metal (and not every metal is iron): the Iron circle lies inside Metals.

2. Wood is not a metal and is not iron: the Wood circle is separate from both.

3. So a small circle sits inside a larger one, with a third circle apart.

AnswerB · Three separate circles

1. No tiger is a sparrow, no tiger is a snake and no sparrow is a snake.

2. No two classes share a member, so the picture is three separate circles.

AnswerA · Two overlapping circles, and a third circle apart from both

1. Some teachers write books and some writers teach, but neither class is inside the other: Teachers and Writers overlap.

2. A mountain is neither a teacher nor a writer: Mountains is apart from both.

3. So two overlapping circles, with a third circle apart from both.

AnswerD · Three circles, each inside the next

1. Every dog is a mammal, and every mammal is an animal.

2. So Dogs sits inside Mammals, which sits inside Animals: three circles, each inside the next.

AnswerA · A small circle inside a larger circle, and a third circle overlapping both of them

1. Every mother is a woman: Mothers sits inside Women.

2. Some doctors are women and some are men: Doctors overlaps Women.

3. Some mothers are doctors and some are not, and many doctors are not mothers: Doctors also overlaps Mothers.

4. So a small circle sits inside a larger one, and a third circle cuts across both.

AnswerB · Two overlapping circles inside a larger circle

1. Every teacher and every parent is a human being: both circles lie inside Human beings.

2. Many teachers are parents, some teachers are not parents and some parents are not teachers: Teachers and Parents overlap.

3. So two overlapping circles sit inside a larger circle.

AnswerD · Two overlapping circles inside a larger circle

1. Every rectangle and every rhombus has four sides: both circles lie inside Quadrilaterals.

2. A square is both a rectangle and a rhombus, but most rectangles are not rhombuses and most rhombuses are not rectangles: the two circles overlap.

3. So two overlapping circles sit inside a larger circle.

AnswerD · Three circles, each overlapping the other two

1. 6 is a multiple of 2 and of 3; 10 is a multiple of 2 and of 5; 15 is a multiple of 3 and of 5: every pair meets.

2. No class is inside another (4 is not a multiple of 3, 9 is not a multiple of 2, and so on).

3. 30 is a multiple of all three, so the three circles share a common part.

4. So the picture is three circles, each overlapping the other two.

AnswerB · Three circles in a chain: the middle one overlaps both, the outer two do not meet

1. 14 is a two-digit multiple of 7, while 10 is two-digit but not a multiple of 7 and 7 is a multiple of 7 with one digit: Two-digit numbers overlaps Multiples of 7.

2. 105 is a three-digit multiple of 7, while 100 is not a multiple of 7 and 1001 has four digits: Three-digit numbers overlaps Multiples of 7.

3. No number has both two digits and three digits: those two circles do not meet.

4. So the picture is a chain: the middle circle (Multiples of 7) overlaps both, and the outer two do not meet.

AnswerA · A small circle inside a larger circle, and a third circle overlapping both of them

1. Every multiple of 4 is even: Multiples of 4 sits inside Even numbers.

2. 6 is even and a multiple of 3, while 3 is not even and 2 is not a multiple of 3: Multiples of 3 overlaps Even numbers.

3. 12 is a multiple of both 3 and 4, and 8 and 9 each belong to only one: Multiples of 3 overlaps Multiples of 4 as well.

4. So a small circle inside a larger one, with a third circle overlapping both.

AnswerD · A small circle inside a larger circle, and a third circle overlapping both of them

1. Every physicist is a scientist: Physicists lies inside Scientists.

2. Some scientists are women and some are not: Women overlaps Scientists.

3. Some physicists are women and some are not: Women overlaps Physicists too.

4. So a small circle inside a larger one, with a third circle overlapping both.

AnswerC · Two overlapping circles with a small circle inside their common part

1. A square has four right angles, so it is a rectangle; it has four equal sides, so it is a rhombus. Squares lies inside both.

2. Some rectangles are not rhombuses and some rhombuses are not rectangles: Rectangles and Rhombuses overlap.

3. Their common part is exactly the squares.

4. So two overlapping circles with a small circle inside their common part.

AnswerA · Two separate circles inside a larger circle

1. Both equilateral triangles and right-angled triangles are triangles: both circles go inside Triangles.

2. Every angle of an equilateral triangle is 60°, so none is right-angled: the two inner circles do not meet.

3. So two separate circles inside a larger circle.

AnswerC · Three circles in a chain: the middle one overlaps both, the outer two do not meet

1. 3 is odd and prime, while 9 is odd but not prime and 2 is prime but not odd: Odd numbers and Prime numbers overlap.

2. 2 is even and prime, and 4 is even but not prime: Prime numbers and Even numbers also overlap.

3. No number is both odd and even: those two circles do not meet.

4. So the picture is a chain with Prime numbers in the middle, overlapping both of the others.

AnswerC · A small circle inside a larger circle, and a third circle overlapping the larger circle only

1. Every 15-year-old is a teenager: 15-year-olds sits inside Teenagers.

2. 18- and 19-year-olds are teenagers who can vote, and voters over 19 are not teenagers: Voters overlaps Teenagers.

3. No 15-year-old can vote: Voters does not meet the 15-year-olds circle.

4. So a small circle sits inside a larger one, with a third circle overlapping the larger circle only.

AnswerD · A small circle inside a larger circle, and a third circle overlapping the larger circle only

1. Every multiple of 6 is a multiple of 3: Multiples of 6 sits inside Multiples of 3.

2. 9 is odd and a multiple of 3; 5 is odd but not a multiple of 3; 6 is a multiple of 3 but not odd: Odd numbers overlaps Multiples of 3.

3. Every multiple of 6 is even, so no odd number is a multiple of 6: Odd numbers misses the small circle.

4. So a small circle inside a larger one, with a third circle overlapping the larger circle only.

AnswerB · Two overlapping circles with a small circle inside their common part

1. Every multiple of 12 is a multiple of 2 and of 3: Multiples of 12 lies inside both.

2. 6 is a multiple of 2 and 3, 4 is a multiple of 2 only, 9 of 3 only: Multiples of 2 and Multiples of 3 overlap.

3. So two overlapping circles with a small circle inside their common part.

AnswerA · 8

1. 'Sing but neither dance nor paint' is the part of Singers outside both other circles: the Only Singers region.

2. That region shows 8.

AnswerB · 11

1. 'Both Tea and Coffee' is every region inside both circles, whether or not the person also drinks Juice.

2. Tea and Coffee only 8, all three 3.

3. Both Tea and Coffee $= 8 + 3 = 11$.

AnswerD · 46

1. Speakers of English are everyone inside the English circle.

2. $12 + 18 + 10 + 6 = 46$.

AnswerB · 12

1. Students who play none of the games are inside the box but outside every circle.

2. That number is 12.

AnswerA · 11

1. All three is the centre region, common to every circle.

2. It shows 11.

AnswerA · 9

1. 'Maths only' is the part of the Maths circle outside both other circles.

2. It shows 9.

AnswerA · 6

1. Metro and Bicycle but not Bus is the 'Metro and Bicycle only' region.

2. It shows 6.

AnswerD · 15

1. Exactly two means the three 'two only' regions, not the centre.

2. Dancers and Singers only 6, Dancers and Painters only 4, Singers and Painters only 5.

3. Exactly two $= 6 + 4 + 5 = 15$.

AnswerC · 69

1. At least one means every region inside the circles.

2. $24 + 15 + 9 + 8 + 6 + 4 + 3 = 69$.

AnswerC · 19

1. Coffee but not Tea: the part of the Coffee circle outside the Tea circle.

2. That is Only Coffee (15) and Coffee and Juice only (4).

3. Total $= 15 + 4 = 19$.

AnswerD · 67

1. Exactly one: the three 'only' regions.

2. $30 + 12 + 25 = 67$.

AnswerA · 23

1. Keep regions in Football or Hockey that lie outside Cricket.

2. Only Football 14, Only Hockey 6, Football and Hockey only 3.

3. Total $= 14 + 6 + 3 = 23$.

AnswerB · 49

1. Keep the parts of Television outside Newspaper.

2. Only Television 40, Radio and Television only 9.

3. Total $= 40 + 9 = 49$.

AnswerD · 47

1. At least two means exactly two or all three.

2. Exactly two $= 5 + 22 + 9 = 36$; all three $= 11$.

3. At least two $= 36 + 11 = 47$.

AnswerB · 23

1. Total students $= 9 + 6 + 8 + 10 + 7 + 5 + 15 + 4 = 64$.

2. Passed Maths $= 9 + 10 + 7 + 15 = 41$.

3. Failed Maths $= 64 - 41 = 23$. (Check: $6 + 8 + 5 + 4 = 23$.)

AnswerA · 9

1. Metro users $= 21 + 13 + 6 + 1 = 41$.

2. Bus users $= 16 + 13 + 2 + 1 = 32$.

3. Difference $= 41 - 32 = 9$.

AnswerB · 32

1. Class 12 has $11 + 8 + 13 + 6 + 4 + 5 + 3 + 7 = 57$ students.

2. Painters $= 13 + 4 + 5 + 3 = 25$.

3. Students who do not paint $= 57 - 25 = 32$. (Check: $11 + 8 + 6 + 7 = 32$.)

AnswerB · 23

1. The residents must be inside Tamil and inside at least one more circle.

2. Hindi and Tamil only 7, English and Tamil only 10, all three 6.

3. Total $= 7 + 10 + 6 = 23$.

AnswerC · 50%

1. All students $= 20 + 14 + 6 + 9 + 4 + 3 + 2 + 12 = 70$.

2. Cricket players $= 20 + 9 + 4 + 2 = 35$.

3. Percentage $= \frac{35}{70} \times 100 = 50\%$.

AnswerC · 36

1. Adding $25 + 18$ counts the 7 students who like both twice.

2. Students $= 25 + 18 - 7 = 36$.

AnswerA · 7

1. Households buying at least one $= 35 + 30 - 12 = 53$.

2. Neither $= 60 - 53 = 7$.

AnswerD · 31

1. French only = French learners who do not also take German.

2. French only $= 40 - 9 = 31$.

AnswerA · 9

1. Tabla + harmonium $= 32 + 27 = 59$, but there are only 50 members.

2. The extra 9 have been counted twice, so 9 play both.

AnswerC · 30%

1. People who like at least one fruit $= 100\% - 10\% = 90\%$.

2. Both $= 70\% + 50\% - 90\% = 30\%$.

AnswerD · 51

1. Bicycle only $= 45 - 12 = 33$; scooter only $= 30 - 12 = 18$.

2. Exactly one $= 33 + 18 = 51$.

AnswerB · 16

1. Split the 32 carrom players: 8 (with chess only), 5 (with ludo only), 3 (all three) and the rest.

2. Only carrom $= 32 - 8 - 5 - 3 = 16$.

AnswerB · 15

1. At least one $= 35 + 30 + 25 - 12 - 10 - 8 + 5$.

2. $= 90 - 30 + 5 = 65$.

3. None $= 80 - 65 = 15$.

AnswerA · 22

1. Each pair count contains the 4 all-three families, so remove them from each: $10, 7, 5$.

2. Exactly two $= 10 + 7 + 5 = 22$, which is $34 - 3 \times 4$.

AnswerC · 44

1. Exactly two $= 9 + 7 + 8 - 3 \times 3 = 15$.

2. All three $= 3$.

3. Exactly one $= 62 - 15 - 3 = 44$.

AnswerD · 52

1. Only Bengali + only Odia $= 80 - 20 - 12 = 48$.

2. If only Odia $= x$, then $2x + x = 48$, so $x = 16$ and only Bengali $= 32$.

3. Bengali speakers $= 32 + 20 = 52$.

AnswerA · 6

1. The three numbers given are separate regions (Art only, Music only, both), so simply add them: $18 + 12 + 10 = 40$.

2. Neither $= 46 - 40 = 6$.

AnswerC · 14

1. The 9 and the 11 both contain the 4 who are in all three clubs, so those 4 were subtracted twice.

2. Science only $= 30 - 9 - 11 + 4 = 14$.

AnswerA · 12%

1. At least one $= 65\% + 48\% - 25\% = 88\%$.

2. Neither $= 100\% - 88\% = 12\%$.

AnswerB · 25

1. Exactly two $= 15 + 12 + 10 - 3 \times 6 = 19$.

2. At least two $= 19 + 6 = 25$, which is $37 - 2 \times 6$.

AnswerC · 75

1. Add the three totals: $42 + 36 + 28 = 106$.

2. Subtract the pair counts: $106 - 36 = 70$.

3. Add back all three: $70 + 5 = 75$.

AnswerC · 25

1. The overlap cannot be bigger than the smaller group, 25.

2. 25 is possible: if every Science-lover also likes Mathematics, the Science circle sits inside the Mathematics circle, and 28 students like at least one, which is within 40.

3. Greatest overlap $= 25$.

AnswerB · 50

1. At least one $= 200 - 30 = 170$.

2. Those who play an instrument but not a sport are the part of the 170 outside the sport circle: $170 - 120 = 50$.

3. (Check: both $= 120 + 90 - 170 = 40$, and $90 - 40 = 50$.)

AnswerB · 15

1. The overlap is smallest when as many students as possible have at least one device, that is, all 50.

2. Then both $= 36 + 29 - 50 = 15$.

3. A smaller overlap would need more than 50 students, so at least 15 have both.

AnswerC · 25

1. 'Neither' is largest when the two groups overlap as much as possible.

2. The largest overlap puts all 28 coffee-lovers inside the 35 tea-lovers; then only 35 like at least one.

3. Neither $= 60 - 35 = 25$.

AnswerB · 35

1. Adding the lists gives 155 names: a student on one list is counted once, on two lists twice, on three lists three times.

2. So (exactly one) + 2 × (exactly two) + $3 \times 10 = 155$, and (exactly one) + (exactly two) + $10 = 100$.

3. Subtract: (exactly two) + $20 = 55$, so exactly two = 35.

AnswerB · 200

1. Passed in at least one $= 100\% - 8\% = 92\%$.

2. Passed in both $= 75\% + 65\% - 92\% = 48\%$.

3. 48% of the total is 96, so total $= \frac{96 \times 100}{48} = 200$.

AnswerC · 79

1. All three: $104 = 50 + 45 + 40 - 15 - 12 - 10 + x$, so $104 = 98 + x$ and $x = 6$.

2. Exactly two $= 15 + 12 + 10 - 3 \times 6 = 19$.

3. Exactly one $= 104 - 19 - 6 = 79$.

AnswerD · 40