Venn Diagrams CAT PYQs , 32 Questions with Solutions

Match List I with List II:

Choose the correct answer from the options given below:

If the triangle represents doctors, the circle represents teachers, and the rectangle represents film-makers in the following diagram, then which numbers represent teachers who are neither doctors nor film-makers?

(A circle overlaps a rightward-pointing triangle and a large rectangle. Regions: 5 = circle only (top, above the rectangle's edge and left of the triangle) = teachers only; 2 = circle only (below 5, still above the rectangle's top edge, left of the triangle) = teachers only; 7 = circle ∩ triangle only = teachers+doctors; 8 = triangle only = doctors only; 3 = circle ∩ rectangle only (below the rectangle's top edge) = teachers+film-makers; 4 = triangle ∩ rectangle only = doctors+film-makers; 9 = rectangle only = film-makers only.)

Take the given statements to be true even if they seem to be at variance from commonly known facts. Which conclusion would follow on the basis of given statements.

Statement: 'Some bags are purses', 'All purses are containers' and 'All containers are suitcases'.

Conclusions : (A) Some suitcases are bags (B) All purses are bags (C) All purses are suitcases (D) Some containers are purses

Choose the correct answer from the options given below :

In the following figure, the smaller triangle represents teachers; the big triangle represents politicians; circle represents graduates and rectangle represents members of Parliament. Different regions are being represented by letters of English alphabet.

On the basis of the above diagram, answer the following questions:

If 'All sweet things are fluids' and 'Some fluids are coloured things', then it implies - A. Some sweet things are coloured things B. Some sweet things are fluids C. All fluids are sweet things D. Some fluids are sweet things Choose the most appropriate answer from the options given below:

Statements: Some M are L. All H are W. Some W are M Conclusions. I. All M are W II. Some H are L III. Some W are H

All needles are threads, All threads are boxes. All trees are boxes. (A) No needle is tree. (B) Some trees are threads (C) Some boxes are needles (D) Some trees are needles Choose the correct answer from the options given below:

Directions: In each of the questions below are given some statements followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known fact. (a) If only conclusion I follows. (b) If only conclusion II follows. (c) If either conclusion I or II follows. (d) If neither conclusion I nor II follows.

Statements: Only a few Ant are Cow No cow is Joker Only a few Joker are Deer Conclusions: I. Some Deer are Ant II. Some Ant are Joker.

Directions: In each of the questions below are given some statements followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known fact. (a) If only conclusion I follows. (b) If only conclusion II follows. (c) If either conclusion I or II follows. (d) If neither conclusion I nor II follows.

Statements: Only a few Chocolate are Table Only a few Tables are Plants Only a few Plants are Fan Conclusions. I. Some fan is Chocolate is a possibility II. All fan are Tables

In a college 200 students are randomly chosen. 140 like tea and 120 like Coffee and 70 like both tea and coffee. How many like neither tea nor coffee?

Statement 1: All Circles are Rectangles Statement 2: No Circle is Triangle Conclusion I: Some Rectangles being Triangles is a Possibility Conclusion II: All Triangles are Rectangles

Given below is a diagram of three circles X, Y and Z which represent musicians, singers and dancers, respectively. The circles intersect with each other and form regions labelled a, b, c and d. (The three equal circles are arranged in a standard 3-circle Venn triangle layout: X top-left, Y top-right, Z bottom-center, all three pairwise overlapping with one common center region. Region d = X∩Y only, at the top between X and Y, not touching Z. Region b = X∩Y∩Z, at the center where all three overlap. Region a = X∩Z only, at the bottom-left. Region c = Y∩Z only, at the bottom-right.) Select the region that represents musicians who are singers but not dancers.

A, B, C and D play tennis. B and C play football also. D does not play chess but plays badminton. Who plays only tennis?

Observe the given figure and read the statements (I), (II) and (III). (The figure shows a triangle labeled Teachers and a circle labeled Doctors that partially overlap, meaning only part of the triangle lies inside the circle and it is not fully contained. A square labeled Surgeon is drawn fully inside the circle (Doctors), not touching the triangle.)

Statements: (I) All teachers are doctors (II) Some doctors are teachers (III) All surgeons are doctors Which of the following statement(s) is/are correct:

Statements: Some science is not maths All maths is physics Only a few physics is chemistry Some chemistry is statistics Conclusions: I) Some maths is chemistry II) All statistics is science is a possibility

Statements: Some planets are earth Only a few earth is sun Only sun is galaxy No sun is milkyway Conclusions: I) Some earth is not milkyway II) Some galaxy is planet is a possibility

Statements: All boats are stream No stream is a cruise Some cruises are captain Some captains are not pilots Conclusions: I) All pilots can be cruise II) No boat is captain

Statements: All myntra is Ajio. Some Ajio is flipkart Only a few flipkart if amazon No amazon is lenskart Conclusions: I) Some flipkart is not lenskart II) All Ajio is lenskart is a possibility

Statements: No gold is bronze Only a few bronzes are silver All silvers are copper Some coppers are diamond Conclusions: I) All golds are diamond II) Some diamonds are not gold

Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.

The following facts are known about these ten musicians.

1. Both A and B are experts in mridangam, but only one of them is also an expert in tabla.

2. D is an expert in both tabla and ghatam.

3. Both F and G are experts in tabla, but only one of them is also an expert in mridangam.

4. Neither I nor J is an expert in tabla.

5. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP).

The following four facilities were studied.

F1: Own software for OTLP

F2: Trained teachers for OTLP

F3: Training materials for OTLP

F4: All students having Laptops

The following observations were summarized from the survey.

1. 80 schools did not have any of the four facilities – F1, F2, F3, F4.

2. 40 schools had all four facilities.

3. The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.

4. The number of schools with exactly three of the facilities was the same irrespective of which three were considered.

5. 313 schools had F2.

6. 26 schools had only F2 and F3 (but neither F1 nor F4).

7. Among the schools having F4, 24 had only F3, and 45 had only F2.

8. 162 schools had both F1 and F2.

9. The number of schools having F1 was the same as the number of schools having F4.

Statements: No House is Luxury. Some Luxury is Car. Only Car is Scooter.

(Take the given statements to be true even if they seem to be at variance with commonly known facts.)

Conclusions: I. Some Scooter can be Car II. Some Car is not House

Statements: Only a few Queue are Long. Some Long are Short. Some Short is Bottle.

(Take the given statements to be true even if they seem to be at variance with commonly known facts.)

Conclusion: I. All Long can be Short II. All Queue can be Long

Statements: Some Apple are Mango. No Mango is Blood. Only Blood is Heart.

(Take the given statements to be true even if they seem to be at variance with commonly known facts.)

Conclusion: I. Some Heart is not Mango II. All Blood can be Apple

Statements: All Black are White. Some Black are Green. Only a few Green are Yellow.

(Take the given statements to be true even if they seem to be at variance with commonly known facts.)

Conclusions: I. All Green can be White II. Some Yellow can be Black

Statements: All Arrogant are Table. Some Table are Tree. All Tree are Parrot.

(Take the given statements to be true even if they seem to be at variance with commonly known facts.)

Conclusion: I. All Tree are Arrogant II. Some Tree are not Arrogant

Students in a college are discussing two proposals --

A: a proposal by the authorities to introduce dress code on campus, and

B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.

A student does not necessarily support either of the two proposals. In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates.

A survey was conducted among the students by picking a sample of 500 students. The following information was noted from this survey.

1. 250 students supported proposal A and 250 students supported proposal B.

2. Among the 200 students who preferred Sunita as student union president, $80 \%$ supported proposal A.

3. Among those who preferred Ragini, $30 \%$ supported proposal A.

4. $20 \%$ of those who supported proposal B preferred Sunita.

5. $40 \%$ of those who did not support proposal B preferred Ragini.

6. Every student who preferred Sunita and supported proposal B also supported proposal A

7. Among those who preferred Ragini, $20 \%$ did not support any of the proposals.

Conclusions: No car is a bike. All bikes being vans is a possibility. Statements: I. All scooters are bikes. No bike is a moped. All cars are bikes. All mopeds are vans II. Some scooters are bikes. No bike is a van. All cars are mopeds. All mopeds are vans. III. Some scooters are bikes. No bike is a moped. All cars are bikes. All mopeds are vans. IV. All scooters are bikes. No bike is a van. All cars are mopeds. All mopeds are vans. V. All scooters are bikes. No bike is a moped. All cars are mopeds. All mopeds are vans

Conclusions: Atleast some states are district. Some towns being district is a possibility. Statements: I. All districts are states. Some states are village. No town is district. II. No districts is states. Some states are towns. No town is village. III. All districts are states. Some states are towns. No town is village. IV. No districts is states. Some states are towns. No town is village. V. All districts are states. Some states are village. Some town are village.

1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B , or C , or S does not serve O . The following facts are known about the satellites:

1. The numbers of satellites serving $B, C$, and $S$ (though may be not exclusively) are in the ratio $2: 1: 1$.

2. The number of satellites serving all three of $B$, $C$, and $S$ is 100 .

3. The number of satellites exclusively serving $C$ is the same as the number of satellites exclusively serving $S$. This number is $30 \%$ of the number of satellites exclusively serving $B$.

4. The number of satellites serving $O$ is the same as the number of satellites serving both $C$ and $S$ but not $B$.

Fun Sports (FS) provides training in three sports - Gilli-danda (G), Kho-Kho (K), and Ludo (L). Currently it has an enrollment of 39 students each of whom is enrolled in at least one of the three sports. The following details are known:

1. The number of students enrolled only in $L$ is double the number of students enrolled in all the three sports.
2. There are a total of 17 students enrolled in G .
3. The number of students enrolled only in G is one less than the number of students enrolled only in L .
4. The number of students enrolled only in K is equal to the number of students who are enrolled in both K and L.
5. The maximum student enrollment is in L .
6. Ten students enrolled in G are also enrolled in at least one more sport.

Study the diagram given below to answer the question. Circle=Educated women, Triangle=Villages, Rectangle=Unemployed women.

Educated unemployed women in villages are represented by which letter?