CAT 3-Set & 4-Set Venn Diagram Questions

The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW). The following additional facts are known about the countries visited by them.

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1. 32 countries were visited by at least one of them.
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2. USA (in ROW) is the only country that was visited by all three of them.
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3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
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4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
$$$$
5. Half of the countries visited by both Samantha and Nitesh are in Europe.
$$

The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW). The following additional facts are known about the countries visited by them.

$$
1. 32 countries were visited by at least one of them.
$$$$
2. USA (in ROW) is the only country that was visited by all three of them.
$$$$
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
$$$$
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
$$$$
5. Half of the countries visited by both Samantha and Nitesh are in Europe.
$$

The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW). The following additional facts are known about the countries visited by them.

$$
1. 32 countries were visited by at least one of them.
$$$$
2. USA (in ROW) is the only country that was visited by all three of them.
$$$$
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
$$$$
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
$$$$
5. Half of the countries visited by both Samantha and Nitesh are in Europe.
$$

The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW). The following additional facts are known about the countries visited by them.

$$
1. 32 countries were visited by at least one of them.
$$$$
2. USA (in ROW) is the only country that was visited by all three of them.
$$$$
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
$$$$
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
$$$$
5. Half of the countries visited by both Samantha and Nitesh are in Europe.
$$

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.

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1. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
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2. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only.
$$$$
3. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only.
$$$$
4. 100 patients were treated with exactly three types of medicines.
$$$$
5. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type В.
$$$$
6. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
$$

3

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.

$$
1. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
$$$$
2. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only.
$$$$
3. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only.
$$$$
4. 100 patients were treated with exactly three types of medicines.
$$$$
5. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type В.
$$$$
6. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
$$

3

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.

$$
1. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
$$$$
2. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only.
$$$$
3. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only.
$$$$
4. 100 patients were treated with exactly three types of medicines.
$$$$
5. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type В.
$$$$
6. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
$$

3

1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.

$$
1. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
$$$$
2. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only.
$$$$
3. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only.
$$$$
4. 100 patients were treated with exactly three types of medicines.
$$$$
5. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type В.
$$$$
6. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
$$

3

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

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

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

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.

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.

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.

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.

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.

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.

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.

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.

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.