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36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
- a)12
- b)11
- c)13
- d)18
Correct answer is option 'A'. Can you explain this answer?
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36 people {a1, a2, ..., a36} meet and shake hands in a circular fashio...
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36 people {a1, a2, ..., a36} meet and shake hands in a circular fashio...
Given:
- There are 36 people denoted by a1, a2, ..., a36.
- The people meet and shake hands in a circular fashion.
- There are a total of 36 handshakes involving the pairs {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}.
To find:
- The size of the smallest set of people such that the rest have shaken hands with at least one person in the set.
Solution:
To solve this problem, we can consider a few cases.
Case 1: If the set contains only one person, i.e., a1.
- In this case, a1 has shaken hands with all other people, so the rest have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 1.
Case 2: If the set contains two people, i.e., {a1, a2}.
- In this case, a1 has shaken hands with a2, and a2 has shaken hands with a1.
- Therefore, the rest have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 2.
Case 3: If the set contains three people, i.e., {a1, a2, a3}.
- In this case, a1 has shaken hands with a2, a2 has shaken hands with a3, and a3 has shaken hands with a1.
- Therefore, the rest have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 3.
Case 4: If the set contains four or more people.
- In this case, we can observe that a person can shake hands with at most two other people.
- If we consider a set of 11 people, i.e., {a1, a2, ..., a11}, each person can shake hands with at most two other people in the set.
- Therefore, the rest of the people (a12, a13, ..., a36) must have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 11.
Therefore, from the above cases, we can conclude that the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is 11 (option A).
- There are 36 people denoted by a1, a2, ..., a36.
- The people meet and shake hands in a circular fashion.
- There are a total of 36 handshakes involving the pairs {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}.
To find:
- The size of the smallest set of people such that the rest have shaken hands with at least one person in the set.
Solution:
To solve this problem, we can consider a few cases.
Case 1: If the set contains only one person, i.e., a1.
- In this case, a1 has shaken hands with all other people, so the rest have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 1.
Case 2: If the set contains two people, i.e., {a1, a2}.
- In this case, a1 has shaken hands with a2, and a2 has shaken hands with a1.
- Therefore, the rest have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 2.
Case 3: If the set contains three people, i.e., {a1, a2, a3}.
- In this case, a1 has shaken hands with a2, a2 has shaken hands with a3, and a3 has shaken hands with a1.
- Therefore, the rest have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 3.
Case 4: If the set contains four or more people.
- In this case, we can observe that a person can shake hands with at most two other people.
- If we consider a set of 11 people, i.e., {a1, a2, ..., a11}, each person can shake hands with at most two other people in the set.
- Therefore, the rest of the people (a12, a13, ..., a36) must have shaken hands with at least one person in the set.
- Therefore, the size of the smallest set is 11.
Therefore, from the above cases, we can conclude that the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is 11 (option A).
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36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer?
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36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer?.
36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer?.
Solutions for 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set isa)12b)11c)13d)18Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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