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12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4
- c)18
- d)11
Correct answer is option 'A'. Can you explain this answer?
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12 people {a1, a2, a12} meet and shake hands in a circular fashion. In...
12 x 11 / 2 = 66 Handshakes.
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12 people {a1, a2, a12} meet and shake hands in a circular fashion. In...
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12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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
Solution:
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, we need to consider the handshakes involving each person. Let's analyze the given information step by step.
1. Handshakes between consecutive people:
In a circular fashion, each person shakes hands with the person standing next to them. So, the handshakes involving consecutive people are:
- a1 shakes hands with a2
- a2 shakes hands with a3
- a11 shakes hands with a12
- a12 shakes hands with a1
So, there are a total of 4 handshakes involving consecutive people.
2. Handshakes between non-consecutive people:
To find the remaining handshakes involving non-consecutive people, we subtract the handshakes involving consecutive people from the total number of handshakes.
Total handshakes = 36
Handshakes involving consecutive people = 4
Remaining handshakes involving non-consecutive people = Total handshakes - Handshakes involving consecutive people
= 36 - 4
= 32
3. Smallest set of people:
To ensure that the rest of the people have shaken hands with at least one person in the set, we need to find the smallest number of people who have shaken hands with all the others.
Since each person shakes hands with 11 other people (excluding themselves), the smallest set of people will be the ones who have shaken hands with all the others. Therefore, the size of the smallest set is 12.
Hence, the correct answer is option A) 12.
12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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
Solution:
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, we need to consider the handshakes involving each person. Let's analyze the given information step by step.
1. Handshakes between consecutive people:
In a circular fashion, each person shakes hands with the person standing next to them. So, the handshakes involving consecutive people are:
- a1 shakes hands with a2
- a2 shakes hands with a3
- a11 shakes hands with a12
- a12 shakes hands with a1
So, there are a total of 4 handshakes involving consecutive people.
2. Handshakes between non-consecutive people:
To find the remaining handshakes involving non-consecutive people, we subtract the handshakes involving consecutive people from the total number of handshakes.
Total handshakes = 36
Handshakes involving consecutive people = 4
Remaining handshakes involving non-consecutive people = Total handshakes - Handshakes involving consecutive people
= 36 - 4
= 32
3. Smallest set of people:
To ensure that the rest of the people have shaken hands with at least one person in the set, we need to find the smallest number of people who have shaken hands with all the others.
Since each person shakes hands with 11 other people (excluding themselves), the smallest set of people will be the ones who have shaken hands with all the others. Therefore, the size of the smallest set is 12.
Hence, the correct answer is option A) 12.
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Community Answer
12 people {a1, a2, a12} meet and shake hands in a circular fashion. In...
12 x 11 / 2 = 66 Handshake
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12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4c)18d)11Correct answer is option 'A'. Can you explain this answer?
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12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4c)18d)11Correct 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 12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4c)18d)11Correct 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 12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4c)18d)11Correct answer is option 'A'. Can you explain this answer?.
12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4c)18d)11Correct 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 12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4c)18d)11Correct 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 12 people {a1, a2, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, {a11, a12}, {a12, 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)4c)18d)11Correct answer is option 'A'. Can you explain this answer?.
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