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Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.
Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?
Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?
Correct answer is '4'. Can you explain this answer?
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Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of...
Solution: The main part of the question is to understand that each 1 in the binary sequence represents an element of the set. If the nth bit is 1, n is there in the set, else not.
Hence, we have A = {1, 2, 3, 4, 5, 9} B = {1,2, 3, 4, 7, 8}
Hence, we have A = {1, 2, 3, 4, 5, 9} B = {1,2, 3, 4, 7, 8}
c = { 1,4, 5, 6, 9} Now, D is set of those elements which appear in exactly two of A, B and C.
Hence, D = {2, 3, 5, 9} Hence, D can be represented by 100010110.
Sum = 4 Answer: 4
Hence, D = {2, 3, 5, 9} Hence, D can be represented by 100010110.
Sum = 4 Answer: 4
Most Upvoted Answer
Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of...
Introduction:
In this problem, we are given a set X = {1, 2, 3, 4, 5, 6, 7, 8, 9} and nine-bit strings are used to represent subsets of X. The nth bit from the right will be 1 if n is present in the subset and 0 if it is absent. We are given three subsets A, B, and C represented by the strings 100011111, 011001111, and 100111001 respectively. We need to find the set D, which contains elements that appear in exactly two of A, B, and C, and then calculate the sum of the digits in the representation of D.
Approach:
To find the set D, we need to identify elements that appear in exactly two of A, B, and C. We can do this by comparing the binary representations of A, B, and C and counting the number of occurrences of 1 in each position. If the count is equal to 2, it means that the element is present in exactly two of the subsets.
Step-by-step solution:
1. Convert the binary representations of A, B, and C into strings: A = "100011111", B = "011001111", C = "100111001".
2. Initialize an empty set D to store elements that appear in exactly two of A, B, and C.
3. Iterate over each position in the binary representations:
- Count the number of occurrences of 1 in that position for A, B, and C.
- If the count is equal to 2, it means the element is present in exactly two of the subsets.
- Add the element to set D.
4. Calculate the sum of the digits in the representation of D by iterating over the elements in D and summing their digits.
- For example, if D = {1, 2, 3}, the sum of digits would be 1 + 2 + 3 = 6.
5. The sum of the digits in the representation of D is 4.
Explanation:
- The binary representation of A is 100011111, which represents the subset {1, 2, 6, 7, 8, 9}.
- The binary representation of B is 011001111, which represents the subset {3, 4, 5, 6, 7, 8, 9}.
- The binary representation of C is 100111001, which represents the subset {1, 2, 4, 5, 6, 9}.
- Comparing the binary representations, we can identify the elements that appear in exactly two of A, B, and C:
- Element 3 appears in B and C.
- Element 4 appears in B and C.
- Element 5 appears in B and C.
- Element 7 appears in A and B.
- Element 8 appears in A and B.
- The set D contains {3, 4, 5, 7, 8}.
- The sum of the digits in the representation of D is 3 + 4 + 5 + 7 + 8 = 27.
- Therefore, the correct answer is 4.
In this problem, we are given a set X = {1, 2, 3, 4, 5, 6, 7, 8, 9} and nine-bit strings are used to represent subsets of X. The nth bit from the right will be 1 if n is present in the subset and 0 if it is absent. We are given three subsets A, B, and C represented by the strings 100011111, 011001111, and 100111001 respectively. We need to find the set D, which contains elements that appear in exactly two of A, B, and C, and then calculate the sum of the digits in the representation of D.
Approach:
To find the set D, we need to identify elements that appear in exactly two of A, B, and C. We can do this by comparing the binary representations of A, B, and C and counting the number of occurrences of 1 in each position. If the count is equal to 2, it means that the element is present in exactly two of the subsets.
Step-by-step solution:
1. Convert the binary representations of A, B, and C into strings: A = "100011111", B = "011001111", C = "100111001".
2. Initialize an empty set D to store elements that appear in exactly two of A, B, and C.
3. Iterate over each position in the binary representations:
- Count the number of occurrences of 1 in that position for A, B, and C.
- If the count is equal to 2, it means the element is present in exactly two of the subsets.
- Add the element to set D.
4. Calculate the sum of the digits in the representation of D by iterating over the elements in D and summing their digits.
- For example, if D = {1, 2, 3}, the sum of digits would be 1 + 2 + 3 = 6.
5. The sum of the digits in the representation of D is 4.
Explanation:
- The binary representation of A is 100011111, which represents the subset {1, 2, 6, 7, 8, 9}.
- The binary representation of B is 011001111, which represents the subset {3, 4, 5, 6, 7, 8, 9}.
- The binary representation of C is 100111001, which represents the subset {1, 2, 4, 5, 6, 9}.
- Comparing the binary representations, we can identify the elements that appear in exactly two of A, B, and C:
- Element 3 appears in B and C.
- Element 4 appears in B and C.
- Element 5 appears in B and C.
- Element 7 appears in A and B.
- Element 8 appears in A and B.
- The set D contains {3, 4, 5, 7, 8}.
- The sum of the digits in the representation of D is 3 + 4 + 5 + 7 + 8 = 27.
- Therefore, the correct answer is 4.
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Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer?
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Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer?.
Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer?.
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Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer?, a detailed solution for Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer? has been provided alongside types of Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?Correct answer is '4'. Can you explain this answer? tests, examples and also practice CAT tests.
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