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S is set of positive integers less than 50 such that each number in the set when divided by five gives remainder three and is not a prime. How many odd numbers are there in S?
Correct answer is '1'. Can you explain this answer?
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S is set of positive integers less than 50 such that each number in th...
Each number in the set has more than two factors i.e. the numbers in the set should be composite numbers.
As each element of S when divided by 5 gives remainder 3, the number has to be of the form 5k + 3, where k = 0, 1,2,...
The composite numbers of the form 5k + 3, less than 50 are 8, 18, 28, 33, 38 and 48.
S = {8, 18, 28, 33, 38, 48}
Only one number in S is odd.
Answer: 1
As each element of S when divided by 5 gives remainder 3, the number has to be of the form 5k + 3, where k = 0, 1,2,...
The composite numbers of the form 5k + 3, less than 50 are 8, 18, 28, 33, 38 and 48.
S = {8, 18, 28, 33, 38, 48}
Only one number in S is odd.
Answer: 1
Most Upvoted Answer
S is set of positive integers less than 50 such that each number in th...
Given:
- The set S consists of positive integers less than 50.
- Each number in the set, when divided by five, gives a remainder of three.
- The numbers in the set are not prime.
To find:
- The number of odd numbers in the set S.
Solution:
To solve this problem, we need to consider the given conditions and find the numbers that satisfy them.
Condition 1: Each number in the set, when divided by five, gives a remainder of three.
- This means that the numbers in the set can be represented as 5k + 3, where k is a positive integer.
- We can generate the numbers in the set by starting with 3 and adding multiples of 5 to it.
Condition 2: The numbers in the set are not prime.
- A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
- We need to find the numbers in the set that are not prime.
Generating the numbers in the set:
- Starting with 3, we can add multiples of 5 to it to generate the numbers in the set.
- The first few numbers in the set are: 3, 8, 13, 18, 23, 28, 33, 38, 43, and 48.
- We can observe that the numbers in the set increase by 5 each time.
Checking for prime numbers:
- To check if a number is prime, we need to divide it by all the numbers less than it and check if it has any divisors other than 1 and itself.
- Let's check if each number in the set is prime or not:
- 3: Not prime (divisible by 1 and 3)
- 8: Not prime (divisible by 1, 2, 4, and 8)
- 13: Prime (not divisible by any number other than 1 and 13)
- 18: Not prime (divisible by 1, 2, 3, 6, 9, and 18)
- 23: Prime (not divisible by any number other than 1 and 23)
- 28: Not prime (divisible by 1, 2, 4, 7, 14, and 28)
- 33: Not prime (divisible by 1, 3, 11, and 33)
- 38: Not prime (divisible by 1, 2, 19, and 38)
- 43: Prime (not divisible by any number other than 1 and 43)
- 48: Not prime (divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48)
Counting the odd numbers:
- We need to count the odd numbers in the set.
- Odd numbers are numbers that are not divisible by 2.
- From the numbers in the set, the odd numbers are: 3, 13, 23, and 43.
- Therefore, the number of odd numbers in the set S is 4
- The set S consists of positive integers less than 50.
- Each number in the set, when divided by five, gives a remainder of three.
- The numbers in the set are not prime.
To find:
- The number of odd numbers in the set S.
Solution:
To solve this problem, we need to consider the given conditions and find the numbers that satisfy them.
Condition 1: Each number in the set, when divided by five, gives a remainder of three.
- This means that the numbers in the set can be represented as 5k + 3, where k is a positive integer.
- We can generate the numbers in the set by starting with 3 and adding multiples of 5 to it.
Condition 2: The numbers in the set are not prime.
- A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
- We need to find the numbers in the set that are not prime.
Generating the numbers in the set:
- Starting with 3, we can add multiples of 5 to it to generate the numbers in the set.
- The first few numbers in the set are: 3, 8, 13, 18, 23, 28, 33, 38, 43, and 48.
- We can observe that the numbers in the set increase by 5 each time.
Checking for prime numbers:
- To check if a number is prime, we need to divide it by all the numbers less than it and check if it has any divisors other than 1 and itself.
- Let's check if each number in the set is prime or not:
- 3: Not prime (divisible by 1 and 3)
- 8: Not prime (divisible by 1, 2, 4, and 8)
- 13: Prime (not divisible by any number other than 1 and 13)
- 18: Not prime (divisible by 1, 2, 3, 6, 9, and 18)
- 23: Prime (not divisible by any number other than 1 and 23)
- 28: Not prime (divisible by 1, 2, 4, 7, 14, and 28)
- 33: Not prime (divisible by 1, 3, 11, and 33)
- 38: Not prime (divisible by 1, 2, 19, and 38)
- 43: Prime (not divisible by any number other than 1 and 43)
- 48: Not prime (divisible by 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48)
Counting the odd numbers:
- We need to count the odd numbers in the set.
- Odd numbers are numbers that are not divisible by 2.
- From the numbers in the set, the odd numbers are: 3, 13, 23, and 43.
- Therefore, the number of odd numbers in the set S is 4
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S is set of positive integers less than 50 such that each number in the set when divided by five gives remainder three and is not a prime. How many odd numbers are there in S?Correct answer is '1'. Can you explain this answer?
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S is set of positive integers less than 50 such that each number in the set when divided by five gives remainder three and is not a prime. How many odd numbers are there in S?Correct answer is '1'. 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 S is set of positive integers less than 50 such that each number in the set when divided by five gives remainder three and is not a prime. How many odd numbers are there in S?Correct answer is '1'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for S is set of positive integers less than 50 such that each number in the set when divided by five gives remainder three and is not a prime. How many odd numbers are there in S?Correct answer is '1'. Can you explain this answer?.
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