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For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?
- a)None
- b)One
- c)Two
- d)Three
- e)Four
Correct answer is option 'A'. Can you explain this answer?
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For any integer m greater than 1, $m denotes the product of all the in...
Understanding the Problem
To find the number of prime numbers between \(7 + 2\) and \(7 + 10\), we first need to calculate these values.
- \(7 + 2 = 9\)
- \(7 + 10 = 17\)
So, we are looking for prime numbers between 9 and 17, inclusive.
Identifying the Range
The numbers we need to examine are:
- 9, 10, 11, 12, 13, 14, 15, 16, 17
Checking for Primality
Now, we will determine which of these numbers are prime:
- 9: Not prime (divisible by 3)
- 10: Not prime (divisible by 2 and 5)
- 11: Prime
- 12: Not prime (divisible by 2, 3, 4, 6)
- 13: Prime
- 14: Not prime (divisible by 2 and 7)
- 15: Not prime (divisible by 3 and 5)
- 16: Not prime (divisible by 2, 4, 8)
- 17: Prime
Counting the Primes
From our checks:
- The prime numbers found are 11, 13, and 17.
Conclusion
Thus, the prime numbers between 9 and 17 are three in total:
- 11
- 13
- 17
However, if the correct answer is indicated as option 'A' (None), it may imply further context or specific criteria not disclosed in the question. Based on the numbers analyzed, there are indeed three primes. However, if the task misinterprets or limits the definition of primes in some way, it could lead to that conclusion.
In standard counting, there are three prime numbers in this range.
To find the number of prime numbers between \(7 + 2\) and \(7 + 10\), we first need to calculate these values.
- \(7 + 2 = 9\)
- \(7 + 10 = 17\)
So, we are looking for prime numbers between 9 and 17, inclusive.
Identifying the Range
The numbers we need to examine are:
- 9, 10, 11, 12, 13, 14, 15, 16, 17
Checking for Primality
Now, we will determine which of these numbers are prime:
- 9: Not prime (divisible by 3)
- 10: Not prime (divisible by 2 and 5)
- 11: Prime
- 12: Not prime (divisible by 2, 3, 4, 6)
- 13: Prime
- 14: Not prime (divisible by 2 and 7)
- 15: Not prime (divisible by 3 and 5)
- 16: Not prime (divisible by 2, 4, 8)
- 17: Prime
Counting the Primes
From our checks:
- The prime numbers found are 11, 13, and 17.
Conclusion
Thus, the prime numbers between 9 and 17 are three in total:
- 11
- 13
- 17
However, if the correct answer is indicated as option 'A' (None), it may imply further context or specific criteria not disclosed in the question. Based on the numbers analyzed, there are indeed three primes. However, if the task misinterprets or limits the definition of primes in some way, it could lead to that conclusion.
In standard counting, there are three prime numbers in this range.
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For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?a)Noneb)Onec)Twod)Threee)FourCorrect answer is option 'A'. Can you explain this answer?
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For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?a)Noneb)Onec)Twod)Threee)FourCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?a)Noneb)Onec)Twod)Threee)FourCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?a)Noneb)Onec)Twod)Threee)FourCorrect answer is option 'A'. Can you explain this answer?.
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