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If k is a positive integer, is k a prime number??
1) k is the sum of three consecutive prime numbers
2) k has only 2 factors
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If k is a positive integer, is k a prime number??1) k is the sum of th...
**Statement 1: k is the sum of three consecutive prime numbers**
To determine if k is a prime number, we need to analyze the sum of three consecutive prime numbers.
Let's consider an example: If k = 5 + 7 + 11 = 23, then k is a prime number.
However, if k = 2 + 3 + 5 = 10, then k is not a prime number.
Therefore, statement 1 alone is not sufficient to determine if k is a prime number.
**Statement 2: k has only 2 factors**
If k has only 2 factors, then k is a prime number. This statement alone is sufficient to determine if k is a prime number.
For example, if k = 7, it has only 2 factors (1 and 7), so k is a prime number.
If k = 9, it has more than 2 factors (1, 3, and 9), so k is not a prime number.
Therefore, statement 2 alone is sufficient to determine if k is a prime number.
**Combining the statements**
From statement 1, we cannot determine if k is a prime number.
From statement 2, we can determine if k is a prime number.
Since the two statements provide contradictory information, we need both statements to answer the question.
**Conclusion**
Both statements are required to determine if k is a prime number. Therefore, the correct answer is option B.
To determine if k is a prime number, we need to analyze the sum of three consecutive prime numbers.
Let's consider an example: If k = 5 + 7 + 11 = 23, then k is a prime number.
However, if k = 2 + 3 + 5 = 10, then k is not a prime number.
Therefore, statement 1 alone is not sufficient to determine if k is a prime number.
**Statement 2: k has only 2 factors**
If k has only 2 factors, then k is a prime number. This statement alone is sufficient to determine if k is a prime number.
For example, if k = 7, it has only 2 factors (1 and 7), so k is a prime number.
If k = 9, it has more than 2 factors (1, 3, and 9), so k is not a prime number.
Therefore, statement 2 alone is sufficient to determine if k is a prime number.
**Combining the statements**
From statement 1, we cannot determine if k is a prime number.
From statement 2, we can determine if k is a prime number.
Since the two statements provide contradictory information, we need both statements to answer the question.
**Conclusion**
Both statements are required to determine if k is a prime number. Therefore, the correct answer is option B.
Community Answer
If k is a positive integer, is k a prime number??1) k is the sum of th...
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If k is a positive integer, is k a prime number??1) k is the sum of three consecutive prime numbers2) k has only 2 factorsa)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer?
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If k is a positive integer, is k a prime number??1) k is the sum of three consecutive prime numbers2) k has only 2 factorsa)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. 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 If k is a positive integer, is k a prime number??1) k is the sum of three consecutive prime numbers2) k has only 2 factorsa)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If k is a positive integer, is k a prime number??1) k is the sum of three consecutive prime numbers2) k has only 2 factorsa)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer?.
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