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If n is a positive integer, which of the following statements are correct?
- All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3
- All numbers of the form 4n + 1 and 4n + 3 are prime numbers
- All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1
- a)1st statement only
- b)2nd statement only
- c)3rd statement only
- d)1st and 2nd statements
- e)1st and 3rd statements
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
If n is a positive integer, which of the following statements are corr...
Step 1: Question statement and Inferences
Let us list the prime numbers less than 50:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 . . .
Step 2: Finding required values
Let’s now evaluate the two forms given and then evaluate which of these is able to describe the list above.
Option A: The form 4n + 1 and 4n + 3
As we see, all the prime numbers greater than 3 can be represented in the form 4n+1 or 4n+3.
Therefore, Statement I is correct.
However, we also see in the table that not every number of the form 4n + 1 and 4n + 3 is a prime number.
Therefore, Statement II is not correct.
Option B: The form 6n – 1 and 6n + 1
As we see, all the prime numbers greater than 3 can be represented in the form 6n+1 or 6n-1.
Therefore, Statement III is correct.
Step 3: Calculating the final answer
Looking at the answer choices, we see that Option E is correct.
Most Upvoted Answer
If n is a positive integer, which of the following statements are corr...
Step 1: Question statement and Inferences
Let us list the prime numbers less than 50:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 . . .
Step 2: Finding required values
Let’s now evaluate the two forms given and then evaluate which of these is able to describe the list above.
Option A: The form 4n + 1 and 4n + 3
As we see, all the prime numbers greater than 3 can be represented in the form 4n+1 or 4n+3.
Therefore, Statement I is correct.
However, we also see in the table that not every number of the form 4n + 1 and 4n + 3 is a prime number.
Therefore, Statement II is not correct.
Option B: The form 6n – 1 and 6n + 1
As we see, all the prime numbers greater than 3 can be represented in the form 6n+1 or 6n-1.
Therefore, Statement III is correct.
Step 3: Calculating the final answer
Looking at the answer choices, we see that Option E is correct.
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If n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. Can you explain this answer?
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If n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. 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 n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. 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 n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. Can you explain this answer?.
If n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. 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 n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. 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 n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. Can you explain this answer?.
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ample number of questions to practice If n is a positive integer, which of the following statements are correct? All the prime numbers greater than 3 can be represented in the form 4n +1 or 4n + 3 All numbers of the form 4n + 1 and 4n + 3 are prime numbers All the prime numbers greater than 3 can be represented in the form 6n – 1 or 6n + 1a)1st statement onlyb)2nd statement onlyc)3rd statement onlyd)1st and 2nd statementse)1st and 3rd statementsCorrect answer is option 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.
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