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If k is an integer greater than 1, is k equal to 2r for some positive integer r?
(1) k is divisible by 26.
(2) k is not divisible by any odd integer greater than 1.
(2) k is not divisible by any odd integer greater than 1.
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
- c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
- d)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If k is an integer greater than 1, is k equal to 2r for some positive ...
Statement (1): k is divisible by 26.
If k is divisible by 26, it means that k is a multiple of 26. However, being divisible by 26 does not guarantee that k is equal to 2r for some positive integer r. For example, if k = 26, it is divisible by 26, but it cannot be expressed as 2r since r would have to be 13, which is not a positive integer. Therefore, statement (1) alone is not sufficient to answer the question.
If k is divisible by 26, it means that k is a multiple of 26. However, being divisible by 26 does not guarantee that k is equal to 2r for some positive integer r. For example, if k = 26, it is divisible by 26, but it cannot be expressed as 2r since r would have to be 13, which is not a positive integer. Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2): k is not divisible by any odd integer greater than 1.
This statement tells us that k is not divisible by any odd prime number greater than 1. In other words, k does not have any odd prime factors. However, this statement also does not provide enough information to determine if k can be expressed as 2r for some positive integer r. For example, if k = 15, it is not divisible by any odd integer greater than 1, but it cannot be expressed as 2r since it does not have a factor of 2. Therefore, statement (2) alone is not sufficient to answer the question.
This statement tells us that k is not divisible by any odd prime number greater than 1. In other words, k does not have any odd prime factors. However, this statement also does not provide enough information to determine if k can be expressed as 2r for some positive integer r. For example, if k = 15, it is not divisible by any odd integer greater than 1, but it cannot be expressed as 2r since it does not have a factor of 2. Therefore, statement (2) alone is not sufficient to answer the question.
By evaluating both statements together, we can see that if k is divisible by 26 (statement 1) and does not have any odd prime factors (statement 2), then k must be divisible by 2 and 13. This implies that k is equal to 2 multiplied by a positive integer (r) since it has a factor of 2. Therefore, statement (2) alone is sufficient to answer the question.
Hence, the answer is (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Most Upvoted Answer
If k is an integer greater than 1, is k equal to 2r for some positive ...
Statement (1): k is divisible by 26.
If k is divisible by 26, it means that k is a multiple of 26. However, being divisible by 26 does not guarantee that k is equal to 2r for some positive integer r. For example, if k = 26, it is divisible by 26, but it cannot be expressed as 2r since r would have to be 13, which is not a positive integer. Therefore, statement (1) alone is not sufficient to answer the question.
If k is divisible by 26, it means that k is a multiple of 26. However, being divisible by 26 does not guarantee that k is equal to 2r for some positive integer r. For example, if k = 26, it is divisible by 26, but it cannot be expressed as 2r since r would have to be 13, which is not a positive integer. Therefore, statement (1) alone is not sufficient to answer the question.
Statement (2): k is not divisible by any odd integer greater than 1.
This statement tells us that k is not divisible by any odd prime number greater than 1. In other words, k does not have any odd prime factors. However, this statement also does not provide enough information to determine if k can be expressed as 2r for some positive integer r. For example, if k = 15, it is not divisible by any odd integer greater than 1, but it cannot be expressed as 2r since it does not have a factor of 2. Therefore, statement (2) alone is not sufficient to answer the question.
This statement tells us that k is not divisible by any odd prime number greater than 1. In other words, k does not have any odd prime factors. However, this statement also does not provide enough information to determine if k can be expressed as 2r for some positive integer r. For example, if k = 15, it is not divisible by any odd integer greater than 1, but it cannot be expressed as 2r since it does not have a factor of 2. Therefore, statement (2) alone is not sufficient to answer the question.
By evaluating both statements together, we can see that if k is divisible by 26 (statement 1) and does not have any odd prime factors (statement 2), then k must be divisible by 2 and 13. This implies that k is equal to 2 multiplied by a positive integer (r) since it has a factor of 2. Therefore, statement (2) alone is sufficient to answer the question.
Hence, the answer is (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
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Community Answer
If k is an integer greater than 1, is k equal to 2r for some positive ...
Understanding the Question
The question asks whether an integer k (greater than 1) can be expressed as 2r for some positive integer r. This means k should be even.
Analyzing Statement (1)
- Divisibility by 26:
- If k is divisible by 26, we can express k as k = 26m for some integer m.
- Since 26 is even (26 = 2 * 13), k is also even.
- Conclusion:
- Statement (1) indicates that k is even, which means k can be expressed as 2r (with r = 13m).
- Thus, Statement (1) alone is sufficient.
Analyzing Statement (2)
- Not Divisible by Odd Integers:
- If k is not divisible by any odd integer greater than 1, it can only be divisible by 2 (and possibly other even integers).
- This means k can only be composed of the prime factor 2, implying k must be a power of 2 (k = 2^n, where n > 0).
- Conclusion:
- Since powers of 2 are always even, k can be expressed as 2r (with r = 2^(n-1)).
- Therefore, Statement (2) alone is also sufficient.
Final Conclusion
- Both statements individually confirm that k is even and can be expressed as 2r. Hence, the correct answer is option 'B' as each statement alone is sufficient to determine the answer.
The question asks whether an integer k (greater than 1) can be expressed as 2r for some positive integer r. This means k should be even.
Analyzing Statement (1)
- Divisibility by 26:
- If k is divisible by 26, we can express k as k = 26m for some integer m.
- Since 26 is even (26 = 2 * 13), k is also even.
- Conclusion:
- Statement (1) indicates that k is even, which means k can be expressed as 2r (with r = 13m).
- Thus, Statement (1) alone is sufficient.
Analyzing Statement (2)
- Not Divisible by Odd Integers:
- If k is not divisible by any odd integer greater than 1, it can only be divisible by 2 (and possibly other even integers).
- This means k can only be composed of the prime factor 2, implying k must be a power of 2 (k = 2^n, where n > 0).
- Conclusion:
- Since powers of 2 are always even, k can be expressed as 2r (with r = 2^(n-1)).
- Therefore, Statement (2) alone is also sufficient.
Final Conclusion
- Both statements individually confirm that k is even and can be expressed as 2r. Hence, the correct answer is option 'B' as each statement alone is sufficient to determine the answer.
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If k is an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer?
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If k is an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect 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 an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect 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 an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer?.
If k is an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect 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 an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect 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 an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer?.
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If k is an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If k is an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If k is an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If k is an integer greater than 1, is k equal to 2r for some positive integer r?(1) k is divisible by 26.(2) k is not divisible by any odd integer greater than 1.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
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