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If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of two different prime numbers.
(2) n and 23 are each divisible by the same number of positive integers.
(2) n and 23 are each divisible by the same number of positive integers.
- 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 'D'. Can you explain this answer?
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If n is an integer, then n is divisible by how many positive integers?...
Statement (1): n is the product of two different prime numbers.
If n is the product of two different prime numbers, then n can be expressed as the product of p and q, where p and q are distinct prime numbers. In this case, n has two distinct prime factors. Since n is an integer, it must also be divisible by 1 and itself. Therefore, n is divisible by at least four positive integers.
Statement (2): n and 23 are each divisible by the same number of positive integers.
This statement tells us that the number of positive divisors of n is the same as the number of positive divisors of 23. Since 23 is a prime number, it has exactly two positive divisors: 1 and 23. If n has the same number of positive divisors as 23, it means that n is also a prime number and has exactly two positive divisors: 1 and itself. Therefore, n is divisible by exactly two positive integers.
From the evaluation of both statements, we can see that each statement alone is sufficient to answer the question. Statement (1) tells us that n is divisible by at least four positive integers, and Statement (2) tells us that n is divisible by exactly two positive integers. Therefore, the answer is (D) EACH statement ALONE is sufficient to answer the question asked.
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If n is an integer, then n is divisible by how many positive integers?...
Statement (1): n is the product of two different prime numbers.
- If n is the product of two different prime numbers, then n can be expressed as p*q, where p and q are distinct prime numbers.
- The number of positive integers by which n is divisible can be determined by finding the number of factors of n.
- The number of factors of n can be calculated by finding the product of the exponents of each prime factor and adding 1 to each exponent, and then multiplying the results.
- For example, if n = p^a * q^b, where p and q are prime numbers and a and b are positive integers, then the number of factors of n is (a+1)*(b+1).
- Therefore, statement (1) alone is sufficient to determine the number of positive integers by which n is divisible.
Statement (2): n and 23 are each divisible by the same number of positive integers.
- This statement does not provide direct information about the factors of n.
- It only states that the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible.
- However, this information is not sufficient to determine the exact number of positive integers by which n is divisible.
- Therefore, statement (2) alone is not sufficient to determine the number of positive integers by which n is divisible.
Combined statements:
- Combining both statements, we know that n is the product of two different prime numbers (statement 1) and the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible (statement 2).
- Since 23 is a prime number, it is only divisible by 1 and itself, so it has 2 positive divisors.
- Therefore, the number of positive integers by which n is divisible is also 2, as stated in statement 2.
- Hence, both statements together are sufficient to determine that n is divisible by 2 positive integers.
- Therefore, the correct answer is option D.
- If n is the product of two different prime numbers, then n can be expressed as p*q, where p and q are distinct prime numbers.
- The number of positive integers by which n is divisible can be determined by finding the number of factors of n.
- The number of factors of n can be calculated by finding the product of the exponents of each prime factor and adding 1 to each exponent, and then multiplying the results.
- For example, if n = p^a * q^b, where p and q are prime numbers and a and b are positive integers, then the number of factors of n is (a+1)*(b+1).
- Therefore, statement (1) alone is sufficient to determine the number of positive integers by which n is divisible.
Statement (2): n and 23 are each divisible by the same number of positive integers.
- This statement does not provide direct information about the factors of n.
- It only states that the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible.
- However, this information is not sufficient to determine the exact number of positive integers by which n is divisible.
- Therefore, statement (2) alone is not sufficient to determine the number of positive integers by which n is divisible.
Combined statements:
- Combining both statements, we know that n is the product of two different prime numbers (statement 1) and the number of positive integers by which n is divisible is the same as the number of positive integers by which 23 is divisible (statement 2).
- Since 23 is a prime number, it is only divisible by 1 and itself, so it has 2 positive divisors.
- Therefore, the number of positive integers by which n is divisible is also 2, as stated in statement 2.
- Hence, both statements together are sufficient to determine that n is divisible by 2 positive integers.
- Therefore, the correct answer is option D.
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If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer?
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If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. 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 an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. 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 an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer?.
If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. 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 an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. 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 an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer?.
Solutions for If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer?, a detailed solution for If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer? has been provided alongside types of If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If n is an integer, then n is divisible by how many positive integers?(1) n is the product of two different prime numbers.(2) n and 23 are each divisible by the same number of positive integers.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 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
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