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The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?
(1) 32 is a factor of k
(2) 72 is NOT a factor of k
(2) 72 is NOT a factor of k
- 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?
Most Upvoted Answer
The positive integer k has exactly two positive prime factors, 3 and 7...
Statement 1: 32 is a factor of k
Statement 2: 72 is NOT a factor of k
To find the value of k, we need to determine the powers of the prime factors 3 and 7 in k's prime factorization. Let's analyze each statement separately:
Statement 1: 32 is a factor of k
If 32 is a factor of k, it means that k must have at least one factor of 2 to the power of 5. Since the only prime factors of k are 3 and 7, this implies that k = 2^5 * 3^a * 7^b, where a and b are positive integers.
Statement 2: 72 is NOT a factor of k
If 72 is not a factor of k, it means that k cannot have a factor of 2^3 * 3^2. This implies that the power of 2 in k's prime factorization must be less than 3, and the power of 3 must be less than 2.
Using both statements together:
From statement 1, we know that k = 2^5 * 3^a * 7^b. From statement 2, we know that the power of 2 is less than 3 and the power of 3 is less than 2. Since the only prime factors of k are 3 and 7, this means that the power of 2 must be 0 or 1, and the power of 3 must be 0 or 1.
Combining all the information, we know that k has the form k = 2^x * 3^y * 7^z, where x is 0 or 1, y is 0 or 1, and z is a positive integer.
Therefore, both statements together are sufficient to determine the possible values of k.
Statement 2: 72 is NOT a factor of k
To find the value of k, we need to determine the powers of the prime factors 3 and 7 in k's prime factorization. Let's analyze each statement separately:
Statement 1: 32 is a factor of k
If 32 is a factor of k, it means that k must have at least one factor of 2 to the power of 5. Since the only prime factors of k are 3 and 7, this implies that k = 2^5 * 3^a * 7^b, where a and b are positive integers.
Statement 2: 72 is NOT a factor of k
If 72 is not a factor of k, it means that k cannot have a factor of 2^3 * 3^2. This implies that the power of 2 in k's prime factorization must be less than 3, and the power of 3 must be less than 2.
Using both statements together:
From statement 1, we know that k = 2^5 * 3^a * 7^b. From statement 2, we know that the power of 2 is less than 3 and the power of 3 is less than 2. Since the only prime factors of k are 3 and 7, this means that the power of 2 must be 0 or 1, and the power of 3 must be 0 or 1.
Combining all the information, we know that k has the form k = 2^x * 3^y * 7^z, where x is 0 or 1, y is 0 or 1, and z is a positive integer.
Therefore, both statements together are sufficient to determine the possible values of k.
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Community Answer
The positive integer k has exactly two positive prime factors, 3 and 7...
To find the value of k, we need to determine its prime factorization based on the given information. We know that k has exactly two prime factors: 3 and 7. Therefore, we can express k as:
k = 3a * 7b
where a and b are positive integers representing the exponents.
Now, let's consider the number of positive factors of k. The total number of factors of a number can be found by multiplying the exponents of each prime factor by one more than each exponent, and then multiplying those results together.
In this case, the number of factors of k is given as 6. So we have:
(a + 1) * (b + 1) = 6
To determine the value of k, we need to find the values of a and b.
Now let's analyze the given statements:
Statement (1): 32 is a factor of k.
This implies that k must be divisible by 32, which is equal to 25. Since k only has prime factors of 3 and 7, it must also have 2 as a prime factor. Therefore, a must be at least 5 in order for k to be divisible by 32. With a = 5, we have:
This implies that k must be divisible by 32, which is equal to 25. Since k only has prime factors of 3 and 7, it must also have 2 as a prime factor. Therefore, a must be at least 5 in order for k to be divisible by 32. With a = 5, we have:
(5 + 1) * (b + 1) = 6
6 * (b + 1) = 6
b + 1 = 1
b = 0
6 * (b + 1) = 6
b + 1 = 1
b = 0
So, k = 35 * 70 = 35 = 243.
Statement (1) alone is sufficient to determine the value of k.
Statement (2): 72 is NOT a factor of k.
This statement doesn't provide direct information about the value of k. It only tells us that k is not divisible by 72. However, we already have sufficient information from statement (1) to determine the value of k.
This statement doesn't provide direct information about the value of k. It only tells us that k is not divisible by 72. However, we already have sufficient information from statement (1) to determine the value of k.
Therefore, statement (2) alone is not sufficient to determine the value of k.
Since statement (1) alone is sufficient to determine k, the correct answer is:
D: EACH statement ALONE is sufficient to answer the question asked.
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The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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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The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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?.
The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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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The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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 The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k, what is the value of K?(1) 32 is a factor of k(2) 72 is NOT a factor of ka)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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