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How many odd positive integers divide the positive integer n completely?
(1) 16 is the highest power of 2 that divides n
(2) n has a total of 68 factors and 3 prime factors.
(1) 16 is the highest power of 2 that divides n
(2) n has a total of 68 factors and 3 prime factors.
- 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 to answer the question asked. - 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 specific to theproblem are needed.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
How many odd positive integers divide the positive integer n completel...
Step 1 & 2: Understand Question and Draw Inference
- n is an integer > 0
- We can write: n = P1a * P2b * P3c ….where P1 , P2 , P3 ..etc. are prime numbers and a, b, c are positive integers
To Find: Number of odd positive integers divide n?
- These are the factors that do not have 2 as their prime factor.
- So, the factors which can be written in the form P1a * P2b ….where P1, P2 ... etc. are greater than 2. The number of such factors = (a+1) (b+1)….
- So, we need to find the powers of all odd prime factors of n.
Step 3 : Analyze Statement 1 independent
- 16 is the highest power of 2 that divides n
Statement-1 tells us that the prime number 2 comes 16 times in n.
So, for n = P1a * P2b * P3c ….we know that P1 = 2 and a = 16.
However it does not tell us anything about the powers of odd prime factors of n.
Hence statement-1 is insufficient to answer the question.
So, for n = P1a * P2b * P3c ….we know that P1 = 2 and a = 16.
However it does not tell us anything about the powers of odd prime factors of n.
Hence statement-1 is insufficient to answer the question.
Step 4 : Analyze Statement 2 independent
2. n has a total of 68 factors and 3 prime factors.
Statement-2 tells us that n has a total of 68 factors and 3 prime factors.
So, for n = P1a * P2b * P3c we know that (a+1) (b+1) (c+1) = 68.
Now, let’s find the number of ways in which 68 can be expressed as a product of 3 integers > 1.
68 = 2 * 2 * 17.
So, (a, b, c) = (1, 1, 16). However, we do not know:
If 2 is a prime factor of n AND
Even if 2 is a prime factor of n, the power of 2 in n.
So, we cannot in any way find out the number of odd positive integers that divide n.
Hence statement-2 is insufficient to answer the question.
Statement-2 tells us that n has a total of 68 factors and 3 prime factors.
So, for n = P1a * P2b * P3c we know that (a+1) (b+1) (c+1) = 68.
Now, let’s find the number of ways in which 68 can be expressed as a product of 3 integers > 1.
68 = 2 * 2 * 17.
So, (a, b, c) = (1, 1, 16). However, we do not know:
If 2 is a prime factor of n AND
Even if 2 is a prime factor of n, the power of 2 in n.
So, we cannot in any way find out the number of odd positive integers that divide n.
Hence statement-2 is insufficient to answer the question.
Step 5: Analyze Both Statements Together (if needed)
Since we do not have a unique answer from either step 3 or 4, we need to
analyze both the steps together.
Step-3 tells us that P1 = 2 and a = 16.
Step- 4 tells us that n = P1a * P2b * P3c and (a+1) (b+1) (c+1) = 68.
Combining both the steps, we can say that (b+1) (c+1) = 4 i.e. there are a total
of 4 odd factors of n.
Hence statements 1 and 2 together are sufficient to answer the question.
analyze both the steps together.
Step-3 tells us that P1 = 2 and a = 16.
Step- 4 tells us that n = P1a * P2b * P3c and (a+1) (b+1) (c+1) = 68.
Combining both the steps, we can say that (b+1) (c+1) = 4 i.e. there are a total
of 4 odd factors of n.
Hence statements 1 and 2 together are sufficient to answer the question.
Answer : C
Most Upvoted Answer
How many odd positive integers divide the positive integer n completel...
Step 1 & 2: Understand Question and Draw Inference
- n is an integer > 0
- We can write: n = P1a * P2b * P3c ….where P1 , P2 , P3 ..etc. are prime numbers and a, b, c are positive integers
To Find: Number of odd positive integers divide n?
- These are the factors that do not have 2 as their prime factor.
- So, the factors which can be written in the form P1a * P2b ….where P1, P2 ... etc. are greater than 2. The number of such factors = (a+1) (b+1)….
- So, we need to find the powers of all odd prime factors of n.
Step 3 : Analyze Statement 1 independent
- 16 is the highest power of 2 that divides n
Statement-1 tells us that the prime number 2 comes 16 times in n.
So, for n = P1a * P2b * P3c ….we know that P1 = 2 and a = 16.
However it does not tell us anything about the powers of odd prime factors of n.
Hence statement-1 is insufficient to answer the question.
So, for n = P1a * P2b * P3c ….we know that P1 = 2 and a = 16.
However it does not tell us anything about the powers of odd prime factors of n.
Hence statement-1 is insufficient to answer the question.
Step 4 : Analyze Statement 2 independent
2. n has a total of 68 factors and 3 prime factors.
Statement-2 tells us that n has a total of 68 factors and 3 prime factors.
So, for n = P1a * P2b * P3c we know that (a+1) (b+1) (c+1) = 68.
Now, let’s find the number of ways in which 68 can be expressed as a product of 3 integers > 1.
68 = 2 * 2 * 17.
So, (a, b, c) = (1, 1, 16). However, we do not know:
If 2 is a prime factor of n AND
Even if 2 is a prime factor of n, the power of 2 in n.
So, we cannot in any way find out the number of odd positive integers that divide n.
Hence statement-2 is insufficient to answer the question.
Statement-2 tells us that n has a total of 68 factors and 3 prime factors.
So, for n = P1a * P2b * P3c we know that (a+1) (b+1) (c+1) = 68.
Now, let’s find the number of ways in which 68 can be expressed as a product of 3 integers > 1.
68 = 2 * 2 * 17.
So, (a, b, c) = (1, 1, 16). However, we do not know:
If 2 is a prime factor of n AND
Even if 2 is a prime factor of n, the power of 2 in n.
So, we cannot in any way find out the number of odd positive integers that divide n.
Hence statement-2 is insufficient to answer the question.
Step 5: Analyze Both Statements Together (if needed)
Since we do not have a unique answer from either step 3 or 4, we need to
analyze both the steps together.
Step-3 tells us that P1 = 2 and a = 16.
Step- 4 tells us that n = P1a * P2b * P3c and (a+1) (b+1) (c+1) = 68.
Combining both the steps, we can say that (b+1) (c+1) = 4 i.e. there are a total
of 4 odd factors of n.
Hence statements 1 and 2 together are sufficient to answer the question.
analyze both the steps together.
Step-3 tells us that P1 = 2 and a = 16.
Step- 4 tells us that n = P1a * P2b * P3c and (a+1) (b+1) (c+1) = 68.
Combining both the steps, we can say that (b+1) (c+1) = 4 i.e. there are a total
of 4 odd factors of n.
Hence statements 1 and 2 together are sufficient to answer the question.
Answer : C
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How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?
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How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. 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 How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?.
How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. 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 How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?.
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How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of How many odd positive integers divide the positive integer n completely?(1) 16 is the highest power of 2 that divides n(2) n has a total of 68 factors and 3 prime factors.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 toanswer the question asked, but NEITHER statement ALONEis sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the questionasked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to theproblem are needed.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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