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How many different factors does the integer n have?
1) n = a4b3, where a and b are different positive prime numbers. ?
2) The only positive prime numbers that are factors of n are 5 and 7. ?
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
How many different factors does the integer n have?1) n = a4b3, where ...
1> n=a^4 . b^3
where a and b are different primes. So the factors of n will be
1, a, a^2,a^3, a^4 , b, b^2, b^3 and n itself
Thus sufficient
2> only positive primes tht are factors are 5 and 7. It doesnt mention about non prime factors. INSUFFICIENT
Most Upvoted Answer
How many different factors does the integer n have?1) n = a4b3, where ...
Statement 1: n = a^4b^3, where a and b are different positive prime numbers.
To determine the number of factors of n, we need to first express n in terms of its prime factors and their exponents.
In this case, we are given that n can be expressed as a^4b^3, where a and b are different positive prime numbers.
The number of factors of n can be calculated using the formula (e1 + 1)(e2 + 1)(e3 + 1)..., where e1, e2, e3, ... are the exponents of the prime factors in the prime factorization of n.
In this case, the exponents of the prime factors a and b are 4 and 3 respectively.
The number of factors of n would be (4 + 1)(3 + 1) = 5 * 4 = 20.
Therefore, statement 1 alone is sufficient to answer the question.
Statement 2: The only positive prime numbers that are factors of n are 5 and 7.
This statement does not provide any information about the exponents of the prime factors in the prime factorization of n. We cannot determine the number of factors of n based on this statement alone.
Therefore, statement 2 alone is not sufficient to answer the question.
Combined:
Combining the information from both statements, we know that n can be expressed as a^4b^3, where a and b are different positive prime numbers, and the only positive prime numbers that are factors of n are 5 and 7.
From statement 1, we know that the exponents of the prime factors a and b are 4 and 3 respectively.
Using the formula (e1 + 1)(e2 + 1)(e3 + 1)..., where e1, e2, e3, ... are the exponents of the prime factors in the prime factorization of n, we can calculate the number of factors of n.
In this case, the number of factors of n would be (4 + 1)(3 + 1) = 5 * 4 = 20.
Therefore, combining both statements, we can answer the question.
Hence, the correct answer is option A.
To determine the number of factors of n, we need to first express n in terms of its prime factors and their exponents.
In this case, we are given that n can be expressed as a^4b^3, where a and b are different positive prime numbers.
The number of factors of n can be calculated using the formula (e1 + 1)(e2 + 1)(e3 + 1)..., where e1, e2, e3, ... are the exponents of the prime factors in the prime factorization of n.
In this case, the exponents of the prime factors a and b are 4 and 3 respectively.
The number of factors of n would be (4 + 1)(3 + 1) = 5 * 4 = 20.
Therefore, statement 1 alone is sufficient to answer the question.
Statement 2: The only positive prime numbers that are factors of n are 5 and 7.
This statement does not provide any information about the exponents of the prime factors in the prime factorization of n. We cannot determine the number of factors of n based on this statement alone.
Therefore, statement 2 alone is not sufficient to answer the question.
Combined:
Combining the information from both statements, we know that n can be expressed as a^4b^3, where a and b are different positive prime numbers, and the only positive prime numbers that are factors of n are 5 and 7.
From statement 1, we know that the exponents of the prime factors a and b are 4 and 3 respectively.
Using the formula (e1 + 1)(e2 + 1)(e3 + 1)..., where e1, e2, e3, ... are the exponents of the prime factors in the prime factorization of n, we can calculate the number of factors of n.
In this case, the number of factors of n would be (4 + 1)(3 + 1) = 5 * 4 = 20.
Therefore, combining both statements, we can answer the question.
Hence, the correct answer is option A.
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How many different factors does the integer n have?1) n = a4b3, where a and b are different positive prime numbers. ?2) The only positive prime numbers that are factors of n are 5 and 7. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?
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How many different factors does the integer n have?1) n = a4b3, where a and b are different positive prime numbers. ?2) The only positive prime numbers that are factors of n are 5 and 7. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. 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 different factors does the integer n have?1) n = a4b3, where a and b are different positive prime numbers. ?2) The only positive prime numbers that are factors of n are 5 and 7. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. 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 different factors does the integer n have?1) n = a4b3, where a and b are different positive prime numbers. ?2) The only positive prime numbers that are factors of n are 5 and 7. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?.
How many different factors does the integer n have?1) n = a4b3, where a and b are different positive prime numbers. ?2) The only positive prime numbers that are factors of n are 5 and 7. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. 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 different factors does the integer n have?1) n = a4b3, where a and b are different positive prime numbers. ?2) The only positive prime numbers that are factors of n are 5 and 7. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. 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 different factors does the integer n have?1) n = a4b3, where a and b are different positive prime numbers. ?2) The only positive prime numbers that are factors of n are 5 and 7. ?a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'A'. Can you explain this answer?.
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