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f(x) = m where m is the number of distinct prime factors of
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30 Jul 2018, 10:32
30 Jul 2018, 10:32
Expert Reply
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Question Stats:
94% (00:38) correct
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\(f(x) = m\) where m is the number of distinct prime factors of x.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(f(30)\) |
\(f(64)\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: f(x) = m where m is the number of distinct prime factors of
[#permalink]
02 Aug 2018, 15:45
02 Aug 2018, 15:45
1
sandy wrote:
\(f(x) = m\) where m is the number of distinct prime factors of x.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(f(30)\) |
\(f(64)\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
The key word here is DISTINCT.
Given:
Quantity A: number of DISTINCT prime factors of 30
Quantity B: number of DISTINCT prime factors of 64
This calls for some prime factorization.
30 = (2)(3)(5). So, 30 has 3 distinct prime factors (2, 3 and 5)
64 = (2)(2)(2)(2)(2)(2). So, 64 has 1 distinct prime factor (2)
So, we get:
Quantity A: 3
Quantity B:1
Answer: A
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Re: f(x) = m where m is the number of distinct prime factors of
[#permalink]
12 Aug 2018, 07:01
12 Aug 2018, 07:01
Expert Reply
Explanation
The problem indicates that f(x) = m where m is the number of distinct (or different) prime factors of x. For example, if x = 6, 6 has two distinct prime factors: 2 and 3. Therefore, the corresponding answer (m value) would be 2.
For Quantity A, f(30): 30 has 3 distinct prime factors (2, 3, and 5), so f(30) = 3.
For Quantity B, f(64): 64 is made of the prime factors 2, 2, 2, 2, 2, and 2). This is only one distinct prime factor, so f(64) = 1.
Quantity A is greater.
The problem indicates that f(x) = m where m is the number of distinct (or different) prime factors of x. For example, if x = 6, 6 has two distinct prime factors: 2 and 3. Therefore, the corresponding answer (m value) would be 2.
For Quantity A, f(30): 30 has 3 distinct prime factors (2, 3, and 5), so f(30) = 3.
For Quantity B, f(64): 64 is made of the prime factors 2, 2, 2, 2, 2, and 2). This is only one distinct prime factor, so f(64) = 1.
Quantity A is greater.
