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f(x) = m where m is the number of distinct prime factors of

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sandy
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f(x) = m where m is the number of distinct prime factors of [#permalink] New post   30 Jul 2018, 10:32
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\(f(x) = m\) where m is the number of distinct prime factors of x.

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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A
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Re: f(x) = m where m is the number of distinct prime factors of [#permalink] New post   02 Aug 2018, 15:45
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sandy wrote:
\(f(x) = m\) where m is the number of distinct prime factors of x.

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] New post   12 Aug 2018, 07:01
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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.
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f(x) = m where m is the number of distinct prime factors of [#permalink] New post   04 Sep 2021, 08:25
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Functions and Factors Problem

\(f(x) = m\) where m is the number of distinct prime factors of x

Quantity A: \(f(30)\)

\(f(30)\) = Number of distinct prime factors of 30
=> \(f(30)\) = 3 ( Prime factors are 2,3, 5)

Quantity B: \(f(64)\)

\(f(64)\) = Number of distinct prime factors of 64
=> \(f(64)\) = 1 ( Prime factor is 2)

Clearly, Quantity A (3) > Quantity A (1)

So, Answer will be A
Hope it helps!

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Re: f(x) = m where m is the number of distinct prime factors of [#permalink] New post   04 Sep 2021, 21:20
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A is greater because 30 has more distinct factors than 64.
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Re: f(x) = m where m is the number of distinct prime factors of [#permalink]
04 Sep 2021, 21:20
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