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

Expert's post

00:00

Question Stats:

93% (00:35) correct
6% (00:32) wrong based on 60 sessions

\(f(x) = m\) 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.

Re: f(x) = m where m is the number of distinct prime factors of [#permalink]
02 Aug 2018, 15:45

1

This post received KUDOS

Expert's post

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]
12 Aug 2018, 07:01

Expert's post

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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