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

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 3043 [0], given: 394

f(x) = m where m is the number of distinct prime factors of [#permalink]  30 Jul 2018, 10:32
Expert's post
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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.
[Reveal] Spoiler: OA

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Sandy
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GRE Instructor
Joined: 10 Apr 2015
Posts: 3917
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Kudos [?]: 4788 [1] , given: 70

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

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 176

Kudos [?]: 3043 [0], given: 394

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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Sandy
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Re: f(x) = m where m is the number of distinct prime factors of   [#permalink] 12 Aug 2018, 07:01
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