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

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GMAT Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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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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Question Stats:

80% (00:35) correct 20% (00:17) wrong based on 15 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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1 KUDOS received
GRE Instructor
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Joined: 10 Apr 2015
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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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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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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4722
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1630 [0], given: 390

CAT Tests
Re: f(x) = m where m is the number of distinct prime factors of [#permalink] New post 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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