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# If a positive integer x has 5 prime factors, how many prime factors

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Current Student
Joined: 12 Aug 2015
Posts: 2621
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If a positive integer x has 5 prime factors, how many prime factors  [#permalink]

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22 Nov 2016, 03:41
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Difficulty:

15% (low)

Question Stats:

81% (00:55) correct 19% (00:54) wrong based on 114 sessions

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If a positive integer x has 5 prime factors, how many prime factors does 3x have?

A) 3
B) 5
C) 8
D) 15
E) cannot be determined

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: If a positive integer x has 5 prime factors, how many prime factors  [#permalink]

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22 Nov 2016, 03:57
stonecold wrote:
If a positive integer x has 5 prime factors, how many prime factors does 3x have?

A) 3
B) 5
C) 8
D) 15
E) cannot be determined

If 3 is a factor of x, then 3x will have as many prime factors as x but if 3 is not a factor of x, then 3x will have one more prime than x.

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Joined: 28 Aug 2016
Posts: 23
Re: If a positive integer x has 5 prime factors, how many prime factors  [#permalink]

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01 Dec 2017, 12:15
Bunuel

But how come? if suppose 3 is a factor of x already, then still there'll be an addition to the total no. of prime factors by 1 more if x is multiplied by 3, since the question hasn't mentioned distinct prime factors.
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: If a positive integer x has 5 prime factors, how many prime factors  [#permalink]

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01 Dec 2017, 23:11
BigUD94 wrote:
Bunuel

But how come? if suppose 3 is a factor of x already, then still there'll be an addition to the total no. of prime factors by 1 more if x is multiplied by 3, since the question hasn't mentioned distinct prime factors.

Intended meaning is that x has 5 unique prime factors.
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Re: If a positive integer x has 5 prime factors, how many prime factors  [#permalink]

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01 Dec 2017, 23:36
stonecold wrote:
If a positive integer x has 5 prime factors, how many prime factors does 3x have?

A) 3
B) 5
C) 8
D) 15
E) cannot be determined

Suppose X = 2*5*13*7*11 with 5 Prime Factors.. 3X will have 6 Prime Factors.

Suppose X = 3*5*7*11*13 with 5 Prime Factors. In this case 3X will 5 Prime Factors.

@Bunuel - Is it correct way to approach this problem?? Please advise.

Sent from my Lenovo P1a42 using GMAT Club Forum mobile app
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Re: If a positive integer x has 5 prime factors, how many prime factors  [#permalink]

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01 Dec 2017, 23:38
rahul16singh28 wrote:
stonecold wrote:
If a positive integer x has 5 prime factors, how many prime factors does 3x have?

A) 3
B) 5
C) 8
D) 15
E) cannot be determined

Suppose X = 2*5*13*7*11 with 5 Prime Factors.. 3X will have 6 Prime Factors.

Suppose X = 3*5*7*11*13 with 5 Prime Factors. In this case 3X will 5 Prime Factors.

@Bunuel - Is it correct way to approach this problem?? Please advise.

Sent from my Lenovo P1a42 using GMAT Club Forum mobile app

Yes. This is basically the same approach as mine but with numbers.
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Re: If a positive integer x has 5 prime factors, how many prime factors   [#permalink] 01 Dec 2017, 23:38
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