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# Is the number of different prime factors of a number 'p' more than 3?

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Intern
Joined: 21 May 2016
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Is the number of different prime factors of a number 'p' more than 3?  [#permalink]

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Updated on: 14 Aug 2018, 03:16
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Difficulty:

75% (hard)

Question Stats:

46% (01:46) correct 54% (02:13) wrong based on 57 sessions

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Is the number of different prime factors of a number 'p' more than 3?

(1) The number of distinct prime factors of 10p is 2 more than the number of distinct prime factors of 10

(2) The number of distinct prime factor of $$(4p)^3$$ is 3 more than that of 18

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Originally posted by a70 on 03 Aug 2018, 10:10.
Last edited by a70 on 14 Aug 2018, 03:16, edited 3 times in total.
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Re: Is the number of different prime factors of a number 'p' more than 3?  [#permalink]

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04 Aug 2018, 01:02
ankit7055
Typo in 1st statement?
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Re: Is the number of different prime factors of a number 'p' more than 3?  [#permalink]

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04 Aug 2018, 19:34
LevanKhukhunashvili Thanks for pointing out. Made the changes
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Re: Is the number of different prime factors of a number 'p' more than 3?  [#permalink]

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04 Aug 2018, 22:06
D

Statement1 - 10 has two distinct prime factors (2,5). So, 10p has four prime factors. 2 and 5 are also prime factors of 10p, so p can have two more prime factors. So, p doesn't have more than three prime factors. Sufficient.

Statement2 - 18 has two prime factors (2,3). (4p)^3 has same number of prime factors as 4p. So, 4p has 5 prime factors. 2 is one of the prime factors of 4p, so, p must have four more prime factors. It means that p has more than 3 prime factors. Sufficient.

And now I'm confused because the two statements contradict each other!?!?!?

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Re: Is the number of different prime factors of a number 'p' more than 3?  [#permalink]

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05 Aug 2018, 00:32
ankitsaroha wrote:
D

Statement1 - 10 has two distinct prime factors (2,5). So, 10p has four prime factors. 2 and 5 are also prime factors of 10p, so p can have two more prime factors. So, p doesn't have more than three prime factors. Sufficient.

Statement2 - 18 has two prime factors (2,3). (4p)^3 has same number of prime factors as 4p. So, 4p has 5 prime factors. 2 is one of the prime factors of 4p, so, p must have four more prime factors. It means that p has more than 3 prime factors. Sufficient.

And now I'm confused because the two statements contradict each other!?!?!?

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From statement one you know that p has 2 factors other than 2 and 5. Let's say x and y. But this doesn't mean that p itself doesn't have 2 and 5 in itself.

For eg-consider 10 and 2100(10p=10 x 210)
10 has 5 and 2
210(p) has 7 and 3 ( and 5 and 2)

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Re: Is the number of different prime factors of a number 'p' more than 3?  [#permalink]

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05 Aug 2018, 01:25
rahulkashyap wrote:
ankitsaroha wrote:
D

Statement1 - 10 has two distinct prime factors (2,5). So, 10p has four prime factors. 2 and 5 are also prime factors of 10p, so p can have two more prime factors. So, p doesn't have more than three prime factors. Sufficient.

Statement2 - 18 has two prime factors (2,3). (4p)^3 has same number of prime factors as 4p. So, 4p has 5 prime factors. 2 is one of the prime factors of 4p, so, p must have four more prime factors. It means that p has more than 3 prime factors. Sufficient.

And now I'm confused because the two statements contradict each other!?!?!?

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

From statement one you know that p has 2 factors other than 2 and 5. Let's say x and y. But this doesn't mean that p itself doesn't have 2 and 5 in itself.

For eg-consider 10 and 2100(10p=10 x 210)
10 has 5 and 2
210(p) has 7 and 3 ( and 5 and 2)

Posted from my mobile device

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Re: Is the number of different prime factors of a number 'p' more than 3? &nbs [#permalink] 05 Aug 2018, 01:25
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