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

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

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New post Updated on: 14 Aug 2018, 04:16
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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, 11:10.
Last edited by a70 on 14 Aug 2018, 04:16, 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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New post 04 Aug 2018, 02:02
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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New post 04 Aug 2018, 20:34
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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New post 04 Aug 2018, 23:06
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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New post 05 Aug 2018, 01:32
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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New post 05 Aug 2018, 02:25
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!?!?!?

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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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I missed that, my bad. Answer is B then.

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Re: Is the number of different prime factors of a number 'p' more than 3? &nbs [#permalink] 05 Aug 2018, 02:25
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