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How many prime factors does positive integer n have?

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How many prime factors does positive integer n have? [#permalink]

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New post 29 Mar 2011, 12:30
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How many prime factors does positive integer n have?

(1) n/5 has only a prime factor.
(2) 3*n^2 has two different prime factors.
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Re: How many prime factors does positive integer n have? [#permalink]

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New post 29 Mar 2011, 13:54
banksy wrote:
49. How many prime factors does positive integer n have?
(1) n/5 has only a prime factor.
(2) 3*n^2 has two different prime factors.



(1) : n/5 has one prime factor. So we know immediately that is a multiple of 5. Either n is of the form 5^k or 5x(another_prime)^k (Eg. n=125 or n=15 both work). Hence n has either 1 or 2 prime factors ... Insufficient

(2) : 3*n^2 has two factors. Again, n could have 1 or 2 factors. Eg n=15 OR n =125 both work

(1+2) : Take the case n = 15 and n = 125 ... both statements can be true together. Hence not clear if n has one prime factor or two


Hence, Answer is (e)
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Re: How many prime factors does positive integer n have? [#permalink]

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New post 29 Mar 2011, 18:00
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(1) n/5 has one prime factor. So n could be 25 or 15, in which case n/5 = 5 or n/5 = 3, so n can have more than one prime factor. So Insufficient.

(2) 3*n^2 has two different prime factors. So if n = 5*3 = 15, or n = 5 or 25, then also the expression has two distinct prime factors. So Insufficient.

In (1) and (2), 15 can work, or 25 can work, so answer is E.
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Re: How many prime factors does positive integer n have? [#permalink]

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Re: How many prime factors does positive integer n have? [#permalink]

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New post 15 Mar 2016, 10:29
Just to add to this excellent question if we we actually asked the prime factors of N
=> N can have as its only prime
or it can have both 5 and 3 as it prime.
No other prime number can be its factor.
Here Clearly answer is E
Re: How many prime factors does positive integer n have?   [#permalink] 15 Mar 2016, 10:29
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