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How many different factors does the integer n have? (1) n =

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Manager
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How many different factors does the integer n have? (1) n = [#permalink]

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New post 11 Nov 2008, 20:37
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many different factors does the integer n have?
(1) n = a^4b^3, where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Re: factors--27 [#permalink]

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New post 11 Nov 2008, 20:41
Jcpenny wrote:
How many different factors does the integer n have?
(1) n = a^4b^3, where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


A for me.

1) number of factors = (4+1) (3+1) = 20 factors.=> suff.
2) We dont know if n = 5*7 or n= 5*7*7 or n= 5*5*7 => insuff

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Manager
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Re: factors--27 [#permalink]

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New post 12 Nov 2008, 01:28
alpha_plus_gamma wrote:
Jcpenny wrote:
How many different factors does the integer n have?
(1) n = a^4b^3, where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


A for me.

1) number of factors = (4+1) (3+1) = 20 factors.=> suff.
2) We dont know if n = 5*7 or n= 5*7*7 or n= 5*5*7 => insuff


Can you please explain more >> number of factors = (4+1) (3+1) = 20 factors.=> suff.
How can you get (4+1) (3+1)?

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Director
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Re: factors--27 [#permalink]

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New post 12 Nov 2008, 01:43
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Natasha0123 wrote:

Can you please explain more >> number of factors = (4+1) (3+1) = 20 factors.=> suff.
How can you get (4+1) (3+1)?


say "n" has prime factors x,y,z... such that
n = x^a * y^b * z^c...
number of factors of n = (a+1)*(b+1)*(c+1)....

Thanks to Walker for this rule :)

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Manager
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Re: factors--27 [#permalink]

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New post 12 Nov 2008, 02:58
alpha_plus_gamma wrote:
Natasha0123 wrote:

Can you please explain more >> number of factors = (4+1) (3+1) = 20 factors.=> suff.
How can you get (4+1) (3+1)?


say "n" has prime factors x,y,z... such that
n = x^a * y^b * z^c...
number of factors of n = (a+1)*(b+1)*(c+1)....

Thanks to Walker for this rule :)


Wow !! that's nice..

+1 kudo for you :)

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Re: factors--27   [#permalink] 12 Nov 2008, 02:58
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