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

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Manager
Joined: 10 Oct 2008
Posts: 56
How many different factors does the integer n have? (1) n = [#permalink]

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11 Nov 2008, 20:37
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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Director
Joined: 14 Aug 2007
Posts: 697

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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
Manager
Joined: 16 Oct 2008
Posts: 54

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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)?
Director
Joined: 14 Aug 2007
Posts: 697

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12 Nov 2008, 01:43
1
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
Manager
Joined: 16 Oct 2008
Posts: 54

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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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: factors--27   [#permalink] 12 Nov 2008, 02:58
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# How many different factors does the integer n have? (1) n =

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