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

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

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New post 12 Nov 2008, 09:07
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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: prime number [#permalink]

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New post 12 Nov 2008, 10:19
It must be A

(1) n = a^4b^3, where a and b are different positive prime numbers.

n will have factors

1,a, b , a*b, a^2*b,a^3 *b,a^4 *b
a*b^2, a*b^3,a2*b^2, a2*b^3,a3*b^2, a3*b^3,a^4*b^2, a^4*b^3

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Re: prime number [#permalink]

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New post 12 Jan 2009, 18:28
vishy007 wrote:
It must be A

(1) n = a^4b^3, where a and b are different positive prime numbers.

n will have factors

1,a, b , a*b, a^2*b,a^3 *b,a^4 *b
a*b^2, a*b^3,a2*b^2, a2*b^3,a3*b^2, a3*b^3,a^4*b^2, a^4*b^3


although its already at many places .. but just for sake of if some one reads this post

number of factors can be calculated easily by =>

Number of factors = (4+1)(3+1)

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Re: prime number [#permalink]

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New post 14 Jan 2009, 00:04
gorden wrote:
How many different factors does the integer n have?
(1) n = a^4b^3, where a and b are different positive prime numbers..



Can u be bit clear in ur question .
Is it \(a[m]{4b}\){3}[/m]

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Re: prime number [#permalink]

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New post 14 Jan 2009, 00:12
mar2hathoda wrote:
vishy007 wrote:
It must be A

(1) n = a^4b^3, where a and b are different positive prime numbers.

n will have factors

1,a, b , a*b, a^2*b,a^3 *b,a^4 *b
a*b^2, a*b^3,a2*b^2, a2*b^3,a3*b^2, a3*b^3,a^4*b^2, a^4*b^3


although its already at many places .. but just for sake of if some one reads this post

number of factors can be calculated easily by =>

Number of factors = (4+1)(3+1)


This is a very useful shortcut.

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Re: prime number [#permalink]

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New post 14 Jan 2009, 03:15
No. of factors can be calculated very easily....

suppose there is n= a^m * b^n where a and b are prime numbers..

then the no. of factors can be calculated as (m+1)*(n+1).......

I hope its clear.......

so the answer is A

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Re: prime number [#permalink]

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New post 14 Jan 2009, 19:09
why cannot the answer be "D"

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Re: prime number [#permalink]

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New post 14 Jan 2009, 21:50
gorden 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.


Answer A.
Statement 1: since a and b a different primes and we know there powers therefore we know that they have (4+1)(3+1)= 20 different factors.
Statement 2: could have endless solutions. Therefore insufficient.

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Re: prime number   [#permalink] 14 Jan 2009, 21:50
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How many different factors does the integer n have? (1) n =

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