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

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Intern
Joined: 08 Nov 2008
Posts: 38
How many different factors does the integer n have? (1) n = [#permalink]

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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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Manager
Joined: 20 Mar 2008
Posts: 153
Location: USA

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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
Intern
Joined: 31 Dec 2008
Posts: 11

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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)
Intern
Joined: 19 Nov 2008
Posts: 43

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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]
Senior Manager
Joined: 02 Nov 2008
Posts: 255

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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.
Senior Manager
Joined: 23 May 2008
Posts: 393

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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.......

Intern
Joined: 14 Jan 2009
Posts: 1

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14 Jan 2009, 19:09
why cannot the answer be "D"
Manager
Joined: 02 Aug 2007
Posts: 221
Schools: Life

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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.

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.

--== 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: 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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