if a, b, k and m are positive integers is a^k factor of b...

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galinaphillips: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat May 26, 2007 10:12 am; Thanked: 1 times

by galinaphillips » Sun Jun 03, 2007 6:34 pm

if a, b, k and m are positive integers is a^k factor of b^m?

(1) a is a factor of b
(2) k less than or equal to m

both together are sufficient but neither alone is sufficient

I saw this at mba.com but am not sure why this is true?
Thanks!

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Source: Beat The GMAT — Data Sufficiency | Sun Jun 03, 2007 6:34 pm

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

Re: if a, b, k and m are positive integers is a^k factor of

by jayhawk2001 » Sun Jun 03, 2007 8:36 pm

galinaphillips wrote:if a, b, k and m are positive integers is a^k factor of b^m?

(1) a is a factor of b
(2) k less than or equal to m

both together are sufficient but neither alone is sufficient

I saw this at mba.com but am not sure why this is true?
Thanks!

Take b=6, a=2

1 - insufficient.
Take b = 6, a = 2. we know a is a factor of b. But a^2 is not a factor of b.
Take b = 8, a = 2, we know a is a factor of b. And a^2, a^3 are factors of b.

2 - insufficient. Without knowing relationship between a and b, we cannot
say for sure

1 and 2 together - sufficient.

If k<=m and a is a factor of b, then b^m / a^k will always be an
integer and hence a^k will be a factor of b^m.

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galinaphillips: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Sat May 26, 2007 10:12 am; Thanked: 1 times

Thanks

by galinaphillips » Mon Jun 04, 2007 5:23 am

Thanks a lot!

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Croyant: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Mar 25, 2009 1:29 am

Re: Thanks

by Croyant » Wed Mar 25, 2009 1:34 am

Hi , I am sorry but I didn't get it

if a = 2 , k = 6
b = 8 , m = 2

In this case a raised to power k is a factor of b raised to power m and k is more than m , how does 'k less than or equal to m' helps here.

Please advise.

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cm47323: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Tue Oct 21, 2008 12:10 pm; Thanked: 3 times; GMAT Score:770

Re: Thanks

by cm47323 » Wed Mar 25, 2009 8:41 am

Croyant wrote:Hi , I am sorry but I didn't get it

if a = 2 , k = 6
b = 8 , m = 2

In this case a raised to power k is a factor of b raised to power m and k is more than m , how does 'k less than or equal to m' helps here.

Please advise.

What if k were 10. Then it isn't a factor, thus insufficient

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rs2010: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jul 04, 2008 4:14 pmFollowed by: 1 member; Thanked: 14 times; GMAT Score:760

by rs2010 » Wed Mar 25, 2009 7:18 pm

Question is

b^m=n*a^K?

For this to be true a must be factor of b ie b=ja...where j is integer
now b^m=n* j^k * b^k

now for that eq to be true k can be less than or equal to m.

So 'C'

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