Last visit was: 26 Apr 2026, 13:52 It is currently 26 Apr 2026, 13:52
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
joemama142000
User avatar
Joined: 17 Oct 2005
Last visit: 16 Jun 2010
Posts: 645
Own Kudos:
1,790
Posts: 645
Kudos: 1,790
if a,b,k, m are positive integers, is a^k a factor of b^m? 12 Feb 2006, 16:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
if a,b,k, m are positive integers, is a^k a factor of b^m?
1) a is a factor of b

2) k=m



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
ywilfred
User avatar
Joined: 07 Jul 2004
Last visit: 06 Mar 2012
Posts: 1,987
Own Kudos:
2,051
Location: Singapore
Posts: 1,987
Kudos: 2,051
if a,b,k, m are positive integers, is a^k a factor of b^m? 12 Feb 2006, 22:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
1) a = 3, b = 6
6^m = (3*2)^m = 3^m(2^m) --> multiple of 3^m (a^m)

Sufficient.

2) k=m. Insufficient. We do not know the base values.

Ans A
User avatar
razrulz
User avatar
Joined: 11 Jan 2006
Last visit: 23 Sep 2006
Posts: 98
Own Kudos:
14
Location: Chennai,India
Posts: 98
Kudos: 14
if a,b,k, m are positive integers, is a^k a factor of b^m? 12 Feb 2006, 22:25
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yep it is C !

plug in values...

1) we just know 3 is a factor is 30 , if k > m - sol is not possible at cerain cases
if k< m sol possible is all cases

2) info inadequeate

1+ 2 ) since we know a is a factor of b and the powers are equal , it is solvable..
avatar
rajkanth
avatar
Joined: 24 Jan 2006
Last visit: 01 Feb 2006
Posts: 5
Posts: 5
Kudos: 0
if a,b,k, m are positive integers, is a^k a factor of b^m? 13 Feb 2006, 12:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
the q asks if (b^m/a^k) = p? p is an integer
1) says that b = p1 * a? p1 is an integer
now b^m/a^k = p1^m * a^(m-k)
p1^m is an integer but we dont know if a^(m-k) is an integer or a fraction.

so 2) is needed to clear that doubt

hence C
User avatar
cJackSparrow
User avatar
Joined: 09 Feb 2006
Last visit: 04 Apr 2006
Posts: 10
Own Kudos:
1
Location: Raleigh, NC
Posts: 10
Kudos: 1
if a,b,k, m are positive integers, is a^k a factor of b^m? 13 Feb 2006, 12:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Consider (i)

Say a=2, k=3. From (i) we know that a is a factor of b. Let b = 4.
Now from (i)
is 2^3 = 8 a factor of 4^m?
No, this is not true case m=0,1.

Rule out A and D.

Consider (ii)

k = m. Is this sufficient in itself? Clearly inadequate,
e.g. is 7^3 a factor of 2^3. No.

Rule out B.

Are (i) and (ii) sufficient?

=> is a^k a factor of b^k: (from ii we know that k=m)

=> is a^k a factor of (a*c)^k : (As a is a factor of b, b=c*a, c is some integer)

Now,
[ (a*c)^k ] / [ a^k ]
= [ (a*c) / a ] ^k
= c^k, which is an Integer.

Hence (i) & (ii) are both necessary. Answer is C.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!