May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th. Jun 01 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jun 02 07:00 AM PDT  09:00 AM PDT Get personalized insights and an accurate assessment of your current quant score to achieve your Target Quant Score.
Author 
Message 
Senior Manager
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 498

If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
Show Tags
07 Apr 2011, 23:32
Question Stats:
56% (00:23) correct 44% (01:01) wrong based on 17 sessions
HideShow timer Statistics
If a,b,k, and m are positive integers, is a^k a factor of b^m? 1) a is a factor of b 2) k ≤ m I don't know OA. OPEN DISCUSSION OF THIS QUESTION IS HERE: ifabkandmarepositiveintegersisakafactorof88503.html== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost 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.
_________________



Manager
Joined: 14 Feb 2011
Posts: 169

Re: If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
Show Tags
07 Apr 2011, 23:54
Baten80 wrote: If a,b,k, and m are positive integers, is a^k a factor of b^m?
1) a is a factor of b
2) k ≤ m
I don't know OA. we need to find out if \(\frac{b^m}{a^k}\) is an integer. Statement 1 says a is a factor of b so \(b = na\) where n is an integer. So \(\frac{b^m}{a^k}\) = \(\frac{(na)^m}{a^k}\) = \(\frac{(n^m*a^m)}{a^k}\) This will be integer if \(a^m \geq a^k\) which will happen only if \(k \leq m\)which is not given in statement 1, so insufficient Statement 2 doesnt say anything about a and b so insufficient Combining statement 1 and 2 we can answer the question in affirmative, hence sufficient and Answer is C.



Retired Moderator
Joined: 16 Nov 2010
Posts: 1391
Location: United States (IN)
Concentration: Strategy, Technology

Re: If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
Show Tags
08 Apr 2011, 00:33
Is b^m = r *a^k ? (where p is as an integer) (1) b = p * a (where p is as an integer) so b^k = p^k * a^k but we don't know the relationship between m and k, so insufficient. e.g. a = 3, b = 6 so 6^2/3^3 is not an integer. (2) No information about a and b, so insufficient. (1) and (2) => b^m = p^k * a^k or, b^m/a^k = p^k (an integer), so sufficient Answer  C
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Director
Joined: 01 Feb 2011
Posts: 646

Re: If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
Show Tags
08 Apr 2011, 18:22
My Answer is C too.
Posted from my mobile device



Manager
Joined: 18 Jan 2011
Posts: 218

Re: If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
Show Tags
08 Apr 2011, 20:22
Take a = 2, b = 6 =>2^k and 6^m =>2^k and 2^m x 3^m If k<=m, for any positive value of k and m, 2^k is always a factor of 2^m So C
_________________
Good Luck!!!
***Help and be helped!!!****



Intern
Joined: 14 Jun 2016
Posts: 17
Location: United States
WE: Engineering (Pharmaceuticals and Biotech)

Re: If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
Show Tags
12 Sep 2016, 11:48
Baten80 wrote: If a,b,k, and m are positive integers, is a^k a factor of b^m?
1) a is a factor of b
2) k ≤ m
I don't know OA. 1) b^m = a^k * n. Since a is factor of B, let a =2, b=8 so 2^3m = 2^k * n. 2^k can only be a factor of 2^3m if the exponents of 2^k is less than 2^3m for all k and m. So not sufficient 2)k <= m, not sufficient because a and b relationship not given. If a = 3, b = 5, can be yes or no for a^k a factor of b^m 1+2) given a is a factor of b and the exponent of a will be smaller than or equal to the exponent of b, a^k is then a factor of b^m. C



Math Expert
Joined: 02 Sep 2009
Posts: 55277

Re: If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
Show Tags
14 Aug 2017, 06:25
Baten80 wrote: If a,b,k, and m are positive integers, is a^k a factor of b^m?
1) a is a factor of b
2) k ≤ m
I don't know OA. Question: is \(a^k\) a factor of \(b^m\) > \(a^kx=b^m\), where \(x\) is an integer? > \(x=\frac{b^m}{a^k}\). So basically the question is: Is \(x\) an integer \(>0\)? (1) \(a\) is a factor of \(b\) > \(ay=b\) > \(x=\frac{a^my^m}{a^k}\) > \(x=a^{mk}y^m\). Now if \(m<k\) and \(a\) is not a factor of \(y\), then \(x\) will not be an integer. Not sufficient. Or even without any algebra: if a and b are equal to say 3 and m<k (there are less b's than a's) then a^k won't be a factor of b^m. Though if k<=m then even if a and b are not equal still a^k will be a factor of b^m as there will be enough b's for a's. (2) \(k\leq{m}\), not sufficient on it's own. (1)+(2) \(x=a^{mk}y^m\) and \(k<m\), hence \(x\) is an integer. Sufficient. (Or again as there are more b's then a's (enough b's for a) then a^k is a factor of b^m, for example (bbb)/(aa)) Answer: C. OPEN DISCUSSION OF THIS QUESTION IS HERE: ifabkandmarepositiveintegersisakafactorof88503.html== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost 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: If a,b,k, and m are positive integers, is a^k a factor of
[#permalink]
14 Aug 2017, 06:25






