GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 May 2019, 20:21

### 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

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

# If a,b,k, and m are positive integers, is a^k a factor of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
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
00:00

Difficulty:

(N/A)

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: if-a-b-k-and-m-are-positive-integers-is-a-k-a-factor-of-88503.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 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.

_________________
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

_________________
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
GMAT 1: 700 Q48 V37
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 $$b$$ --> $$ay=b$$ --> $$x=\frac{a^my^m}{a^k}$$ --> $$x=a^{m-k}y^m$$. 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) $$x=a^{m-k}y^m$$ 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))

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-b-k-and-m-are-positive-integers-is-a-k-a-factor-of-88503.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 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: If a,b,k, and m are positive integers, is a^k a factor of   [#permalink] 14 Aug 2017, 06:25
Display posts from previous: Sort by

# If a,b,k, and m are positive integers, is a^k a factor of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.