NEW HERE? LEARN MORE
closeclose
Last visit was: 13 May 2024, 05:12 It is currently 13 May 2024, 05:12
Decision Tracker
My Rewards
New posts
New comers' posts

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

Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q

User avatar
AJB77
Manager
Manager
Joined: 30 May 2005
Posts: 236
Own Kudos [?]: 51 [0]
Given Kudos: 0
Send PM
Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   14 Aug 2005, 16:06
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Hide Show timer Statistics
Is q^b a divisor of p^a ?

1. a>b

2. p is a multiple of q

All numbers are integers.



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 Data Sufficiency (DS) 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
vasild
Intern
Intern
Joined: 14 Jul 2005
Posts: 46
Own Kudos [?]: 15 [0]
Given Kudos: 0
Location: Sofia, Bulgaria
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   14 Aug 2005, 16:25
The question is if p^a divided by q^b equals an integer. (I am assuming q isn't zero)

(1) doesn't help much by itself. Obviously insufficient.

(2) tells us that p=q*x, where x is some random integer

Substitute into the stem and we now have to evaluate the following number: (q*x)^a / q^b

We can rewrite it as

(q^a)*(x^a) / q^b = q^(a-b) * x^a

x^a is definitely an integer, and if a>=b the same is true for the other factor. This is when statement (1) somes into play, because it gives us the needed information

=> (C) is the answer.

Am I missing something?

Vasil
User avatar
HIMALAYA
Director
Director
Joined: 05 Apr 2005
Posts: 800
Own Kudos [?]: 255 [0]
Given Kudos: 0
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   14 Aug 2005, 16:27
if a>b and p is a multiple of q, then q^b can be divisor of p^a. suppose, if a=3, b =2, and p=q=1, p^a can be divided by q^b. so I go with C.
User avatar
prep_gmat
Manager
Manager
Joined: 13 Oct 2004
Posts: 113
Own Kudos [?]: 37 [0]
Given Kudos: 0
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   14 Aug 2005, 20:30
E.

a = -1 > b = -2
p=6 a multiple of q = 2.

Also, q = p can be zero.
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 770 [0]
Given Kudos: 0
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   14 Aug 2005, 20:39
I would expect a real GMAT question to define q, p, a, and b positive integers. If this is the case, then C should be the correct answer.

From 2, p=mq
p^a/q^b=m^aq^a/q^b=m^aq^(a-b)
From 1, a-b>0
then p^a/q^b=m^aq^(a-b) is also an integer. In other words q^b is a divisor of p^a.

However if pqab are not defined, then we don't know if they are integers. For example, a-b might be 1/2 or something. Then the answer would be E.
User avatar
AJB77
Manager
Manager
Joined: 30 May 2005
Posts: 236
Own Kudos [?]: 51 [0]
Given Kudos: 0
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   15 Aug 2005, 20:50
OA is C

HongHu, I noted in the Question that all numbers are integers.
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 770 [0]
Given Kudos: 0
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   15 Aug 2005, 21:05
You are very right AJB, though I would prefer they are positive integers, them being integers are the most important one and it is defined in the question. Now can 0 be a divisor to another number? :hmmm:
User avatar
prep_gmat
Manager
Manager
Joined: 13 Oct 2004
Posts: 113
Own Kudos [?]: 37 [0]
Given Kudos: 0
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   16 Aug 2005, 23:08
If p,q,a,b are not positive integers, How can the answer be C?.

p=6, q=2, a=-1, b=-2 satisfy both statements and yield a 'no' answer. One can find several easy examples of 'yes' answer for a given set of p,q,a,b if all are positive and both statements are true.
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 770 [0]
Given Kudos: 0
Send PM
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink] New post   17 Aug 2005, 06:39
I believe that the domain is the natural numbers when we are talking about multiples and factors. However, 0 should be included. 0 is a multiple of any number, including 0 itself. In other words for this question both q and p can be zero to satisfy (2), and then we would get a "No" to the question (since 0 can't be a divisor) instead of "Yes" when they are not zeros.

Also to make sure q^b and p^a are natural numbers so that "divisor" is defined, a and b must not be negative.

Therefore for this question to be strictly defined it should say all numbers are positive integers.



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 Data Sufficiency (DS) 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!
GMAT Club Bot
gmatclubot
Re: Is q^b a divisor of p^a ? 1. a>b 2. p is a multiple of q [#permalink]
17 Aug 2005, 06:39
Moderators:
Bunuel
Math Expert
93219 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 posts
GMATBusters
GMAT Tutor
1904 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions