Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Sep 2014, 05:47

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If p, q and r are positive integers greater than 1, and p

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 09 Oct 2012
Posts: 23
Concentration: Strategy
Schools: Bocconi '15 (A)
GMAT 1: Q V
Followers: 0

Kudos [?]: 14 [0], given: 33

If p, q and r are positive integers greater than 1, and p [#permalink] New post 25 Apr 2013, 21:39
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

53% (02:08) correct 47% (01:20) wrong based on 89 sessions
If p, q and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^(pq)?

I. p+q
II. q^p
III. p^2 * q^2

A. I only
B. II only
C. III only
D. I and II
E. II and III
[Reveal] Spoiler: OA
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627
Followers: 41

Kudos [?]: 563 [0], given: 135

Premium Member
Re: If p.q and r are positive integers greater than 1, and p and [#permalink] New post 25 Apr 2013, 22:35
Expert's post
rajatr wrote:
If p.q and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^pq?

I. p+q
II. q^p
III. p^2 * q^2

A. I only

B. II only

C. III only

D. I and II

E. II and III


We know that p and q are factors of r. Thus, for 2 non-negative integers,m and n, we have : r = pm and r = qn. Now, r^{pq} = (pm)^{pq} = (qn)^{pq}.

Thus, we see that q^p will always be a factor of the given expression.

Also, from the given problem p,q>2. Thus, the minimum value of p*q = 4.


Thus,r^{pq} = At-least r^4. Now, as r = pm = qn, thus, r^4 = (p*q*m*n)^2 = p^2*q^2*m^2*n^2.Thus, p^2 * q^2 is also a factor of the given expression.

E.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 384
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 12

Kudos [?]: 131 [0], given: 73

GMAT ToolKit User
Re: If p, q and r are positive integers greater than 1, and p [#permalink] New post 26 Apr 2013, 00:29
given that p and q are factors of r.
so we can picture it this way r=p*q*n (n-some another factor of r)
so, r^pq= (p*q*n)^pq

I. p+q .since the question is MUST BE TRUE, we eleminate this option
II. (p*q*n)^pq / q^p= integer YES!
III.(p*q*n)^pq/ p^2 * q^2 YEs, since we are said that integer p>1 and integer q>1
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1125
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 112

Kudos [?]: 1136 [0], given: 219

GMAT ToolKit User GMAT Tests User
Re: If p, q and r are positive integers greater than 1, and p [#permalink] New post 26 Apr 2013, 00:34
LalaB wrote:
given that p and q are factors of r.
so we can picture it this way r=p*q*n (n-some another factor of r)
so, r^pq= (p*q*n)^pq



Hi LalaB,

this part is incorrect.
Consider the case r=30 and its factor p=15 q=10

According to your statement 30=10*15*other factor
As you can see this is not true: no factor of 30 will fit into that equation . (What you say can be true only in some cases....)

Hope this clarifies, let me know
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1627
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 156 [0], given: 254

GMAT ToolKit User
Re: If p.q and r are positive integers greater than 1, and p and [#permalink] New post 25 Dec 2013, 15:29
mau5 wrote:
rajatr wrote:
If p.q and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^pq?

I. p+q
II. q^p
III. p^2 * q^2

A. I only

B. II only

C. III only

D. I and II

E. II and III


We know that p and q are factors of r. Thus, for 2 non-negative integers,m and n, we have : r = pm and r = qn. Now, r^{pq} = (pm)^{pq} = (qn)^{pq}.

Thus, we see that q^p will always be a factor of the given expression.

Also, from the given problem p,q>2. Thus, the minimum value of p*q = 4.


Thus,r^{pq} = At-least r^4. Now, as r = pm = qn, thus, r^4 = (p*q*m*n)^2 = p^2*q^2*m^2*n^2.Thus, p^2 * q^2 is also a factor of the given expression.

E.


What about the first statement?

Cheers
J :)
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 15 Jun 2012
Posts: 1023
Location: United States
Followers: 117

Kudos [?]: 1192 [1] , given: 119

Premium Member
Re: If p.q and r are positive integers greater than 1, and p and [#permalink] New post 26 Dec 2013, 00:40
1
This post received
KUDOS
jlgdr wrote:
mau5 wrote:
rajatr wrote:
If p.q and r are positive integers greater than 1, and p and q are factors of r, which of the following must be the factor of r^pq?

I. p+q
II. q^p
III. p^2 * q^2

A. I only

B. II only

C. III only

D. I and II

E. II and III


We know that p and q are factors of r. Thus, for 2 non-negative integers,m and n, we have : r = pm and r = qn. Now, r^{pq} = (pm)^{pq} = (qn)^{pq}.

Thus, we see that q^p will always be a factor of the given expression.

Also, from the given problem p,q>2. Thus, the minimum value of p*q = 4.


Thus,r^{pq} = At-least r^4. Now, as r = pm = qn, thus, r^4 = (p*q*m*n)^2 = p^2*q^2*m^2*n^2.Thus, p^2 * q^2 is also a factor of the given expression.

E.


What about the first statement?

Cheers
J :)


For this kind of question, I like to plug in numbers.

p = 2
q = 3
r = 6
==>6^(2*3) = (6^2)^3 = 36^3
Clearly, 36 is not divisible by 5 (2+3 =5)
Only number ending with 5 or 0 can be divisible by 5
==> 1st statement is not a "must be true" answer.

Best!
_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMV Chief of Design.

Re: If p.q and r are positive integers greater than 1, and p and   [#permalink] 26 Dec 2013, 00:40
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If p and q are positive integers each greater than 1, and 17 arifaisal 3 12 Jul 2014, 16:24
2 Are positive integers p and q both greater than n? 1. p-q is vksunder 5 17 Jun 2008, 16:49
are positive integers p and q both greater than n? 1. el1981 1 05 Feb 2008, 21:24
Are positive integers P and Q both greater than n? 1.P-Q is dreamgmat1 4 08 Jul 2007, 13:26
P is a positive integer and greater than 1. What is the gamjatang 10 26 Nov 2005, 06:40
Display posts from previous: Sort by

If p, q and r are positive integers greater than 1, and p

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.