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

 It is currently 29 Aug 2016, 21:21

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Oct 2012
Posts: 23
Concentration: Strategy
Schools: Bocconi '15 (A)
GMAT 1: Q V
Followers: 0

Kudos [?]: 41 [0], given: 33

If p, q and r are positive integers greater than 1, and p [#permalink]

### Show Tags

25 Apr 2013, 22:39
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

61% (02:25) correct 39% (01:18) wrong based on 132 sessions

### HideShow timer Statistics

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
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 76

Kudos [?]: 1012 [0], given: 136

Re: If p.q and r are positive integers greater than 1, and p and [#permalink]

### Show Tags

25 Apr 2013, 23:35
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.
_________________
Current Student
Joined: 23 Oct 2010
Posts: 386
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 21

Kudos [?]: 285 [0], given: 73

Re: If p, q and r are positive integers greater than 1, and p [#permalink]

### Show Tags

26 Apr 2013, 01:29
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

I am still on all gmat forums. msg me if you want to ask me smth

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1123
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Followers: 173

Kudos [?]: 1801 [0], given: 219

Re: If p, q and r are positive integers greater than 1, and p [#permalink]

### Show Tags

26 Apr 2013, 01:34
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]

Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 54

Kudos [?]: 516 [0], given: 355

Re: If p.q and r are positive integers greater than 1, and p and [#permalink]

### Show Tags

25 Dec 2013, 16:29
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
Verbal Forum Moderator
Joined: 16 Jun 2012
Posts: 1153
Location: United States
Followers: 237

Kudos [?]: 2570 [1] , given: 123

Re: If p.q and r are positive integers greater than 1, and p and [#permalink]

### Show Tags

26 Dec 2013, 01:40
1
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 BMW Chief of Design.

Re: If p.q and r are positive integers greater than 1, and p and   [#permalink] 26 Dec 2013, 01:40
Similar topics Replies Last post
Similar
Topics:
3 If p and q are two positive integers and p/q = 1.15 4 06 Feb 2016, 12:45
8 p, q, and r are positive integers. If p, q, and r are assembled into t 3 27 Oct 2014, 20:51
7 If p and q are positive integers each greater than 1, and 17 4 12 Jul 2014, 17:24
7 If p, q, and r are positive integers such that q is a factor 5 06 Jul 2014, 09:58
13 If n is a positive integer greater than 1, then p(n) represe 5 22 Dec 2012, 07:24
Display posts from previous: Sort by

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

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

 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®.