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

 It is currently 15 Dec 2018, 08:39

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Oct 2012
Posts: 22
Concentration: Strategy
Schools: Bocconi '15 (A)
If p, q and r are positive integers greater than 1, and p  [#permalink]

### Show Tags

25 Apr 2013, 21:39
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:57) correct 34% (02:01) wrong based on 243 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
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611
Re: If p.q and r are positive integers greater than 1, and p and  [#permalink]

### Show Tags

25 Apr 2013, 22:35
1
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.
_________________
Senior Manager
Joined: 23 Oct 2010
Posts: 350
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: If p, q and r are positive integers greater than 1, and p  [#permalink]

### Show Tags

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

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: 1063
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: If p, q and r are positive integers greater than 1, and p  [#permalink]

### Show Tags

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
Joined: 06 Sep 2013
Posts: 1720
Concentration: Finance
Re: If p.q and r are positive integers greater than 1, and p and  [#permalink]

### Show Tags

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.

Cheers
J
Retired Moderator
Joined: 15 Jun 2012
Posts: 1017
Location: United States
Re: If p.q and r are positive integers greater than 1, and p and  [#permalink]

### Show Tags

26 Dec 2013, 00:40
3
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.

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.

Non-Human User
Joined: 09 Sep 2013
Posts: 9164
Re: If p, q and r are positive integers greater than 1, and p  [#permalink]

### Show Tags

13 Oct 2017, 07:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If p, q and r are positive integers greater than 1, and p &nbs [#permalink] 13 Oct 2017, 07:00
Display posts from previous: Sort by