Last visit was: 24 Jun 2025, 15:08 It is currently 24 Jun 2025, 15:08
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
goodyear2013
Joined: 21 Oct 2013
Last visit: 29 May 2020
Posts: 390
Own Kudos:
5,466
 [29]
Given Kudos: 289
Posts: 390
Kudos: 5,466
 [29]
4
Kudos
Add Kudos
25
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Jun 2025
Posts: 102,292
Own Kudos:
735,211
 [7]
Given Kudos: 94,011
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,292
Kudos: 735,211
 [7]
6
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
avatar
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,538
Own Kudos:
7,865
 [6]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,538
Kudos: 7,865
 [6]
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
veergmat
Joined: 08 Nov 2014
Last visit: 17 Oct 2015
Posts: 61
Own Kudos:
Given Kudos: 90
Location: India
GPA: 3
WE:Engineering (Manufacturing)
Posts: 61
Kudos: 53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I am not able to get the right answer :?

1)If q is a factor of r, then r=aq (a any constant )
2)If r is a multiple of p,then p=br (b any constant)

Now checking options
1. (p+q)/r= (br+r/a)/r= b+1/a .................... It can b an Integer if a=1
2. (r+p)/q= (r+br)/(r/a)= a(1+b)............ Always an Integer
3. p/q =rb/(r/a)=b/a ................................ Can be an Integer if b is divisible by a
4. r(p+q)/pq= r(rb+r/a)/(rb*r/a)=(ab+1)/b ...............:(


I think I m doing some basic mistake ,please tell.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Jun 2025
Posts: 102,292
Own Kudos:
Given Kudos: 94,011
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,292
Kudos: 735,211
Kudos
Add Kudos
Bookmarks
Bookmark this Post
veerdonjuan
I am not able to get the right answer :?

1)If q is a factor of r, then r=aq (a any constant )
2)If r is a multiple of p,then p=br (b any constant)

Now checking options
1. (p+q)/r= (br+r/a)/r= b+1/a .................... It can b an Integer if a=1
2. (r+p)/q= (r+br)/(r/a)= a(1+b)............ Always an Integer
3. p/q =rb/(r/a)=b/a ................................ Can be an Integer if b is divisible by a
4. r(p+q)/pq= r(rb+r/a)/(rb*r/a)=(ab+1)/b ...............:(


I think I m doing some basic mistake ,please tell.

r is a multiple of p means r = bp, not p = br.
User avatar
veergmat
Joined: 08 Nov 2014
Last visit: 17 Oct 2015
Posts: 61
Own Kudos:
Given Kudos: 90
Location: India
GPA: 3
WE:Engineering (Manufacturing)
Posts: 61
Kudos: 53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
:shock: Thankyou Bunuel !!I think I need good sleep :P
Please tell substituting a value is good (less time consuming & accurate ) approach or assuming variables
Bunuel
veerdonjuan
I am not able to get the right answer :?

1)If q is a factor of r, then r=aq (a any constant )
2)If r is a multiple of p,then p=br (b any constant)

Now checking options
1. (p+q)/r= (br+r/a)/r= b+1/a .................... It can b an Integer if a=1
2. (r+p)/q= (r+br)/(r/a)= a(1+b)............ Always an Integer
3. p/q =rb/(r/a)=b/a ................................ Can be an Integer if b is divisible by a
4. r(p+q)/pq= r(rb+r/a)/(rb*r/a)=(ab+1)/b ...............:(


I think I m doing some basic mistake ,please tell.

r is a multiple of p means r = bp, not p = br.
User avatar
elegantm
Joined: 28 May 2017
Last visit: 11 Sep 2018
Posts: 223
Own Kudos:
Given Kudos: 12
Concentration: Finance, General Management
Posts: 223
Kudos: 744
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aarushi00
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?

A. (p+q)/r
B. (r+p)/q
C. p/q
D. pq/r
E. r(p+q)/pq

One of the simple way to solve such kind of questions is to use values for different variables given.

Lets Assume
r = 8
q = 2
p= Either 1 or 4. Need to assume two value since relationship between p & q is not given

Let's plug these values
A. (p+q)/r = 3/8 = Not an Integer
B. (r+p)/q = 12/2 or 9/2 = Not an Integer in 2nd Scenario
C. p/q = 1/2 or 2/2 = Not an Integer in 1st Scenario
D. pq/r = 2/8 or 8/8 = Not an Integer in 1st Scenario
E. r(p+q)/pq = 8.3/3 or 8.6/8 = Integer in Both the Scenarios'.

Hence Answer E
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 24 Jun 2025
Posts: 20,993
Own Kudos:
Given Kudos: 293
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 20,993
Kudos: 26,044
Kudos
Add Kudos
Bookmarks
Bookmark this Post
goodyear2013
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?

A. (p + q)/r
B. (r + p)/q
C. p/q
D. pq/r
E. r(p + q)/pq

Since q is a factor of r and r is a multiple of p:

r/q = integer; r/p = integer.

After scanning the choices, we see that we can simplify answer choice E, so let’s do that first:

r(p + q)/pq = (rp + rq)/pq = rp/pq + rq/pq = r/q + r/p

Since we’ve mentioned that r/q = integer and r/p = integer, r/q + r/p must equal an integer also. Thus, answer choice E is correct.

Answer: E
User avatar
sonalchhajed2019
Joined: 06 Apr 2018
Last visit: 29 May 2023
Posts: 115
Own Kudos:
Given Kudos: 336
Location: India
Schools: ISB '23 (S)
GMAT 1: 560 Q43 V23
GMAT 2: 680 Q50 V33
GMAT 3: 710 Q49 V37
GPA: 3.64
Products:
Schools: ISB '23 (S)
GMAT 3: 710 Q49 V37
Posts: 115
Kudos: 27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
goodyear2013
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?

A. (p + q)/r
B. (r + p)/q
C. p/q
D. pq/r
E. r(p + q)/pq

Premier P716

We have that r is a multiple of both q and p.

A. (p + q)/r. Not necessarily true. Consider r = 3, and p = q = 1.

B. (r + p)/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

C. p/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

D. pq/r. Not necessarily true. Consider r = 3, and p = q = 1.

E. \(\frac{r(p + q)}{pq}= \frac{rp+rq}{pq}=\frac{rp}{pq}+\frac{rq}{pq}=\frac{r}{q}+\frac{r}{p}=integer+integer=integer.\)

Answer: E.
How did you go about choosing these numbers ? At the time of examination how to decide which numbers to choose Bunuel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Jun 2025
Posts: 102,292
Own Kudos:
735,211
 [1]
Given Kudos: 94,011
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,292
Kudos: 735,211
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
givinggmat
Bunuel
goodyear2013
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?

A. (p + q)/r
B. (r + p)/q
C. p/q
D. pq/r
E. r(p + q)/pq

Premier P716

We have that r is a multiple of both q and p.

A. (p + q)/r. Not necessarily true. Consider r = 3, and p = q = 1.

B. (r + p)/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

C. p/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

D. pq/r. Not necessarily true. Consider r = 3, and p = q = 1.

E. \(\frac{r(p + q)}{pq}= \frac{rp+rq}{pq}=\frac{rp}{pq}+\frac{rq}{pq}=\frac{r}{q}+\frac{r}{p}=integer+integer=integer.\)

Answer: E.
How did you go about choosing these numbers ? At the time of examination how to decide which numbers to choose Bunuel

Good question. We have number of articles on this. Check below.

Number plugging:


How to Do Math on the GMAT Without Actually Doing Math
The Power of Estimation for GMAT Quant
How to Plug in Numbers on GMAT Math Questions
Number Sense for the GMAT
Can You Use a Calculator on the GMAT?
Why Approximate?
GMAT Math Strategies — Estimation, Rounding and other Shortcuts
The 4 Math Strategies Everyone Must Master, Part 1 (1. Test Cases and 2. Choose Smart Numbers.)
The 4 Math Strategies Everyone Must Master, part 2 (3. Work Backwards and 4. Estimate)
Intelligent Guessing on GMAT
How to Avoid Tedious Calculations on the Quantitative Section of the GMAT
GMAT Tip of the Week: No Calculator? No Problem.
The Importance of Sorting Answer Choices on the GMAT

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 24 Jun 2025
Posts: 5,617
Own Kudos:
5,119
 [1]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
GMAT 1: 690 Q50 V34
Posts: 5,617
Kudos: 5,119
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
goodyear2013
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?

A. (p + q)/r
B. (r + p)/q
C. p/q
D. pq/r
E. r(p + q)/pq

Premier P716

Given:
1. p, q, and r are positive integers
2. q is a factor of r
3. r is a multiple of p

Asked: Which of the following must be an integer?

r = k1*q
r = k2*p
r = k1*q = k2*p where k1 & k2 are integers

Let us take r = 12; p=4; q=3
A. (p + q)/r
7/12
Not necessarily an integer
B. (r + p)/q
16/3
Not necessarily an integer
C. p/q
4/3
Not necessarily an integer
D. pq/r
1
Let us take r = 12 ; p=2; q =3
6/12
Not necessarily an integer
E. r(p + q)/pq
12*5/6=10
r (1/p + 1/q) = r/p + r/q = k1 + k2 = integer

IMO E
avatar
valedipalo
Joined: 20 Jan 2020
Last visit: 20 Jun 2020
Posts: 10
Own Kudos:
Given Kudos: 12
Posts: 10
Kudos: 3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The first thing is about writing the information in the right way. We know that:
r= N*q
r= M*p 
In whihc M and N are just random numbers. 
At this point to make the problem easier we are going to take the simplest number made out of 4 different prime factor: 210 ( 2*3*5*7 ) and put p=2 and q=3. 
At this point we go to test he cases. 

E)210*5 / 6 = 175
User avatar
GMAT4goodunis
Joined: 26 Jan 2025
Last visit: 15 Apr 2025
Posts: 1
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunel, maybe I think incorrectly about it by why isn't the answer C?

We know:
1) r=aq (where a is a factor, i.e. ingeter)
2) p=br (where b is a factor, i.e. integer)

So: p=abq
p/q = ab = integer * integer = integer

Could you kindly clarify what you thinking is / where my reasoning is incorrect?

Thank you in advance!

Bunuel
goodyear2013
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?

A. (p + q)/r
B. (r + p)/q
C. p/q
D. pq/r
E. r(p + q)/pq

Premier P716

We have that r is a multiple of both q and p.

A. (p + q)/r. Not necessarily true. Consider r = 3, and p = q = 1.

B. (r + p)/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

C. p/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

D. pq/r. Not necessarily true. Consider r = 3, and p = q = 1.

E. \(\frac{r(p + q)}{pq}= \frac{rp+rq}{pq}=\frac{rp}{pq}+\frac{rq}{pq}=\frac{r}{q}+\frac{r}{p}=integer+integer=integer.\)

Answer: E.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Jun 2025
Posts: 102,292
Own Kudos:
Given Kudos: 94,011
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,292
Kudos: 735,211
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMAT4goodunis
Hi Bunel, maybe I think incorrectly about it by why isn't the answer C?

We know:
1) r=aq (where a is a factor, i.e. ingeter)
2) p=br (where b is a factor, i.e. integer)

So: p=abq
p/q = ab = integer * integer = integer

Could you kindly clarify what you thinking is / where my reasoning is incorrect?

Thank you in advance!

Bunuel
goodyear2013
If p, q, and r are positive integers such that q is a factor of r, and r is a multiple of p, which of the following must be an integer?

A. (p + q)/r
B. (r + p)/q
C. p/q
D. pq/r
E. r(p + q)/pq

Premier P716

We have that r is a multiple of both q and p.

A. (p + q)/r. Not necessarily true. Consider r = 3, and p = q = 1.

B. (r + p)/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

C. p/q. Not necessarily true. Consider r = 6, and p = 2 and q=3.

D. pq/r. Not necessarily true. Consider r = 3, and p = q = 1.

E. \(\frac{r(p + q)}{pq}= \frac{rp+rq}{pq}=\frac{rp}{pq}+\frac{rq}{pq}=\frac{r}{q}+\frac{r}{p}=integer+integer=integer.\)

Answer: E.
r is a multiple of p means r = p * integer, not p = r * integer.
Moderators:
Math Expert
102292 posts
PS Forum Moderator
657 posts