NEW HERE? LEARN MORE
closeclose
Last visit was: 10 May 2024, 02:24 It is currently 10 May 2024, 02:24
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

If p, q and r are integers, and pq + r is an odd integer, is p an even

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
ashikaverma13
Manager
Manager
Joined: 19 Aug 2016
Posts: 129
Own Kudos [?]: 294 [61]
Given Kudos: 59
Location: India
Schools: ISB '20 (WD) Schulich Sept 18 Intake (A) Rotman '20 (S)
GMAT 1: 640 Q47 V31
GPA: 3.82
Send PM
Reviews Badge
If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   12 Nov 2017, 11:35
60
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

49% (02:40) correct 51% (02:44) wrong based on 324 sessions
Hide Show timer Statistics
If p, q and r are integers, and pq + r is an odd integer, is p an even integer?


(1) pq + pr is an even integer.
(2) p + qr is an odd integer.
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11233
Own Kudos [?]: 32382 [30]
Given Kudos: 301
Send PM
Reviews Badge Forum Quiz Mode
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   20 Mar 2018, 18:38
27
Kudos
3
Bookmarks
Expert Reply
itisSheldon wrote:
chetan2u
Even Though i got the answer right, I took more than 2 minutes here. Is there any way to solve this question within a minute or two. I arrived at the correct answer by assuming 2 cases for each statement. Like
pq+r = odd, So case 1 pq=odd; r= even
Case 2 pq=even; r=odd



Hi..
pq is common in statement I and the main statement..
So try and remove it to get a fresh equation..
pq+pr is EVEN and pq+r is odd..
Subtract them so pq+pr-(pq+r)=EVEN-ODD=ODD..
So pq+pr-pq-r=pr-r=(p-1)r is ODD
So both p-1 and r are ODD..
If p-1 is odd, p will be even
Suff
User avatar
D
niks18
Retired Moderator
Joined: 25 Feb 2013
Posts: 894
Own Kudos [?]: 1529 [12]
Given Kudos: 54
Location: India
GPA: 3.82
Send PM
GMAT ToolKit User Reviews Badge
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   12 Nov 2017, 12:08
9
Kudos
3
Bookmarks
ashikaverma13 wrote:
If p, q and r are integers, and pq + r is an odd integer, is p an even integer?


(1) pq + pr is an even integer.
(2) p + qr is an odd integer.


Given \(pq+r=Odd\)

Statement 1: \(pq+pr=Even\), add \(r\) to both sides

\(pq+r+pr=Even+r => Odd+pr=Even+r\)

or \(pr-r=Even-Odd => r(p-1)=Odd\)

\(1\) is odd so \(p\) has to be even because if \(p\) is odd then \(p-1\) is even and \(r(p-1)\) will be even which is not possible. Sufficient

Statement 2: \(p+qr=Odd\)

so if \(p=even\) & \(r=Odd\) or \(p=odd\), \(q=odd\) and \(r=even\). So no unique solution. Insufficient

Option A

-------------------------------------------

Another method. Plug in some values and test
General Discussion
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3723
Own Kudos [?]: 16949 [8]
Given Kudos: 165
Send PM
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   26 Mar 2018, 04:51
5
Kudos
3
Bookmarks
Expert Reply

Solution



We are given:
    • \(p\), \(q\), and \(r\) are \(3\) integers.
    • \((p*q + r)\) is an odd integer.

\((p*q + r)\) can be odd for different cases, let us see:



Statement-1 “\((p * q + p * r)\) is an even integer.”

    • We can conclude \(p * (q + r)\) is an even integer.
    • \(p * (q + r)\) is an even integer for different cases among the above table.
      1. \(p\)= Even, \(q\)= Even, \(r\)= Odd
      2. \(p\)= Even, \(q\)= Odd, \(r\)= Odd

In both the cases, \(p\) is an even integer.
Hence, Statement 1 alone is sufficient to answer the question.


Statement-2 “\((p + q * r)\) is an odd integer”.

    • \(p + (q * r)\) is an odd integer for different cases among the above table.
      1. \(p\) = Odd, \(q\)= Even, \(r\)=Odd
      2. \(p\) = Odd, \(q\)= odd, \(r\)=Even
      3. \(p\) = Even, \(q\)= Odd, \(r\)=Odd

\(p\) can be even or odd.
Hence, Statement 2 alone is not sufficient to answer the question.

Answer: A
User avatar
P
itisSheldon
Manager
Manager
Joined: 03 Mar 2018
Posts: 165
Own Kudos [?]: 637 [2]
Given Kudos: 101
Send PM
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   20 Mar 2018, 11:01
2
Kudos
chetan2u
Even Though i got the answer right, I took more than 2 minutes here. Is there any way to solve this question within a minute or two. I arrived at the correct answer by assuming 2 cases for each statement. Like
pq+r = odd, So case 1 pq=odd; r= even
Case 2 pq=even; r=odd
User avatar
G
sambitspm
Senior Manager
Senior Manager
Joined: 05 Aug 2019
Posts: 317
Own Kudos [?]: 279 [0]
Given Kudos: 130
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GMAT 2: 670 Q50 V28 (Online)
GPA: 4
Send PM
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   24 Aug 2020, 02:58
It honestly took me 2-3 attempts to get to the right answer. We need to find the cases for p,q,r for pq+r as odd. And that's it. That was the trick.
Attachments

Method 1.png
Method 1.png [ 271.86 KiB | Viewed 14404 times ]

avatar
B
deepalidmoon
Intern
Intern
Joined: 23 Sep 2016
Posts: 9
Own Kudos [?]: 4 [0]
Given Kudos: 14
Send PM
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   07 Sep 2020, 10:45
Hi Payal Mam,

Why can't odd(odd+odd) which is even be considered in this case? P then becomes odd as well.

I am not able to understand this why p is not considered odd in this problem
User avatar
B
Anshu0012
Intern
Intern
Joined: 03 Jun 2018
Posts: 19
Own Kudos [?]: 4 [0]
Given Kudos: 32
Location: India
Schools: ISB '23 NTU NUS Bocconi
GMAT 1: 450 Q35 V17
Send PM
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   02 Oct 2020, 19:01
I have a doubt in Statement 1,Please clarify
If p(q+r)
If p=odd(3)
q+r=even(5+5)or (6+6)
then p(q+r) is also even.
so how could we so sure that P is even.

Need Experts advice

Thanks
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11233
Own Kudos [?]: 32382 [0]
Given Kudos: 301
Send PM
Reviews Badge Forum Quiz Mode
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   02 Oct 2020, 19:53
Expert Reply
Anshu0012 wrote:
I have a doubt in Statement 1,Please clarify
If p(q+r)
If p=odd(3)
q+r=even(5+5)or (6+6)
then p(q+r) is also even.
so how could we so sure that P is even.

Need Experts advice

Thanks


Then it will not satisfy pq+r to be an odd integer, a condition given in main statement.
3*5+5=20=even
3*6+6=24=even
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32896
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink] New post   31 Mar 2023, 02:51
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.
GMAT Club Bot
gmatclubot
Re: If p, q and r are integers, and pq + r is an odd integer, is p an even [#permalink]
31 Mar 2023, 02:51
Moderator:
Bunuel
Math Expert
93146 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