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

It is currently 16 Aug 2018, 06:45

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

If p, q and r are integers, and pq + r

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

Hide Tags

Manager
Manager
avatar
G
Joined: 19 Aug 2016
Posts: 153
Location: India
GMAT 1: 640 Q47 V31
GPA: 3.82
Reviews Badge
If p, q and r are integers, and pq + r  [#permalink]

Show Tags

New post 12 Nov 2017, 11:35
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

48% (02:11) correct 52% (01:58) wrong based on 82 sessions

HideShow 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.

_________________

Consider giving me Kudos if you find my posts useful, challenging and helpful!

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1201
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
If p, q and r are integers, and pq + r  [#permalink]

Show Tags

New post 12 Nov 2017, 12:08
2
1
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
Manager
Manager
User avatar
G
Joined: 03 Mar 2018
Posts: 183
Premium Member
Re: If p, q and r are integers, and pq + r  [#permalink]

Show Tags

New post 20 Mar 2018, 11:01
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
_________________

Please mention my name in your valuable replies.

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6527
Re: If p, q and r are integers, and pq + r  [#permalink]

Show Tags

New post 20 Mar 2018, 18:38
2
1
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 1894
Re: If p, q and r are integers, and pq + r  [#permalink]

Show Tags

New post 26 Mar 2018, 04:51

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:

Image

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
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: If p, q and r are integers, and pq + r &nbs [#permalink] 26 Mar 2018, 04:51
Display posts from previous: Sort by

If p, q and r are integers, and pq + r

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

Events & Promotions

PREV
NEXT


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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.