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

It is currently 21 Jan 2019, 06:34

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

     January 21, 2019

     January 21, 2019

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
  • The winners of the GMAT game show

     January 22, 2019

     January 22, 2019

     10:00 PM PST

     11:00 PM PST

    In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

If x and y are integers, is xy + 1 divisible by 3?

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52343
If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 09 Dec 2014, 15:02
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:21) correct 25% (01:24) wrong based on 289 sessions

HideShow timer Statistics

Project DS Butler: Day 27: Data Sufficiency (DS54)


For DS butler Questions Click Here


Tough and Tricky questions: Word Problems.

Tough and Tricky questions: Remainders.



If x and y are integers, is xy + 1 divisible by 3?

(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.

Kudos for a correct solution.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
Joined: 08 Jul 2012
Posts: 47
Re: If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 09 Dec 2014, 20:00
3
1
If x and y are integers, is xy + 1 divisible by 3?

(1) When x is divided by 3, the remainder is 1 --> x=3n+1, if x=1, then 1*y+1 when y=1 not div by 3 and when y=2 div by 3 => insufficient
(2) When y is divided by 9, the remainder is 8 -->y=9m+8, if y=1, then x*1+1 when x=1 not div by 9 and when x=8 div by 9 => insufficient

(1) + (2) :
x=3n+1 and y=9m+8 where m and n are integers=> xy+1=(3n+1)(9m+8)+1 =27mn+9m+24n+8+1 =27mn+9m+24n+9 => this is div by 3 always hence is sufficient => C

Ans. C)
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison

Manager
Manager
avatar
Joined: 22 Sep 2012
Posts: 129
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 09 Dec 2014, 20:15
Given x and y are integers. We have to find out whether xy+1 is divisible by 3 ?

Statement 1: When x is divided by 3, the remainder is 1

Therefore, x can be represented as 3*a+1 ( where a is an integer)
therefore, xy+1 => (3*a+1)*y+1

Since 3*a*y is divisible by 3, we have to find out whether (y+1) is divisible by 3.


Statement 2:
When y is divided by 9, the remainder is 8. Clearly insufficient, since we don't know the value of x.
But, we can say that y => 9*b+8 ( where b is an integer)

Combining 1) and 2), we can say y+1 = 9*b + 9 is divisible by 3. Hence the answer should be C
Manager
Manager
User avatar
Joined: 14 Oct 2014
Posts: 66
Location: United States
GMAT 1: 500 Q36 V23
Re: If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 09 Dec 2014, 20:22
2
Question: remainder of (x*y +1)?
(1) Not sufficient. Just tells that x could be equal to 4, 10, 13,.... but nothing about y.
(2) Not sufficient. Just tell that y could be 17, 26, 35,...but no information about x.

(1)+(2) Sufficient.
If x=10, y=26, then (10*26 + 1) = 261 ----->which is divisible by 3, so the remainder is 0
If x=4, y=35, then (4*35 + 1) = 141 ----> divisible by 3, so the remainder equals 0

Answer C
Manager
Manager
avatar
Joined: 04 Oct 2013
Posts: 152
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
GMAT ToolKit User Premium Member Reviews Badge
Re: If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 10 Dec 2014, 01:11
4
If x and y are integers, is xy + 1 divisible by 3?

(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.


Statement 1
x = 3m+1; m is an integer
no information on y, hence insufficient.

Statement 2
y= 9n +8; n is an integer
no information on x, hence insufficient.

Combining statements (1) and (2) and substituting x and y as (3m+1) and (9n+8)
xy +1 = (3m+1)(9n+8)+1 = 27mn+24m+9n+9 = 3*(9mn+8m+3n+3) --> xy+1 is divisible by 3
Hence, both statements together are sufficient

Answer: C
Intern
Intern
avatar
B
Joined: 07 Jun 2018
Posts: 24
Location: India
Concentration: Entrepreneurship, Marketing
Schools: Wharton '21, Haas '21
Re: If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 24 Nov 2018, 21:47
Should be C, since:
xy + 1 = (3ka+1)y = 3ka*y +y = 3kb + 1 + 9kc + 8 = 3kb + 9kc + 9 = multiple of 3.
Hence C.
_________________

If you liked my post, kindly give me a Kudos. Thanks.

VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1287
Re: If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 25 Nov 2018, 02:39
Bunuel wrote:

Tough and Tricky questions: Remainders.



If x and y are integers, is xy + 1 divisible by 3?

(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.

Kudos for a correct solution.



Statement One: If x is divided by 3, then x is even number, i.e. 4 (since no info is given on Y- INSFFICIENT y can be 1 or 3 for example)

Statement Two: When Y is divided by 9, remainder is 8, I.E. y = 9q+8 , so possible values for Y are 8, 17, 26, 35 etc (INSUFFICIENT)


Combining both we know that x is 4, 7, 10 etc and y is 8, 17, 26, 35 etc. hence xy + 1 divisible by 3


C :)
Intern
Intern
avatar
B
Joined: 03 Sep 2018
Posts: 44
Re: If x and y are integers, is xy + 1 divisible by 3?  [#permalink]

Show Tags

New post 09 Dec 2018, 10:15
My approach:
Stem: If x and y are integers, is xy + 1 divisible by 3?
–> notice that xy+1 is divisible by three if xy is even (but not iff it is even)

(1) When x is divided by 3, the remainder is 1.
x=3q+1
–> not divisible by 3
–> y could be divisible by 3 or it could not be, producing two different answers
–> Hence, NOT SUFFICIENT

(2) When y is divided by 9, the remainder is 8.
–>Hence, the remainder when divided by 3 is also 8
–>However, x could be divisible by 3 or it could not be, producing two different answers
–>Hence, NOT SUFFICIENT

(1) & (2) together
—>From 1, we know that remainder is 1
—>From 2, we know that remainder is 8
—>Iff the remainder product of xy and the sum of the remainder product of xy and 1 add to 3, xy+1 must be divisible

HENCE, (remainder x) * (remainder y) + (1) = 8*1+1= 9, hence, xy+1 is always divisible by 3: C
_________________

Please consider giving Kudos if my post contained a helpful reply or question.

GMAT Club Bot
Re: If x and y are integers, is xy + 1 divisible by 3? &nbs [#permalink] 09 Dec 2018, 10:15
Display posts from previous: Sort by

If x and y are integers, is xy + 1 divisible by 3?

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


cron
Copyright

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®.