It is currently 23 Sep 2017, 06:10
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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 Workbook Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

If x is an integer, is x^3 divisible by 9?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Intern
Intern
avatar
Joined: 17 Jun 2013
Posts: 24

Kudos [?]: 52 [0], given: 20

If x is an integer, is x^3 divisible by 9? [#permalink]

Show Tags

New post 13 Jan 2014, 01:03
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

67% (00:55) correct 33% (00:46) wrong based on 216 sessions

HideShow timer Statistics

If x is an integer, is x^3 divisible by 9?

(1) x^2 is divisible by 9.

(2) x^4 is divisible by 9.
[Reveal] Spoiler: OA

Kudos [?]: 52 [0], given: 20

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41695

Kudos [?]: 124572 [1], given: 12079

Premium Member CAT Tests
Top Member of the Month
If x is an integer, is x^3 divisible by 9? [#permalink]

Show Tags

New post 13 Jan 2014, 01:13
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
If x is an integer, is x^3 divisible by 9?

Important thing to know when solving this problem is that exponentiation does not "produce" primes. For example, for integer x if x^(positive integer) is divisible by 3, then x must be divisible by 3. How else would 3 appear in x^(positive integer)?

(1) x^2 is divisible by 9 --> x^2 is divisible by 3^2 --> x is divisible by 3 --> x^3 is divisible by 3^3*k, thus it's divisible by 9 too. Sufficient.

(2) x^4 is divisible by 9 --> the same here: x^4 is divisible by 3^2 --> x is divisible by 3 --> x^3 is divisible by 3^3*k, thus it's divisible by 9 too. Sufficient.

Answer: D.

Hope it's clear.
_________________

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

Kudos [?]: 124572 [1], given: 12079

Manager
Manager
avatar
Joined: 25 Oct 2013
Posts: 169

Kudos [?]: 68 [0], given: 56

Re: If x is an integer, is x^3 divisible by 9? [#permalink]

Show Tags

New post 01 Feb 2014, 07:47
Hi Bunuel, is it okay to reason stmt2 as below?

\(x^4\) is divisible by 9.
then either
a. x is divisible by 9 or
b. \(x^3\) is divisible by 9.

If a is true then b is also true.
if a is not true then b has to be true. therefore for \(x^4\) to be divisible by 9, \(x^3\) MUST be divisible by 9.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

Kudos [?]: 68 [0], given: 56

Intern
Intern
User avatar
Joined: 11 Oct 2012
Posts: 42

Kudos [?]: 9 [0], given: 74

GMAT 1: 610 Q42 V32
GMAT ToolKit User Reviews Badge
Re: If x is an integer, is x^3 divisible by 9? [#permalink]

Show Tags

New post 26 Sep 2014, 21:31
Bunuel wrote:
russ9 wrote:
If x is an integer, is x^3 divisible by 9?

1) x^2 is divisible by 9
2) x^4 is divisible by 9


Merging similar topics. Please refer to the discussion above.



Why cant we consider the case where x= sqrt 3; in that case x^3 will be divisible by 3sqrt 3

Kudos [?]: 9 [0], given: 74

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41695

Kudos [?]: 124572 [0], given: 12079

Premium Member CAT Tests
Top Member of the Month
If x is an integer, is x^3 divisible by 9? [#permalink]

Show Tags

New post 27 Sep 2014, 01:23
Expert's post
ani781 wrote:
Bunuel wrote:
russ9 wrote:
If x is an integer, is x^3 divisible by 9?

1) x^2 is divisible by 9
2) x^4 is divisible by 9


Merging similar topics. Please refer to the discussion above.



Why cant we consider the case where x= sqrt 3; in that case x^3 will be divisible by 3sqrt 3


Because we are told that x is an integer, while \(\sqrt{3}\) is not. Also, what does divisibility by \(3\sqrt{3}\) has to do with the question? We need to find whether x^3 divisible by 9.

Also, note two things:
1. Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers (ALL GMAT divisibility questions are limited to positive integers only).

2. On the GMAT when we are told that \(a\) is divisible by \(b\) (or which is the same: "\(a\) is multiple of \(b\)", or "\(b\) is a factor of \(a\)"), we can say that:
(i) \(a\) is an integer;
(ii) \(b\) is an integer;
(iii) \(\frac{a}{b}=integer\).

For more check [url=http://gmatclub.com/forum/divisibility-multiples-factors-tips-and-hints-174998.html]Divisibility/Multiples/Factors: Tips and hints
[/url].

Hope it helps.
_________________

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

Kudos [?]: 124572 [0], given: 12079

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17613

Kudos [?]: 271 [0], given: 0

Premium Member
Re: If x is an integer, is x^3 divisible by 9? [#permalink]

Show Tags

New post 14 Sep 2016, 06:44
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 271 [0], given: 0

Re: If x is an integer, is x^3 divisible by 9?   [#permalink] 14 Sep 2016, 06:44
Print view
First unread post
    Similar topics Author Replies Last post
Similar
Topics:
 47 EXPERTS_POSTS_IN_THIS_TOPIC Is x^2*y^4 an integer divisible by 9 ? seekmba 21 31 May 2017, 07:32
1 EXPERTS_POSTS_IN_THIS_TOPIC If x is an integer, is 9^x + 9^-^x = b ? (1) 3^x + 3^-^x = b TehJay 6 15 Aug 2017, 05:21
2 If x is an integer, is x^3 divisible by 49 ? (1) x is guygmat 12 05 Jul 2011, 08:40
2 EXPERTS_POSTS_IN_THIS_TOPIC If x is an integer, is x^3 divisible by 7 abhinav008 6 14 Sep 2016, 06:41
1 EXPERTS_POSTS_IN_THIS_TOPIC If x is an integer, is x^3 divisible by 9? Bunuel 2 14 Jun 2016, 05:16
Display posts from previous: Sort by

If x is an integer, is x^3 divisible by 9?

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

Moderators: msk0657, abhimahna, Bunuel, Vyshak, Engr2012, mikemcgarry, Abhishek009, VeritasPrepKarishma, Skywalker18

Search for:


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions