Find all School-related info fast with the new School-Specific MBA Forum

It is currently 29 Jul 2014, 08:50

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is x divisible by 30?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
VP
VP
User avatar
Joined: 22 Oct 2006
Posts: 1443
Schools: Chicago Booth '11
Followers: 7

Kudos [?]: 146 [3] , given: 12

GMAT Tests User
Is x divisible by 30? [#permalink] New post 13 Mar 2008, 07:57
3
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

32% (03:27) correct 68% (02:04) wrong based on 77 sessions
Is x divisible by 30?

(1) x = k(m^3 - m), where m and k are both integers > 9

(2) x = n^5 - n, where n is an integer > 9

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-divisible-by-126857.html
[Reveal] Spoiler: OA
Kaplan GMAT Prep Discount CodesKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3604
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 351

Kudos [?]: 1693 [0], given: 354

GMAT ToolKit User GMAT Tests User Premium Member
Re: DS - Divsibility [#permalink] New post 13 Mar 2008, 09:11
Expert's post
B

30=2*3*5

1. x = k(m^3 - m)=k*m*(m^2-1)=k*m*(m-1)(m+1)

(m-1),m,(m+1) are consecutive integers and the product of these integers will always be divisible by 6 (2 and 3).
But the consequence can be divisible by 5 or cannot be. Therefore, if k and the product are not divisible by 5, x will not be divisible by 30; if k or the product is divisible by 5, x will be divisible by 30. INSUFF.

2. x = n^5 - n=n*(n^4-1)=n*(n^2-1)*(n^2+1)=n*(n-1)*(n+1)*(n^2+1)

(n-1),n,(n+1) are consecutive integers and the product of these integers will always be divisible by 6 (2 and 3).

if n=5k, 5k+1, or 5k+4, the product will be divisible by 5 and therefore, by 30.
if n=5k+2 or 5k+3 the product will not be divisible by 5.
but: n=5k+2: (n^2+1)=(5k+2)^2+1=25k^2+20k+5=5*(5k^2+4k+1) Therefore, x is divisible by 30
n=5k+3: (n^2+1)=(5k+3)^2+1=25k^2+30k+10=5*(5k^2+6k+2) Therefore, x is also divisible by 30.
SUFF.
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

CEO
CEO
User avatar
Joined: 29 Aug 2007
Posts: 2501
Followers: 51

Kudos [?]: 484 [0], given: 19

GMAT Tests User
Re: DS - Divsibility [#permalink] New post 13 Mar 2008, 09:13
terp26 wrote:
Is x divisible by 30?

(1) x = k(m^3 - m), where m and k are both integers > 9
(2) x = n^5 - n, where n is an integer > 9


1: x = k(m^3 - m)
x = k m (m^2 - 1)
x = k m (m - 1) (m+1)
x = (k) (m - 1) (m) (m+1)

so x is a product of k and 3 consequtive integers (m-1) (m) and (m+1).
if k = 11 and m = 13, x is not divisible by 30.
if k = 10 and m = 13, x is divisible by 30. so nsf.

2: x = (n^5 - n) and integer n is >9,
x = n (n-1) (n+1) (n^2 + 1)

in this case, no matter the value of n, x is divisible by 30.
if n is, lets say, 12, x = 11(12) (13) (145) suff.
if n is, lets say, 13, x = 13 (12) (14) (13^2 + 1) = 12x13x14x140. suff.
if n is, lets say, 17, x = 16(17) (18) (290). so suff.

so B.
_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html
Math: new-to-the-math-forum-please-read-this-first-77764.html
Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1798
Followers: 166

Kudos [?]: 33 [0], given: 0

Premium Member
Re: Is x divisible by 30? (1) x = k(m^3 - m), where m and k are [#permalink] New post 06 Feb 2014, 09:38
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

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18816
Followers: 3263

Kudos [?]: 22698 [1] , given: 2640

Re: Is x divisible by 30? [#permalink] New post 07 Feb 2014, 04:09
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Is x divisible by 30?

(1) x = k*(m^3 - m), where m and k are both integers > 9 --> x=k*(m-1)m(m+1). Well, if k=30 then the answer is YES, but if k=11, then (m-1)m(m+1) only guarantees divisibility by 6, so the answer might be NO (for example m=12). Not sufficient.

(2) x = n^5 - n, where n is an integer > 9 --> the last digit of any integer in positive integer power repeats in pattern of 4 (some numbers have the pattern of 2 or 1, but pattern of 4 holds for them too). So, n^5 has the same last digit as n^1 or simply n, therefore the last digit of n^5-n is ALWAYS zero, so its ALWAYS divisible by 10. Next, n^5-n=n(n^4-1)=n(n^2-1)(n^2+1)=(n-1)n(n+1)(n^2+1) --> (n-1)n(n+1) is divisible by 3 (as there are 3 consecutive integers) --> n^5-n is divisible by 10*3=30. Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-divisible-by-126857.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Is x divisible by 30?   [#permalink] 07 Feb 2014, 04:09
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic If X is divisible by 2,6,9,12,15,30, is X divisible by 8? feellikequitting 6 12 Dec 2012, 12:28
15 Experts publish their posts in the topic Is x divisible by 30? enigma123 9 31 Jan 2012, 15:52
Is x divisible by 30? (1) X = k*(m^3 - m), where m and k are yezz 9 27 Sep 2006, 14:14
Is x divisible by 30? (1) X = k*(m^3 - m), where m and k are yezz 11 05 Sep 2006, 07:57
Is x divisible by 30? (1) X = k*(m^3 - m), where m and k are Professor 7 07 Jun 2006, 21:00
Display posts from previous: Sort by

Is x divisible by 30?

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.