|
Author |
Message |
|
TAGS:
|
|
|
Director
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 664
Followers: 21
Kudos [?]:
109
[1] , given: 31
|
If n is a positive integer, is n^3 n divisible by 4 ? [#permalink]
 23 Feb 2011, 22:25
1
This post received
KUDOS
Question Stats:
63% (02:03) correct
36% (01:40) wrong based on 30 sessions
Last edited by Baten80 on 24 Feb 2011, 03:52, edited 1 time in total.
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12099
Followers: 1876
Kudos [?]:
10100
[2] , given: 959
|
Re: OG DS 170Arithmetic [#permalink]
24 Feb 2011, 03:29
2
This post received
KUDOS
Baten80 wrote: 170. If n is a positive integer, is n3 – n divisible by 4 ?
(1) n = 2k + 1, where k is an integer.
(2) n2 + n is divisible by 6. If n is a positive integer, is n^3 – n divisible by 4 ?n^3-n=n(n^2-1)=(n-1)n(n+1), so we are asked whether the product of 3 consecutive integers is divisible bu 4. (1) n = 2k + 1, where k is an integer --> n=odd --> as n is odd then both n-1 and n+1 are even hence (n-1)n(n+1) is divisible by 4. Sufficient. (2) n^2 + n is divisible by 6 --> if n=2 then n^3-n=6 and the answer is NO but if n=3 then n^3-n=24 and the answer is YES. Not sufficient. Answer: A. P. S. Baten80 please format the questions properly.
_________________
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
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 26 Dec 2011
Posts: 118
Followers: 1
Kudos [?]:
6
[0], given: 17
|
Re: If n is a positive integer, is n^3 n divisible by 4 ? (1) n [#permalink]
18 Apr 2012, 04:11
In the statement one when we express n=2k+1, why cant we take k=0, in that case n=1 and the product will be zero...Can we say then zero is divisible by 4?
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12099
Followers: 1876
Kudos [?]:
10100
[0], given: 959
|
Re: If n is a positive integer, is n^3 n divisible by 4 ? (1) n [#permalink]
18 Apr 2012, 04:14
pavanpuneet wrote: In the statement one when we express n=2k+1, why cant we take k=0, in that case n=1 and the product will be zero...Can we say then zero is divisible by 4? Zero is a divisible by every integer, except zero itself. Or which is the same: zero is a multiple of every integer, except zero itself. Integer a is a multiple of integer b means that a is "evenly divisible" by b, i.e., divisible by b without a remainder. Now, since zero/integer=integer then zero is a multiple of every integer (except zero itself). Check Number Theory chapter of Math Book for more: math-number-theory-88376.htmlHope it helps.
_________________
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
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 01 Apr 2010
Posts: 212
Location: Kuwait
GMAT 1: 710 Q49 V37
GPA: 3.2
WE: Information Technology (Consulting)
Followers: 1
Kudos [?]:
16
[0], given: 4
|
Re: If n is a positive integer, is n^3 n divisible by 4 ? (1) n [#permalink]
23 Apr 2012, 12:32
Great info on number theory, did not know that... have to brush up on the basics.
|
|
|
|
|
|
Manager
Joined: 28 Jul 2011
Posts: 212
Followers: 0
Kudos [?]:
15
[0], given: 12
|
If n is a positive integer, is n^3 n divisible by 4 ? [#permalink]
10 Jun 2012, 14:18
If n is a positive integer, is n^3 - n divisible by 4?
(1) n = 2K + 1, where k is an integer
(2) n^2 + n is divisible by 6
Vote for A
(A) n = 2K + 1 therefore n = {1,3,5,7,9,11 ......}
when n=3 then 3(9-1) is divisible by 4 sufficient
all values of n = {1,3,5,7,9,11 ......} will be divisiable by 4
Information sufficent
(B) n^2 + n is divisible by 6
n(n+1) = 6q (q = any multiple of 6)
n & (n+1) are +ve consecutive integers and therefore co-prime numbers
therefore when
n=6 (n+1) = 7 divisible by 6 but not by 4
n=12 (n+1) = 13 divisible by 6 and 4
Information not sufficent
|
|
|
|
|
|
Intern
Joined: 14 Mar 2012
Posts: 28
Concentration: International Business, Finance
GMAT 1: 590 Q32 V30
GMAT 2: 700 Q48 V37
GPA: 3.6
Followers: 0
Kudos [?]:
14
[0], given: 28
|
Re: If n is a positive integer, is n^3 n divisible by 4 ? (1) n [#permalink]
15 Jun 2012, 15:37
Bunuel wrote: pavanpuneet wrote: In the statement one when we express n=2k+1, why cant we take k=0, in that case n=1 and the product will be zero...Can we say then zero is divisible by 4? Zero is a divisible by every integer, except zero itself. Or which is the same: zero is a multiple of every integer, except zero itself. Integer a is a multiple of integer b means that a is "evenly divisible" by b, i.e., divisible by b without a remainder. Now, since zero/integer=integer then zero is a multiple of every integer (except zero itself). Check Number Theory chapter of Math Book for more: math-number-theory-88376.htmlHope it helps. Sorry Bunuel, just to make this clear if k = 0 then n = 1 (2 * 0 + 1) this means that (n-1)(n)(n+1) is 0 * 1 * 2 which is 0 (zero) and therefore divisible by 4 because zero is divisible by 4 ... right?
_________________
Give kudos if you find my post helpful 
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12099
Followers: 1876
Kudos [?]:
10100
[1] , given: 959
|
Re: If n is a positive integer, is n^3 n divisible by 4 ? (1) n [#permalink]
15 Jun 2012, 19:02
1
This post received
KUDOS
solarzj wrote: Bunuel wrote: pavanpuneet wrote: In the statement one when we express n=2k+1, why cant we take k=0, in that case n=1 and the product will be zero...Can we say then zero is divisible by 4? Zero is a divisible by every integer, except zero itself. Or which is the same: zero is a multiple of every integer, except zero itself. Integer a is a multiple of integer b means that a is "evenly divisible" by b, i.e., divisible by b without a remainder. Now, since zero/integer=integer then zero is a multiple of every integer (except zero itself). Check Number Theory chapter of Math Book for more: math-number-theory-88376.htmlHope it helps. Sorry Bunuel, just to make this clear if k = 0 then n = 1 (2 * 0 + 1) this means that (n-1)(n)(n+1) is 0 * 1 * 2 which is 0 (zero) and therefore divisible by 4 because zero is divisible by 4 ... right? Exactly so: if n=1 then (n-1)(n)(n+1)=0*1*2=0 and 0 is divisible by every positive integer including 4.
_________________
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
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
Re: If n is a positive integer, is n^3 n divisible by 4 ? (1) n
[#permalink]
15 Jun 2012, 19:02
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
If n is a positive integer, is n^3 - n divisible by 4? (1) n
|
TeHCM |
15 |
24 Oct 2005, 22:12 |
 |
|
|
If n is a positive integer, is n^3-n divisible by 4? 1) n =
|
Matador |
7 |
15 Apr 2006, 21:07 |
|
|
|
|
If n is a positive integer, is n^3 - n divisible by 4? (1) n
|
focused07 |
5 |
20 Jan 2007, 22:26 |
|
|
|
|
If n is positive integer, is (n^3 - n) divisible by 4? 1. n
|
LoyalWater |
5 |
08 Sep 2008, 14:34 |
|
|
|
|
If n is a positive integer, is n^3 - n divisible by 4? (1) n
|
btm3 |
2 |
18 Jun 2011, 22:09 |
|
|
|
|
|
|
close
