Author 
Message 
TAGS:

Hide Tags

Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 327

Given that n is an integer, is n 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 05:36
2
This post received KUDOS
7
This post was BOOKMARKED
Question Stats:
65% (02:10) correct
35% (01:30) wrong based on 385 sessions
HideShow timer Statistics
Given that n is an integer, is n — 1 divisible by 3? (1) n^2 + n is not divisible by 3 (2) 3n +5 >= k+8 , where k is a positive multiple of 3
Official Answer and Stats are available only to registered users. Register/ Login.



Senior Manager
Joined: 25 Jun 2009
Posts: 302

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 05:59
dimitri92 wrote: Given that n is an integer, is n — 1 divisible by 3? (1) n^2 + n is not divisible by 3 (2) 3n +5 >= k+8 , where k is a positive multiple of 3 A, St1 \(n^2 + n = n* (n +1)\) is not divisible by 3 which means neither n nor n+1 is divisble by 3 hence n1 will be divisble by 3 St2  3n +5 >= k +8 = > 3n >= K Now n can be a divisble by 3 or not for .e g take n = 3 and k = 2 then n is divisble by 3 but if n =4 and k = 2 then n is not. OA please?



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2783
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 07:48
1
This post received KUDOS
dimitri92 wrote: Given that n is an integer, is n — 1 divisible by 3? (1) n^2 + n is not divisible by 3 (2) 3n +5 >= k+8 , where k is a positive multiple of 3 IMO C. n^2+n = n(n+1) is not divisible by 3 => n1 is divisible by 3 IF N is no equal to 0,1,1 else this wont hold true, thus not sufficient. 3n +5 >= k+8 => 3n >= k+3 , take k = 3m as k is positive multiple of 3 => 3n>=3m+3 => n >= m+1 => n>1 Not sufficient. But if we combine the both then n1 is divisible by 3 when n>1 Thus C
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Senior Manager
Joined: 25 Jun 2009
Posts: 302

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 07:55
1
This post received KUDOS
gurpreetsingh wrote: dimitri92 wrote: Given that n is an integer, is n — 1 divisible by 3? (1) n^2 + n is not divisible by 3 (2) 3n +5 >= k+8 , where k is a positive multiple of 3 IMO C. n^2+n = n(n+1) is not divisible by 3 => n1 is divisible by 3 IF N is no equal to 0,1,1 else this wont hold true, thus not sufficient. 3n +5 >= k+8 => 3n >= k+3 , take k = 3m as k is positive multiple of 3 => 3n>=3m+3 => n >= m+1 => n>1 Not sufficient. But if we combine the both then n1 is divisible by 3 when n>1 Thus C n^2+n = n(n+1) is not divisible by 3 => n1 is divisible by 3 IF N is no equal to 0,1,1 else this wont hold true, thus not sufficient.I guess you overlooked some facts, Let me try to explain them with examples, Say, n=0 then n(n+1) = 0 > which is divisble by 3 and hence the st 1 is not valid for this example Now let n=1 then n(n+1)  > 2 which is not diviable by 3 but then n1 = 0 which is divisble by 3 Now let n=1 then n(n+1) = 0 which is again divisble y 3 and hence St 1 does not hold true for this example as well. Cheers,



Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 327

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 08:07
nitishmahajan wrote: gurpreetsingh wrote: dimitri92 wrote: Given that n is an integer, is n — 1 divisible by 3? (1) n^2 + n is not divisible by 3 (2) 3n +5 >= k+8 , where k is a positive multiple of 3 IMO C. n^2+n = n(n+1) is not divisible by 3 => n1 is divisible by 3 IF N is no equal to 0,1,1 else this wont hold true, thus not sufficient. 3n +5 >= k+8 => 3n >= k+3 , take k = 3m as k is positive multiple of 3 => 3n>=3m+3 => n >= m+1 => n>1 Not sufficient. But if we combine the both then n1 is divisible by 3 when n>1 Thus C n^2+n = n(n+1) is not divisible by 3 => n1 is divisible by 3 IF N is no equal to 0,1,1 else this wont hold true, thus not sufficient.I guess you overlooked some facts, Let me try to explain them with examples, Say, n=0 then n(n+1) = 0 > which is divisble by 3 and hence the st 1 is not valid for this example Now let n=1 then n(n+1)  > 2 which is not diviable by 3 but then n1 = 0 which is divisble by 3 Now let n=1 then n(n+1) = 0 which is again divisble y 3 and hence St 1 does not hold true for this example as well. Cheers, ok great catch ..but are you suggesting A or C then ?



CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2783
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 08:08
1
This post received KUDOS
yes right, got it Thanks should be A
_________________
Fight for your dreams :For all those who fear from Verbal lets give it a fight
Money Saved is the Money Earned
Jo Bole So Nihaal , Sat Shri Akaal
Support GMAT Club by putting a GMAT Club badge on your blog/Facebook
GMAT Club Premium Membership  big benefits and savings
Gmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Manager
Joined: 04 Feb 2010
Posts: 63
Schools: IESE '13
WE 1: Engineer

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 19:47
3
This post received KUDOS
1  neither n or n+1 are divisible by 3. Thus, n1 must be divisible by 3, since every 3rd integer is divisible by 3. SUFF
2  3n + 5 >= k + 8
3n  3 >= k
3(n1) >= k
Because we know k is divisible by 3, but not 9 (3x3), n1 could or could not be divisible by 3. INS
Answer A



Manager
Joined: 08 May 2010
Posts: 143

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
18 May 2010, 22:39
I completely understand how statement 1 is sufficient, but am going to have to review statement 2 further to understand why it is not sufficient. I understand the simple math just not the explanation that follows.
Good question though. Had me thinking. Thank you very much.



Current Student
Joined: 26 May 2005
Posts: 563

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
19 Jul 2011, 03:30
its MGMAT
The OE for statement 1.
Since we are told in Statement (1) that the product n^2+n is not divisible by 3, we know that neither n nor n + 1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3. However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does not tell us this, it is not sufficient.
I dont buy this ...



Current Student
Joined: 08 Jan 2009
Posts: 326

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
19 Jul 2011, 03:45
sudhir18n wrote: its MGMAT
The OE for statement 1.
Since we are told in Statement (1) that the product n^2+n is not divisible by 3, we know that neither n nor n + 1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3. However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does not tell us this, it is not sufficient.
I dont buy this ... Neither. Here is my logic: We know this from the question stem: n = Set of all integers = {..., 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, ... } 1) n^2 + n is not divisible by 3We now know: n = {... 11, 8, 5, 2, 1, 4, 7, 10, ...} < very clear pattern here We are interested in n1 (but only from the above set, which meet our condition imposed on 1) n  1 = {..., 12, 9, 6, 3, 0, 3, 6, 9, ... } Let's check these against what ware testing for, are these divisible by three? Very clearly, yes. 1 is sufficient.



Manager
Joined: 14 Apr 2011
Posts: 196

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
19 Jul 2011, 04:47
Answer seems to be A. if n(n+1) is not divisible by 3 that itself means that n or n+1 cannot be 0.
_________________
Looking for Kudos



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
19 Jul 2011, 05:48
sudhir18n wrote: its MGMAT
The OE for statement 1.
Since we are told in Statement (1) that the product n^2+n is not divisible by 3, we know that neither n nor n + 1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3. However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does not tell us this, it is not sufficient. I dont buy this ... Thanks Sudhir. Please notify MGMAT. Product of three consecutive integers must be divisible by 3 irrespective of 0, ves or +ves. (n1)n(n+1) must be divisible by 3. n(n+1): Not Divisible (n1): must be divisible
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 07 Mar 2011
Posts: 51

Re: is n — 1 divisible by 3? [#permalink]
Show Tags
19 Jul 2011, 05:58
A is the answer, if we consider "0" is divisible by "3" otherwise C. I would lean towards A



Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]
Show Tags
31 Mar 2013, 07:16
Can experts say the final word regarding option (1)? I wonder whether A is sufficient
_________________
Happy are those who dream dreams and are ready to pay the price to make them come true
I am still on all gmat forums. msg me if you want to ask me smth



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]
Show Tags
31 Mar 2013, 07:55
LalaB wrote: Can experts say the final word regarding option (1)? I wonder whether A is sufficient Given that n is an integer, is n — 1 divisible by 3?(1) n^2 + n is not divisible by 3 > n(n+1) is not divisible by 3 > neither n nor n+1 is divisible by 3. Now, n1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n1 must be. Sufficient. (2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient. Answer: A. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 28 Jan 2013
Posts: 9
Location: India
Concentration: Marketing, International Business
GPA: 3
WE: Marketing (Manufacturing)

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]
Show Tags
02 Jun 2013, 13:25
Bunuel wrote: LalaB wrote: Can experts say the final word regarding option (1)? I wonder whether A is sufficient Given that n is an integer, is n — 1 divisible by 3?(1) n^2 + n is not divisible by 3 > n(n+1) is not divisible by 3 > neither n nor n+1 is divisible by 3. Now, n1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n1 must be. Sufficient. (2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient. Answer: A. Hope it's clear. Can you kindly explain why B is not sufficient...



Math Expert
Joined: 02 Sep 2009
Posts: 39673

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]
Show Tags
02 Jun 2013, 13:56
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
karjan07 wrote: Bunuel wrote: LalaB wrote: Can experts say the final word regarding option (1)? I wonder whether A is sufficient Given that n is an integer, is n — 1 divisible by 3?(1) n^2 + n is not divisible by 3 > n(n+1) is not divisible by 3 > neither n nor n+1 is divisible by 3. Now, n1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n1 must be. Sufficient. (2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient. Answer: A. Hope it's clear. Can you kindly explain why B is not sufficient... Sure. (2) says that 3n +5 >= k+8 , where k is a positive multiple of 3 > k=3x, for some positive integer x > \(3n +5\geq{3x+8}\) > \(3n3\geq{3x}\) > \(n1\geq{x}\). So, basically we just have that n1 is greater or equal to some positive integer x, thus it may or may not be a multiple of 3. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Feb 2013
Posts: 59

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]
Show Tags
03 Sep 2013, 06:12
Quote: (2) says that 3n +5 >= k+8 , where k is a positive multiple of 3 > k=3x, for some positive integer x > \(3n +5\geq{3x+8}\) > \(3n3\geq{3x}\) > \(n1\geq{x}\). So, basically we just have that n1 is greater or equal to some positive integer x, thus it may or may not be a multiple of 3. Just to go a bit further on this, in what case would \(n1\) be divisible by \(3\)? Say if you ended up with \(n1\geq{3x}\) it would still be insufficient, is not it so? The fact that we have \(\geq\) seems to necessarily mean that \(n1\) may not necessarily be divisible because we have so many options, or I am missing the point here?
_________________
There are times when I do not mind kudos...I do enjoy giving some for help



Current Student
Joined: 06 Sep 2013
Posts: 1997
Concentration: Finance

Re: Given that n is an integer, is n 1 divisible by 3? [#permalink]
Show Tags
30 Dec 2013, 10:10
dimitri92 wrote: Given that n is an integer, is n — 1 divisible by 3?
(1) n^2 + n is not divisible by 3 (2) 3n +5 >= k+8 , where k is a positive multiple of 3 The product of three consecutive integers (n1)(n)(n+1) must be divisible by 2 Statement 1 If n^2+n= n(n+1) is not divisible by three then (n1) must be divisible by 3 Suff Statement 2 If k is a multiple of three Then we get that 3n >= k + 3 This only tell us that n >=1 but nothing else. Could be any number Hence, answer is A Hope it helps Cheers! J That means that n



Manager
Joined: 10 Mar 2014
Posts: 245

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink]
Show Tags
26 Apr 2014, 04:25
Bunuel wrote: LalaB wrote: Can experts say the final word regarding option (1)? I wonder whether A is sufficient Given that n is an integer, is n — 1 divisible by 3?(1) n^2 + n is not divisible by 3 > n(n+1) is not divisible by 3 > neither n nor n+1 is divisible by 3. Now, n1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n1 must be. Sufficient. (2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient. Answer: A. Hope it's clear. Hi Bunnel, I choose ans as D. st1 is fine no issue. my reasoning in st2 3n+5 >= k+8 3n+5 >= k+5+3 3n >= k+3 3n3>k 3(n1)>k cant we say that n1 is a multiple of 3? Please clarify Thanks.




Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 +
[#permalink]
26 Apr 2014, 04:25



Go to page
1 2
Next
[ 23 posts ]




