Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 15 Aug 2013
Posts: 272

If n is a positive integer greater than 6, what is the remai [#permalink]
Show Tags
Updated on: 19 May 2014, 03:25
Question Stats:
54% (02:58) correct 46% (01:44) wrong based on 358 sessions
HideShow timer Statistics
If n is a positive integer greater than 6, what is the remainder when n is divided by 6? (1) n^2 – 1 is not divisible by 3. (2) n^2 – 1 is even.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by russ9 on 18 May 2014, 12:58.
Last edited by Bunuel on 19 May 2014, 03:25, edited 1 time in total.
Edited the question.



Intern
Joined: 16 Feb 2014
Posts: 20

Re: If n is a positive integer greater than 6, what? [#permalink]
Show Tags
18 May 2014, 20:01
How it can be C, because the n value where n^21 is not divisible by 6 is 9; and also if we consider n^21 is even we can get a lot numbers 48, 120, 80 etc.



Director
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If n is a positive integer greater than 6, what? [#permalink]
Show Tags
18 May 2014, 20:53
krishna789 wrote: How it can be C, because the n value where n^21 is not divisible by 6 is 9; and also if we consider n^21 is even we can get a lot numbers 48, 120, 80 etc. Q:If n is a positive integer greater than 6, what is the remainder when n is divided by 6?
(1) n2 – 1 is not divisible by 3.
(2) n2 – 1 is even. Ans is C and here is how St 1 tells us that n^21 is not divisible by 3 and we know n>6 so possible values of n =9,12,15,18...... Now if n =12,18,24... then n/6 gives remainder as 0 but if n=9,15,21 then remainder is 3 So from St1 we see that remainder will follow a pattern of 0,1,0,1.... Not sufficient from St 2 we we have n^21=even or n^2= Even +1 =odd, so we see that n is odd. Now if n=7 then n/6 gives remainder 1 but if n=9 then remainder is 3
if n=11 then remainder is 5 So St2 is not sufficient alone Combining we see that n is odd and n>6 so possible value of n satisfying the above conditions are n=9,15,21,27.....so on Remainder will be 3 Ans is C
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Intern
Joined: 08 Aug 2011
Posts: 22

Re: If n is a positive integer greater than 6, what? [#permalink]
Show Tags
Updated on: 19 May 2014, 15:12
russ9 wrote: If N is a positive integer greater than 6, what is the remainder when N is divided by 6? (1) N^2 – 1 is not divisible by 3. (2) N^2 – 1 is even. N is a positive integer > 6, what is the remainder when N is divided by 6?(1) N^2 – 1 is not divisible by 3.> N^2  1 = (N1)*(N+1) , and this is not divisible by three. Notice that (N1)*N*(N+1) is the product of three consecutive positive integers. Such a product will always contain exactly one multiple of 3. If this multiple of three is not (N1) or (N+1), then the multiple of 3 must be N. If N = 3*3=9, the remainder when divided by 6 is 3. If N = 3*4=12, the remainder when divided by 6 is 0. > Not sufficient. (Note: The product of K consecutive positive integers is always divisible by K!) (2) N^2 – 1 is even> N^2 = even + 1 = odd > N is odd. If N = 7, the remainder when divided by 6 is 1. If N = 9, the remainder when divided by 6 is 3. > Not sufficient. (1) and (2)N is an odd multiple of 3 greater than 6. > N = 3*(2k1) = 6k  3 for k >1. Thus, since N is three less than a multiple of six, the remainder is always 3. Sufficient.
Originally posted by Reinfrank2011 on 18 May 2014, 22:40.
Last edited by Reinfrank2011 on 19 May 2014, 15:12, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 46151

Re: If n is a positive integer greater than 6, what is the remai [#permalink]
Show Tags
19 May 2014, 03:34
If n is a positive integer greater than 6, what is the remainder when n is divided by 6? (1) n^2 – 1 is not divisible by 3 > (n1)(n+1) is not divisible by 3 > neither n1 not n+1 is divisible by 3. Since from any 3 consecutive integers one is divisible by 3, then n must be divisible by 3. If n is even too (12, 18, ...) then the remainder is 0 but if n is odd (9, 15, ...) then the reminder is 3. Not sufficient. (2) n^2 – 1 is even > n^2 = even + 1 = odd > n=odd. Not sufficient. (1)+(2) n is odd multiple of 3: 9, 15, 21, ... The remainder when n is divided by 6 is 3. Sufficient. Answer: C.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 15 Aug 2013
Posts: 272

Re: If n is a positive integer greater than 6, what is the remai [#permalink]
Show Tags
19 May 2014, 17:49
Bunuel wrote: If n is a positive integer greater than 6, what is the remainder when n is divided by 6? (1) n^2 – 1 is not divisible by 3 > (n1)(n+1) is not divisible by 3 > neither n1 not n+1 is divisible by 3. Since from any 3 consecutive integers one is divisible by 3, then n must be divisible by 3. If n is even too (12, 18, ...) then the remainder is 0 but if n is odd (9, 15, ...) then the reminder is 3. Not sufficient. (2) n^2 – 1 is even > n^2 = even + 1 = odd > n=odd. Not sufficient.
(1)+(2) n is odd multiple of 3: 9, 15, 21, ... The remainder when n is divided by 6 is 3. Sufficient.
Answer: C. Thanks for the explanation. I can definitely follow what you have outlined above but I wouldn't have been able to derive it on my own. Two questions: 1) Is it better to plug in numbers for these type of problems or work through the theory? 2) How do I get better at these specific types of problems? Is it just practice and if so, can you suggest similar problems please? Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 46151

Re: If n is a positive integer greater than 6, what is the remai [#permalink]
Show Tags
20 May 2014, 01:38
russ9 wrote: Bunuel wrote: If n is a positive integer greater than 6, what is the remainder when n is divided by 6? (1) n^2 – 1 is not divisible by 3 > (n1)(n+1) is not divisible by 3 > neither n1 not n+1 is divisible by 3. Since from any 3 consecutive integers one is divisible by 3, then n must be divisible by 3. If n is even too (12, 18, ...) then the remainder is 0 but if n is odd (9, 15, ...) then the reminder is 3. Not sufficient. (2) n^2 – 1 is even > n^2 = even + 1 = odd > n=odd. Not sufficient.
(1)+(2) n is odd multiple of 3: 9, 15, 21, ... The remainder when n is divided by 6 is 3. Sufficient.
Answer: C. Thanks for the explanation. I can definitely follow what you have outlined above but I wouldn't have been able to derive it on my own. Two questions: 1) Is it better to plug in numbers for these type of problems or work through the theory? 2) How do I get better at these specific types of problems? Is it just practice and if so, can you suggest similar problems please? Thanks! 1. Questions on remainders are good for plugin, but not all of them. It depends on a question and your skills/preferences what approach to choose. 2. By studying theory and practicing: Hope this 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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 04 Oct 2015
Posts: 349
Location: Viet Nam
Concentration: Finance, Economics
GPA: 3.56

Re: If n is a positive integer greater than 6, what is the remai [#permalink]
Show Tags
14 Apr 2017, 20:11
Here is my take! Statement 1: n^2  1 is not divisible by 3 > (n1)(n+1) is not divisible by 3 > n is divisible by 3 > insuff Statement 2: n^2  1 is odd > (n1)(n+1) is odd > n 1 is even > n is odd > insuff Statement 1+2: n is divisible by 3 > n = 3a n is even > n = 2b +1 So, n = 6c +3 > remainder when n is divided by 6 is 3 Hence, C!
_________________
Do not pray for an easy life, pray for the strength to endure a difficult one  Bruce Lee



Manager
Joined: 23 Dec 2013
Posts: 205
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44
GPA: 3.76

Re: If n is a positive integer greater than 6, what is the remai [#permalink]
Show Tags
22 May 2017, 20:44
russ9 wrote: If n is a positive integer greater than 6, what is the remainder when n is divided by 6? (1) n^2 – 1 is not divisible by 3. (2) n^2 – 1 is even. Goal: We need to know the remainder when n is divided by 6. Statement 1: (N^21)/3 =int. So (n+1)(n1)/3 is not an integer. Thus, n must be a multiple of three because every three consecutive integers has at least one multiple of three within it. Not sufficient because all it tells us is that n is a multiple of 3, so its remainder when divided by 6 has multiple potential values. Statement 2: N^2  1 is even. Hence (n+1)*(n1) is even, so n must be odd. Not sufficient because some odd numbers have different remainders when divided by 6. Combined: We know that N is an integer greater than 6 that is odd and a multiple of 3. Start testing cases: n=9 (r=3); n=15 (r=3); and so on. Sufficient.




Re: If n is a positive integer greater than 6, what is the remai
[#permalink]
22 May 2017, 20:44






