Author 
Message 
TAGS:

Hide Tags

Director
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 514
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
21 Jan 2012, 17:57
Question Stats:
60% (01:08) correct 40% (01:07) wrong based on 1579 sessions
HideShow timer Statistics
If n is a positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r? (1) n is not divisible by 2 (2) n is not divisible by 3 As the OA is not provided can someone please let me know whether my solution is correct or not?
Considering question stem
Cannot be simplified any further apart from prime factorization for 24 which are 2^3 * 3
Considering Statement 1
n is ODD.
When n =1 Remainder will be zero. n=3 Remainder won't be zero n =5 Remainder will be zero Two answers therefore insufficient.
Considering Statement 2
n is not a multiple of 3. As it will give different value of r this statement alone is insufficient.
Combining both statement 1 & 2
n is not a multiple of 6 i.e. 2 and 3. So n is prime without 2. Therefore n can be 5, 7, 11,..etc and the remainder will be ZERO.Therefore answer should be c i.e. both statements together are sufficient to answer the question.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730



Math Expert
Joined: 02 Sep 2009
Posts: 46305

If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
21 Jan 2012, 18:12
enigma123 wrote: If n is a positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r? 1). n is not divisible by 2 2). n is not divisible by 3 If n is a positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r?Plugin method:\((n1)(n+1)=n^21\) (1) n is not divisible by 2 > pick two odd numbers: let's say 1 and 3 > if \(n=1\), then \(n^21=0\) and as zero is divisible by 24 (zero is divisible by any integer except zero itself) so remainder is 0 but if \(n=3\), then \(n^21=8\) and 8 divided by 24 yields remainder of 8. Two different answers, hence not sufficient. (2) n is not divisible by 3 > pick two numbers which are not divisible by 3: let's say 1 and 2 > if \(n=1\), then \(n^21=0\), so remainder is 0 but if \(n=2\), then \(n^21=3\) and 3 divided by 24 yields remainder of 3. Two different answers, hence not sufficient. (1)+(2) Let's check for several numbers which are not divisible by 2 or 3: \(n=1\) > \(n^21=0\) > remainder 0; \(n=5\) > \(n^21=24\) > remainder 0; \(n=7\) > \(n^21=48\) > remainder 0; \(n=11\) > \(n^21=120\) > remainder 0. Well it seems that all appropriate numbers will give remainder of 0. Sufficient. Algebraic approach:(1) n is not divisible by 2. Insufficient on its own, but this statement says that \(n=odd\) > \(n1\) and \(n+1\) are consecutive even integers > \((n1)(n+1)\) must be divisible by 8 (as both multiples are even and one of them will be divisible by 4. From consecutive even integers one is divisible by 4: (2, 4); (4, 6); (6, 8); (8, 10); (10, 12), ...). (2) n is not divisible by 3. Insufficient on its own, but form this statement either \(n1\) or \(n+1\) must be divisible by 3 (as \(n1\), \(n\), and \(n+1\) are consecutive integers, so one of them must be divisible by 3, we are told that it's not \(n\), hence either \(n1\) or \(n+1\)). (1)+(2) From (1) \((n1)(n+1)\) is divisible by 8, from (2) it's also divisible by 3, therefore it must be divisible by \(8*3=24\), which means that remainder upon division \((n1)(n+1)\) by 24 will be 0. Sufficient. Answer: C. 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? Extrahard Quant Tests with Brilliant Analytics



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1271
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: What is the remainder? (n1)(n+1) divided by 24 [#permalink]
Show Tags
31 Dec 2012, 21:18
Nadezda wrote: If n is positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r?
(1) is not divisible by 2 (2) is not divisible by 3 Statement 1) When n is not divisible by 2, then n can be \(1, 3, 5, 7, 9 etc\) For n=1, the remainder is 0 For n=3, the remainder is 16. For n=5, the remainder is 0. Different answers. Hence insufficient. statement 2) When n is not divisible by 3, then n can be \(1,2, 4, 6 etc\) Here also different remainders. Insufficient. On combining these two statements, n is \(1,5, 7 etc\) For such numbers, the remainder is 0. Sufficient. +1C
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Retired Moderator
Joined: 05 Jul 2006
Posts: 1734

Re: If n is a positive integer and r is the remainder when [#permalink]
Show Tags
12 Jan 2013, 03:34
kiyo0610 wrote: If n is a positive integer and r is the remainder when (n1)(n+1)is divided by 24, what is the value of r?
(1) n is not divisible by 2 (2) n is not divisible by 3 n1,n, n+1 are consecutive +ve intigers, and thus if n is even both n1,n+1 are odd and vice versa. also in every 3 consecutive numbers we get one that is a multiple of 3 from 1 n is odd thus both n1, n+1 are even and their product has at least 2^3 as a factor however if n = 3 thus n1,n+1 are 2,4 and since , 24 = 2^3*3 , thus reminder is 3 but if n = 5 for example thus n1,n+1 are 4,6 and therofre in this case r = 0.....insuff from 2 n is a multiple of 3 and thus both n1,n+1 are either even (e.g: n=3) or odd (n=6) and therfore this is insuff both together n is odd and is a multiple of 3 and therfore the reminder of the product (n1)(n+1) when devided by 24 is always 3..suff C



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: DS Problem : [#permalink]
Show Tags
25 Mar 2013, 21:02
vbodduluri wrote: If n is a positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r? a)n is not divisible by 2 b) n is not divisible by 3 A few things: 1. Exactly one of any two consecutive positive integers is even. 2. Exactly one of any three consecutive positive integers must be a multiple of 3 3. Exactly one of any four consecutive positive integers must be a multiple of 4 etc Check this post for the explanation: http://www.veritasprep.com/blog/2011/09 ... cormath/a) n is not divisible by 2 Since every alternate number is divisible by 2, (n1) and (n+1) both must be divisible by 2. Since every second multiple of 2 is divisible by 4, one of (n1) and (n+1) must be divisible by 4. Hence, the product (n1)*(n+1) must be divisible by 8. But if n is divisible by 3, then neither (n1) nor (n+1) will be divisible by 3 and hence, when you divide (n1)(n+1) by 24, you will get some remainder. If n is not divisible by 3, one of (n1) and (n+1) must be divisible by 3 and hence the product (n1)(n+1) will be divisible by 24 and the remainder will be 0. Not sufficient. b) n is not divisible by 3 We don't know whether n is divisible by 2 or not. As discussed above, we need to know that to figure whether the product (n1)(n+1) is divisible by 8. Hence not sufficient. Take both together, we know that (n1)*(n+1) is divisible by 8 and one of (n1) and (n+1) is divisible by 3. Hence, the product must be divisible by 8*3 = 24. So r must be 0. Sufficient. Answer (C)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Director
Joined: 17 Dec 2012
Posts: 635
Location: India

Re: DS Problem : [#permalink]
Show Tags
Updated on: 26 Mar 2013, 02:15
vbodduluri wrote: If n is a positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r? a)n is not divisible by 2 b) n is not divisible by 3 Given: (n1)(n+1) = 24m + r  (1) where m=1,2,3... Statement 1: n = 2w + x  (2) Statement 1 alone is not sufficient Statement 2: n= 3y + z  (3) Statement 2 alone is not sufficient. Taken together: 1. x has to be 1 and z can be 1 or 2 2. When x and z are 1, the values of n are 7, 13, 19 etc 3. When x=1 and z=2, the values of n are 5, 11, 17 etc 4. Substitute one of the above values, say 5 in (1) 5. For n=5 we have 4*6 = 24m + r or 24m +r = 24 r=0 We will get the same value of r for the other values of n too. Therefore answer is choice C.
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com/bestonlinegrepreparation.php
Improve Intuition and Your Score Systematic Approaches



Director
Joined: 26 Oct 2016
Posts: 666
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
31 Jan 2017, 17:12
1) n not divisible by 2=> n is odd=> (n1) and (n+1) must be consective even numbers. if n=1, 0*2/24 leaves remainder 0 if n=3, 2*4/24 leaves remainder 8 not sufficient 2) n not divisible by 3=> n can be even or 1, 5, 7, 11, 13.... if n=5, 4*6/24 leaves remainder 0 if n=2, 1*3/24 leaves remainder 3 not sufficient together, n must be odd and not divisible by 3=> n can be 1, 5, 7, 11, 13... if n=7, 6*8/24 leaves remainder 0 if n=11, 10*12/24 leaves remainder 0 hence C.
_________________
Thanks & Regards, Anaira Mitch



Intern
Joined: 03 Apr 2014
Posts: 2

If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
11 Sep 2017, 06:28
BunuelVeritasPrepKarishmaWhat if n=1? If so, (n1) will = 0. Please advise. Thank you.



Math Expert
Joined: 02 Sep 2009
Posts: 46305

Re: If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
11 Sep 2017, 06:32



Manager
Joined: 30 Jul 2014
Posts: 145
GPA: 3.72

Re: If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
14 Sep 2017, 03:01
By combining both the statement, we know that if a number is a prime number apart from 2, and 3, then it can be written in the form of (6n+1) or (6n1)  plugging these values, we get that (n1)(n+1) is always a multiple of 24; hence sufficient. Answer C.
_________________
A lot needs to be learned from all of you.



Manager
Joined: 30 Mar 2017
Posts: 117

Re: If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
02 Jun 2018, 18:09
Want to offer another approach when evaluating both statements together:
if n is not divisible by 2 and 3, then that means n is not divisible by 6. so we can express n as 6a+1 substituting into (n1)(n+1) > (6a)(6a+2) > 36a^2+12a > 12a(3a+1) If a is even, then 12a is div by 24 and thus (n1)(n+1) is div by 24 If a is odd, then (3a+1) is even and thus (n1)(n+1) is div by 24 In both cases, r=0
Answer: C



Manager
Joined: 14 Dec 2017
Posts: 224

Re: If n is a positive integer and r is the remainder when (n1) [#permalink]
Show Tags
15 Jun 2018, 08:30
enigma123 wrote: If n is a positive integer and r is the remainder when (n1)(n+1) is divided by 24, what is the value of r?
(1) n is not divisible by 2 (2) n is not divisible by 3
Given , n > 0, r is remainder when (n1)(n+1) is divided by 24, r = ? (n1)(n+1) is the product two consecutive even or odd integers, depending on whether n is odd or even. Statement 1: n is not divisible by 2 n = odd, then we have, for n = 3, (n1)(n+1) = (31)(3+1) = 8, hence r = 8 for n = 5, (n1)(n+1) = (51)(5+1) = 4*6 = 24, hence r = 0 Statement 1 alone is Not Sufficient. Statement: n is not divisible by 3. hence, for n = 5, we have from above r = 0 & for n = 8, we have (n1)(n+1) = (81)(8+1) = 7*9 = 63, hence r = 15 Statement 2 alone is Not Sufficient. Combining the two statements, we get, n is not divisible by 2 or 3 for n = 7, (n1)(n+1) = (71)(7+1) = 6*8 = 48, hence r = 0 for n = 11, (n1)(n+1) = (111)(11+1) = 10*12 = 120, hence r = 0 Both Statements together are Sufficient. Answer C. Thanks, GyM




Re: If n is a positive integer and r is the remainder when (n1)
[#permalink]
15 Jun 2018, 08:30






