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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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.

Re: +integer with remainder R [#permalink]
21 Jan 2012, 17:12

33

This post received KUDOS

Expert's post

16

This post was BOOKMARKED

enigma123 wrote:

If n is a positive integer and r is the remainder when (n-1)(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 (n-1)(n+1) is divided by 24, what is the value of r?

Plug-in method:

\((n-1)(n+1)=n^2-1\)

(1) n is not divisible by 2 --> pick two odd numbers: let's say 1 and 3 --> if \(n=1\), then \(n^2-1=0\) 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 \(n^2-1=8\) 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 \(n^2-1=0\), so remainder is 0 but if \(n=2\), then \(n^2-1=3\) 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: \(n=1\) --> \(n^2-1=0\) --> remainder 0; \(n=5\) --> \(n^2-1=24\) --> remainder 0; \(n=7\) --> \(n^2-1=48\) --> remainder 0; \(n=11\) --> \(n^2-1=120\) --> 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 \(n=odd\) --> \(n-1\) and \(n+1\) are consecutive even integers --> \((n-1)(n+1)\) 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 \(n-1\) or \(n+1\) must be divisible by 3 (as \(n-1\), \(n\), 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 \(n-1\) or \(n+1\)).

(1)+(2) From (1) \((n-1)(n+1)\) 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 \((n-1)(n+1)\) by 24 will be 0. Sufficient.

Re: What is the remainder? (n-1)(n+1) divided by 24 [#permalink]
31 Dec 2012, 20:18

3

This post received KUDOS

Expert's post

Nadezda wrote:

If n is positive integer and r is the remainder when (n-1)(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 _________________

Re: If n is a positive integer and r is the remainder when [#permalink]
12 Jan 2013, 02:34

1

This post received KUDOS

kiyo0610 wrote:

If n is a positive integer and r is the remainder when (n-1)(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

n-1,n, n+1 are consecutive +ve intigers, and thus if n is even both n-1,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 n-1, n+1 are even and their product has at least 2^3 as a factor however if n = 3 thus n-1,n+1 are 2,4 and since , 24 = 2^3*3 , thus reminder is 3 but if n = 5 for example thus n-1,n+1 are 4,6 and therofre in this case r = 0.....insuff

from 2

n is a multiple of 3 and thus both n-1,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 (n-1)(n+1) when devided by 24 is always 3..suff

If n is a positive integer and r is the remainder when (n-1)(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 ... c-or-math/

a) n is not divisible by 2

Since every alternate number is divisible by 2, (n-1) and (n+1) both must be divisible by 2. Since every second multiple of 2 is divisible by 4, one of (n-1) and (n+1) must be divisible by 4. Hence, the product (n-1)*(n+1) must be divisible by 8. But if n is divisible by 3, then neither (n-1) nor (n+1) will be divisible by 3 and hence, when you divide (n-1)(n+1) by 24, you will get some remainder. If n is not divisible by 3, one of (n-1) and (n+1) must be divisible by 3 and hence the product (n-1)(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 (n-1)(n+1) is divisible by 8. Hence not sufficient.

Take both together, we know that (n-1)*(n+1) is divisible by 8 and one of (n-1) and (n+1) is divisible by 3. Hence, the product must be divisible by 8*3 = 24. So r must be 0. Sufficient.

If n is a positive integer and r is the remainder when (n-1)(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:

(n-1)(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.

Re: If n is a positive integer and r is the remainder when (n-1) [#permalink]
13 Jan 2015, 14:00

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. _________________

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

McCombs Acceptance Rate Analysis McCombs School of Business is a top MBA program and part of University of Texas Austin. The full-time program is small; the class of 2017...