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 500,000 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:
If n is a positive integer, and r is the remainder when 4 + 7n is divided by 3, what is the value of r?
r is the remainder when 4n+7 is divided by 3 --> \(4+7n=3q+r\), where \(r\) is an integer \(0\leq{r}<3\). \(r=?\)
(1) n+1 is divisible by 3 --> \(n+1=3k\), or \(n=3k-1\) --> \(4+7(3k-1)=3q+r\) --> \(3(7k-1-q)=r\) --> so \(r\) is multiple of 3, but it's an integer in the range \(0\leq{r}<3\). Only multiple of 3 in this range is 0 --> \(r=0\). Sufficient.
(2) n>20. Clearly not sufficient. \(n=21\), \(4+7n=151=3q+r\), \(r=1\) BUT \(n=22\), \(4+7n=158=3q+r\), \(r=2\). Not sufficient.
Answer: A.
P.S. Please post DS questions in DS subforum. _________________
If n is an integer, and r is the remainder when 4+7n is divided by 3, what is the value of r?
r is the remainder when 4n+7 is divided by 3 --> \(4+7n=3q+r\), where \(r\) is an integer \(0\leq{r}<3\). \(r=?\)
(1) n+1 is divisible by 3 --> \(n+1=3k\), or \(n=3k-1\) --> \(4+7(3k-1)=3q+r\) --> \(3(7k-1-p)=r\) --> so \(r\) is multiple of 3, but it's an integer in the range \(0\leq{r}<3\). Only multiple of 3 in this range is 0 --> \(r=0\). Sufficient.
(2) n>20. Clearly not sufficient. \(n=21\), \(4+7n=151=3q+r\), \(r=1\) BUT \(n=22\), \(4+7n=158=3q+r\), \(r=2\). Not sufficient.
Answer: A.
P.S. Please post DS questions in DS subforum.
Thanks for detailed explanation. Sorry...in a haste I posted the DS questions in different forum. I will rectify this mistake next time onwards. Exam date is nearby ..so was in haste to get the explanations...thanks again..
You mentioned the \(0\leq{r}<3\) above, because remainder can't be more than the divisor. Is this correct?
i think i may have an easier way.... s1) 7n+4 = (6n+3)+(n+1) if (n+1)/3 = an integer, so must 3 times (n+1)....which is (6n+3) s2) Obviously NS _________________
i think i may have an easier way.... s1) 7n+4 = (6n+3)+(n+1) if (n+1)/3 = an integer, so must 3 times (n+1)....which is (6n+3) s2) Obviously NS
Little correction: 3 times (n+1) is 3n+3 not (6n+3).
But you are right, we can solve with this approach as well:
(1) n+1 is divisible by 3 --> \(7n+4=(4n+4)+3n=4(n+1)+3n\) --> \(4(n+1)\) is divisible by 3 as \(n+1\) is, and \(3n\) is obviously divisible by 3 as it has 3 as multiple, thus their sum, \(7n+4\), is also divisible by 3, which means that remainder upon division \(7n+4\) by 3 will be 0. Sufficient.
Re: Remainder Problem [#permalink]
30 Sep 2010, 21:51
The information in the statement A is used favorably to tweak the equation in the question.
Hence 7n+4 becomes 3(2n+1) + (n+1). Now since 3(2n+1) leaves a remainder 0 when divided by 3, the remainder of 7n+4 will be the same as the remainder of (n+1).
Since (n+1) is also given in option A to be divisible by 3, hence remainder 0. Statement A is sufficient. _________________
Support GMAT Club by putting a GMAT Club badge on your blog
Re: Remainder Problem [#permalink]
01 Oct 2010, 09:36
Michmax3 wrote:
shrouded1 wrote:
Michmax3 wrote:
Can you explain how you get to 7n+4=3(2n+1)?
Just trying to split it out into parts divisible by 3 7n becomes 6n+n 4 becomes 3+1
Thanks I see it now...btw is your avatar from the opening credits of Dexter?
YES !!
It took me a lot of time to erase the credits which were in deep red painted right across the face and still maintain a semblance of originality in the image .... _________________
If n is a positive integer, and r is the remainder when 4 + 7n i [#permalink]
26 Oct 2012, 04:47
A.
1) n+1 = 3 X (X is your Quotient) + 0(Remainder) n+1=3X Any Multiple of N+1 will be divisible by 3 Multiply by 7 --> 7(n+1) So 7n+7 is divisible by 3 , implies 7n+4 is divisible by 3.
Re: If n is a positive integer, and r is the remainder when [#permalink]
09 Aug 2013, 08:17
Q. What is r?
(1). (n+1) div by 3
By question stem we know that
4 + 7n = 3Q + r
Splitting the equation as below
4+4n+3n = 3Q + r
=> 3n + 4 (n+1) = 3Q + r
LHS is divisible by 3 as (n+1) is div by 3, so RHS should also be divisible by 3 hence r should be 0
(2).
4 + 7n = 3Q +r
Case 1: n=21
4 + 7*21 = 3Q +r
LHS gives 4 as remainder when divided by 3 so r=4
Case 2: n=22
4 + 7*22 = 3Q + r
No info about r, hence inconsistent
(A) it is! _________________
Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________
Re: If n is a positive integer, and r is the remainder when [#permalink]
12 Aug 2013, 10:31
As n is +ve, so to fulfill the condition that (n+1) is divisible by 3, n can be 2, 5, 8, 11, 14 and for these values, when (4+7n) is divided by 3, it leaves remainder 0 everytime. so (1) is sufficient.
(2) n>20 is not required as for 0<n<20, we get the same remainder as for n>20.
Correct me if this method is wrong.
gmatclubot
Re: If n is a positive integer, and r is the remainder when
[#permalink]
12 Aug 2013, 10:31
The “3 golden nuggets” of MBA admission process With ten years of experience helping prospective students with MBA admissions and career progression, I will be writing this blog through...
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...