GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Jun 2018, 17:04

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If n is a positive integer, and r is the remainder when

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 08 Dec 2012
Posts: 40
Re: GMAT PREP (DS) [#permalink]

Show Tags

New post 14 Sep 2013, 02:29
Bunuel wrote:
LM wrote:
Please explain the answer......


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.


another way of seeing it 4+7n = 3+6n +n+1; 3+6n is divisible by 3; n+1 is divisible by 3; so 4+7n is divisible by three.
Intern
Intern
User avatar
Status: Finance Analyst
Affiliations: CPA Australia
Joined: 10 Jul 2012
Posts: 16
Location: Australia
Concentration: Finance, Healthcare
Schools: AGSM '16 (A)
GMAT 1: 470 Q38 V19
GMAT 2: 600 Q44 V34
GPA: 3.5
WE: Accounting (Health Care)
Re: GMAT PREP (DS) [#permalink]

Show Tags

New post 11 Nov 2013, 19:02
Bunuel wrote:
LM wrote:
Please explain the answer......


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.



I am not sure if it has been asked/discussed before, but can we use the following approach:

re-write 4 + 7n as (3+1) + (6n + 1). now if we divide this by 3 we are left with (1) + (2n +1), which is essentially (2n + 2) ------> 2(n+1)/3 leaves no remainder or in other words 0 - using statement 1 information.

Please correct me if I this approach is incorrect.
_________________

Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light not our darkness that most frightens us.

Your playing small does not serve the world. There's nothing enlightened about shrinking so that other people won't feel insecure around you.

It's not just in some of us; it's in everyone. And as we let our own light shine, we unconsciously give other people permission to do the same.

As we are liberated from our own fear, our presence automatically liberates others.

—Marianne Williamson

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46035
Re: GMAT PREP (DS) [#permalink]

Show Tags

New post 12 Nov 2013, 02:03
vaishnogmat wrote:
Bunuel wrote:
LM wrote:
Please explain the answer......


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.



I am not sure if it has been asked/discussed before, but can we use the following approach:

re-write 4 + 7n as (3+1) + (6n + 1). now if we divide this by 3 we are left with (1) + (2n +1), which is essentially (2n + 2) ------> 2(n+1)/3 leaves no remainder or in other words 0 - using statement 1 information.

Please correct me if I this approach is incorrect.


4 + 7n = (3+1) + (6n + n) not (3+1) + (6n + 1).

You can solve (1) in another way: \(4 + 7n = 4 + 4n + 3n = 4(n + 1) + 3n\). First statement says that \(n + 1\) is is divisible by 3, thus \(4(n + 1) + 3n = (a \ multiple \ of \ 3) + (a \ multiple \ of \ 3)\). Therefore \(4 + 7n\) yields the remainder of 0, when divided by 3.

Hope it 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?
Extra-hard Quant Tests with Brilliant Analytics

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2730
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: If n is a positive integer, and r is the remainder when [#permalink]

Show Tags

New post 09 Apr 2016, 14:36
my approach
4+4n+3n
4+4n is divisible by 3
3n is divisible by 3
so r=0

2 alone can yield multiple answers. so no.
1 KUDOS received
Intern
Intern
User avatar
B
Joined: 26 Aug 2015
Posts: 35
Concentration: Strategy, Economics
GMAT 1: 570 Q40 V28
GMAT 2: 740 Q49 V41
Re: If n is a positive integer, and r is the remainder when [#permalink]

Show Tags

New post 06 Aug 2016, 08:28
1
I had a less algebraic approach, let me know what you think:

\(4+7n\) can be expressed in numbers where n is positive integer:

\(4+7(1) = 11\)
\(4+7(2) = 18\)

you get the idea.


Statement 1) \(n+1\) is divisible by 3:

So we should experiment with a few n+1's .... if \(n=2\), then \(n+1 = 3\) is divisible by \(3\).

\((4+(7*2)) / 3 = 18 / 3 = 6\) with \(0\) remainder.

if \(n = 5\), then \(n+1=6\) which is divisible by 3.

\((4+7(5))/3 = 39 / 3 = 13\) with \(0\) remainder. So with those 2 I assumed it is sufficient.

Statement 2) is clearly insufficient.

Greetings!
_________________

Send some kudos this way if I was helpful! :)!

Intern
Intern
avatar
Joined: 23 Sep 2015
Posts: 39
Re: If n is a positive integer, and r is the remainder when [#permalink]

Show Tags

New post 11 Oct 2016, 07:48
Bunuel wrote:
LM wrote:
Please explain the answer......


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.


is there any other method to solve this problem?? can we solve it by plugging in numbers?
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3638
Premium Member Reviews Badge CAT Tests
Re: If n is a positive integer, and r is the remainder when [#permalink]

Show Tags

New post 11 Oct 2016, 09:21
nishantdoshi wrote:
Bunuel wrote:
LM wrote:
Please explain the answer......


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.


is there any other method to solve this problem?? can we solve it by plugging in numbers?


I solved it by plugging in the numbers.

Statement 2 is clearly insufficient, so I am not discussing more on that.

Statement 1 : n+1 is divisible by 3. It means n is not going to be a multiple of 3. Also, n will be 1 less than the multiple of 3. Try taking the values of n as 2,5,8,20,23.

In all the cases, we will get the original expression a multiple of 3. or remainder, r = 0; hence A.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - Click here.



NEW VISA FORUM - Ask all your Visa Related Questions - Click here.



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Director
Director
User avatar
G
Joined: 26 Oct 2016
Posts: 666
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: If n is a positive integer, and r is the remainder when [#permalink]

Show Tags

New post 30 Jan 2017, 22:58
1) n+1 is a multiple of 3.

If n=2 (we're allowed to pick 2 since 2+1 is a multiple of 3), then (4+14)/3 = 18/3 = 6rem0
If n=5 (we're allowed to pick 5 since 5+1 is a multiple of 3), then (4+35)/3 = 39/3 = 13rem0

at this point you might already be conviced that you'll always get the same answer, but we could try one more just to be safe:

If n=8 (we're allowed to pick 8 since 8+1 is a multiple of 3), then (4+56) = 60/3 = 20rem0

For all 3 plug-ins we get r=0.. sufficient!

2) n > 20

If n=21, then (4+147)/3 = 151/3 = 50rem1
Insuff.

Hence A.
_________________

Thanks & Regards,
Anaira Mitch

Intern
Intern
User avatar
Joined: 24 Nov 2015
Posts: 18
Re: If n is a positive integer, and r is the remainder when [#permalink]

Show Tags

New post 15 Jul 2017, 14:33
"If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?"

In other words... find "r" when

\(r ≡ 7n + 4 (mod 3)\)

Which can be simplified to:

\(r ≡ 7n + 1 (mod 3)\)


Right away, we see a pattern:
When \(n = 1, r =2\).
When \(n = 2, r =0\).
When \(n = 3, r = 1.\) ...
And the pattern repeats over and over.


Statement A.)

"n+1 is divisible by 3"


In other words: \(n + 1 ≡ 0 (mod 3)\)

Which is equivalent to... \(n ≡ 2 (mod 3)\)

So since we now know "n," we can plug in its value of "2" for our original congruence...

\(r ≡ 7n + 1 (mod3)\)

\(r ≡ 7*2 + 1 (mod3)\)
\(r ≡ 15 (mod3)\)
\(r ≡ 0(mod3)\)


...and we find that the remainder is ZERO.

SUFFICIENT.




Statement B.)

"n>20"


Remembering our pattern from earlier (When \(n = 1, r =2\). When \(n = 2, r =0\). When \(n = 3, r = 1\)......etc)

Statement B is obviously insufficient. At values of "n" greater than 20, the value of "r" continues to cycle \(0,1,2,0,1,2,0,1,2.... etc\), so we have no idea what "r" is equal to without knowing a specific value for "n" (in mod 3).



Answer is A.
Intern
Intern
User avatar
B
Joined: 29 Aug 2017
Posts: 20
GMAT 1: 700 Q50 V33
Re: If n is a positive integer, and r is the remainder when [#permalink]

Show Tags

New post 22 Sep 2017, 10:46
jordanhendrix wrote:
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



or,
given that n+1 is divisible by 3
7n+4 = 7(n+1)-3 and because both 7(n+1) and 3 are divisible by 3, the remainder r = 0.
Re: If n is a positive integer, and r is the remainder when   [#permalink] 22 Sep 2017, 10:46

Go to page   Previous    1   2   [ 30 posts ] 

Display posts from previous: Sort by

If n is a positive integer, and r is the remainder when

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.