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

It is currently 21 Feb 2019, 12:38

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 in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
  • Free GMAT RC Webinar

     February 23, 2019

     February 23, 2019

     07:00 AM PST

     09:00 AM PST

    Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

What is the remainder when integer n is divided by 3?

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53063
What is the remainder when integer n is divided by 3?  [#permalink]

Show Tags

New post 11 Jan 2017, 02:25
2
4
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (02:29) correct 49% (02:27) wrong based on 129 sessions

HideShow timer Statistics

What is the remainder when integer n is divided by 3?

(1) When 8n is divided by 3, the remainder is odd.
(2) When 5n is divided by 3, the remainder is odd.

_________________

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

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: What is the remainder when integer n is divided by 3?  [#permalink]

Show Tags

New post 11 Jan 2017, 03:05
1
2
Bunuel wrote:
What is the remainder when integer n is divided by 3?

(1) When 8n is divided by 3, the remainder is odd.
(2) When 5n is divided by 3, the remainder is odd.


3 has three remainders 0, 1 and 2 and only one of them is odd - 1.

We just need to solve linear congruences:

(1) 8n = 1(mod 3), 2n = 4(mod 3), n = 2(mod 3) Sufficient.

(2) 5n = 1(mod 3), 5n = 10(mod 3), n = 2(mod 3) Sufficient.

D.
Intern
Intern
avatar
B
Joined: 05 Mar 2017
Posts: 3
Re: What is the remainder when integer n is divided by 3?  [#permalink]

Show Tags

New post 10 Jun 2017, 09:57
vitaliyGMAT wrote:
Bunuel wrote:
What is the remainder when integer n is divided by 3?

(1) When 8n is divided by 3, the remainder is odd.
(2) When 5n is divided by 3, the remainder is odd.


3 has three remainders 0, 1 and 2 and only one of them is odd - 1.

We just need to solve linear congruences:

(1) 8n = 1(mod 3), 2n = 4(mod 3), n = 2(mod 3) Sufficient.

(2) 5n = 1(mod 3), 5n = 10(mod 3), n = 2(mod 3) Sufficient.

D.



VitaliyGMAT: Can you please explain the above modular operation??
Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: What is the remainder when integer n is divided by 3?  [#permalink]

Show Tags

New post 11 Jun 2017, 23:50
3
1
Hi

Linea congruencies and their systems is not the subject that can be thoroughly elucidated in just one post. Although addition, subtraction and multiplication are fairly straightforward, division requires taking into account common factor of a remainder, divisor and number itself. May be it wasn’t correct from my side to put such solution, because you don’t need linear congruencies to solve it.

Please refer to the following solution:

(1) When 8n is divided by 3, the remainder is odd.

In other words when 8n is divided by 3 the remainder is 1 (because 3 has only one odd remainder – 1).

Now: possible remainders are 0, 1 and 2.

(Remainder of 8) * (remainder of n) = 1.

The above equation can be achieved only in case when both 8 and n have same remainders 1 or 2 (1*1 = 1 or 2*2 = 4 = 1) Because 8 has remainder 2 upon division by 3, this leaves us with only one choice for the remainder of n – 2. Sufficient.

(2) When 5n is divided by 3, the remainder is odd.

Same logic for the second option. 5 has a remainder 2, hence n should also have remainder 2.

2*2 = 4 which has remainder 1 when divided by 3. Sufficient

Hope this helps and sorry for confusion.

Cheers

Vitaliy
Senior Manager
Senior Manager
User avatar
G
Joined: 06 Jul 2016
Posts: 365
Location: Singapore
Concentration: Strategy, Finance
GMAT ToolKit User Premium Member
What is the remainder when integer n is divided by 3?  [#permalink]

Show Tags

New post 12 Jun 2017, 09:06
Bunuel wrote:
What is the remainder when integer n is divided by 3?

(1) When 8n is divided by 3, the remainder is odd.
(2) When 5n is divided by 3, the remainder is odd.


S1 -> 8n = 3P + r, r = odd numbers
3 can only have 0,1,2 as remainders => r = 1.
To try, plug in numbers.
40 = 3*13 + 1
64 = 3*31 + 1... and so on.
Sufficient.

S2 -> 5n = 3Q + r, r = odd numbers
3 can only have 0,1,2 as remainders => r = 1.
To try, plug in numbers
10 = 3*3 + 1
25 = 3*8 + 1
Sufficient.

Therefore, Answer is D.
N = PQ + R => IMO, this question is testing the property wherein R < P.
_________________

Put in the work, and that dream score is yours!

SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 2068
Reviews Badge CAT Tests
Re: What is the remainder when integer n is divided by 3?  [#permalink]

Show Tags

New post 12 Jun 2017, 17:30
What is the remainder when integer n is divided by 3?

(1) When 8n is divided by 3, the remainder is odd.

The reminder is less the divisor. The only odd reminder possible is 1

8n = 3k + 1

Possible number of 8n:

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64

Green colored number gives Integer values for n as follows:

8n = 16....n=2.......Reminder when divided by 3 is 2

8n = 40....n=5.......Reminder when divided by 3 is 2

8n = 64....n =8.......Reminder when divided by 3 is 2

Always reminder is 2

Sufficient


(2) When 5n is divided by 3, the remainder is odd.

Use same numbers as above.

1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64

Green colored number gives Integer values for n as follows:

5n = 10....n=2.......Reminder when divided by 3 is 2

5n = 25....n=5.......Reminder when divided by 3 is 2

5n = 40....n =8.......Reminder when divided by 3 is 2

Always reminder is 2

Sufficient

Answer: D
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9880
Premium Member
Re: What is the remainder when integer n is divided by 3?  [#permalink]

Show Tags

New post 23 Oct 2018, 08:42
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: What is the remainder when integer n is divided by 3?   [#permalink] 23 Oct 2018, 08:42
Display posts from previous: Sort by

What is the remainder when integer n is divided by 3?

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


Copyright

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®.