It is currently 18 Oct 2017, 05:00

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

When the positive integer x is divided by 9, the remainder

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

Hide Tags

1 KUDOS received
Director
Director
avatar
Joined: 10 Feb 2006
Posts: 660

Kudos [?]: 621 [1], given: 0

When the positive integer x is divided by 9, the remainder [#permalink]

Show Tags

New post 22 Nov 2007, 18:04
1
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (00:40) correct 13% (00:40) wrong based on 312 sessions

HideShow timer Statistics

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6
[Reveal] Spoiler: OA

_________________

GMAT the final frontie!!!.


Last edited by Bunuel on 20 May 2014, 01:00, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.

Kudos [?]: 621 [1], given: 0

1 KUDOS received
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1098

Kudos [?]: 141 [1], given: 0

Location: London
Re: MGMT - Remainder [#permalink]

Show Tags

New post 22 Nov 2007, 18:11
1
This post received
KUDOS
1
This post was
BOOKMARKED
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6


I could use the plug in no. approach but it's too time consuming. Please help.
thanks


X=9K+5

3X=3(9K+5)

then

(27K+15)/9
3K+15/9
15/9 ends with remainder 6.

E
also plug any number into K to test

Kudos [?]: 141 [1], given: 0

Director
Director
User avatar
Joined: 08 Jun 2007
Posts: 575

Kudos [?]: 109 [0], given: 0

Re: MGMT - Remainder [#permalink]

Show Tags

New post 22 Nov 2007, 18:32
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6


I could use the plug in no. approach but it's too time consuming. Please help.
thanks


6
Plugging is simple here.

x = 9k + 5
for k =1 x = 14
3x = 42 . Divide by 9 , you get remainder 6.
Same with k=2 and other k's

Kudos [?]: 109 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2007
Posts: 360

Kudos [?]: 35 [0], given: 0

Re: MGMT - Remainder [#permalink]

Show Tags

New post 22 Nov 2007, 20:50
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6


I could use the plug in no. approach but it's too time consuming. Please help.
thanks


Answer is 6

lets say the quotient is y.

So from the first part 9y+ 5 = x

so 3x = 27y + 15(remainder)

since 15 when divided by 9 gives you 6....

Kudos [?]: 35 [0], given: 0

SVP
SVP
User avatar
B
Joined: 05 Jul 2006
Posts: 1750

Kudos [?]: 430 [0], given: 49

GMAT ToolKit User
Re: MGMT - Remainder [#permalink]

Show Tags

New post 02 Dec 2007, 03:40
[quote="alimad"]When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6


x= 9k+5 ie: 3x = 27k+15, 27k+15 / 9 = a reminder of 15-9 = 6

Kudos [?]: 430 [0], given: 49

Intern
Intern
avatar
Joined: 29 Apr 2011
Posts: 25

Kudos [?]: 3 [0], given: 0

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

Show Tags

New post 29 Apr 2011, 22:47
plug in nos.

Let x = 14, 23, 32
x/9
Reminder is 5

Let 3x = 3*14, 3*23, 3*32
3x/9
Reminder is 6

Kudos [?]: 3 [0], given: 0

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1598

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

Show Tags

New post 29 Apr 2011, 23:32
x= 9k + 5

=> 3x = 27k + 15

=> 3x = 27k + 9 + 6

=> 3x/9 = 9(3k + 1)/9 + 6/9

So remainder is 6


Otherwise, just take 5 as an example :

So 5/9 = remainder 5

15/9 = remainder 6

Answer - E
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 592 [0], given: 36

VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1285

Kudos [?]: 281 [0], given: 10

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

Show Tags

New post 29 Apr 2011, 23:35
x = 9 * q + 5
3x = 27 *q + 15

15-9 = 6. Hence the remainder is 6. Which is less than 9.

If suppose
x = 9 *q + 7
3x = 27 * q + 21

Remainder will be 21-9*2 = 3.
Hope this will help you.

E.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Kudos [?]: 281 [0], given: 10

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 726

Kudos [?]: 143 [0], given: 42

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

Show Tags

New post 30 Apr 2011, 15:07
i tried plugging in numbers

x = 9q+5

x = 14

3x = 42 = 36 + 6 = 9*4+6

remainder is 6.

Answer is E.

Kudos [?]: 143 [0], given: 42

Manager
Manager
avatar
Joined: 26 May 2013
Posts: 65

Kudos [?]: 38 [0], given: 243

Re: MGMT - Remainder [#permalink]

Show Tags

New post 19 May 2014, 20:56
Are we not supposed to reduce the fraction in such questions? I'm getting 2 as a remainder to this problem. I reduced 42/9 to 14/3 leaving 2 as the remainder. Please point out my error.

Thanks



yezz wrote:
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?
0

1

3

4

6


x= 9k+5 ie: 3x = 27k+15, 27k+15 / 9 = a reminder of 15-9 = 6

Kudos [?]: 38 [0], given: 243

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128688 [1], given: 12182

Re: MGMT - Remainder [#permalink]

Show Tags

New post 20 May 2014, 01:16
1
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Amit0507 wrote:
Are we not supposed to reduce the fraction in such questions? I'm getting 2 as a remainder to this problem. I reduced 42/9 to 14/3 leaving 2 as the remainder. Please point out my error.

Thanks


42 divided by 9 gives the reminder of 6. If you reduce 42/9 by 3 to 14/3, then the remainder you get dividing 14 by 3 is 2. The remainders are not the same which means that this approach is not correct. Actually the remainder will be 3 times as great (by the factor you reduced), so 6.

When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6

Approach 1:

When the positive integer x is divided by 9, the remainder is 5: \(x=9q+5\).

\(3x=27q+15\). Now, 27 is divisible by 9, so the remainder is obtained only by division 15 by 9. 15 gives the remainder of 6 upon dividing by 9.

Answer: E.

Approach 2:

When the positive integer x is divided by 9, the remainder is 5 --> let x=5. Then 3x=15. 15 divided by 9 gives the remainder of 6.

Answer: E.

Theory on remainders problems: remainders-144665.html

Units digits, exponents, remainders problems: new-units-digits-exponents-remainders-problems-168569.html

All DS remainders problems to practice: search.php?search_id=tag&tag_id=198
All PS remainders problems to practice: search.php?search_id=tag&tag_id=199


Hope this 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

Kudos [?]: 128688 [1], given: 12182

Intern
Intern
User avatar
Joined: 14 May 2014
Posts: 45

Kudos [?]: 51 [0], given: 1

Re: When the positive integer x is divided by 9, the remainder [#permalink]

Show Tags

New post 20 May 2014, 03:50
Lets take the number as x

when x is divided by 9 the remainder is 5 hence x can be written as

x=9k +5

Multiplying by 3 will give

3x = 27k + 15

we can also write
3x = 27k + 9 + 6

Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence E is the answer.
_________________

Help me with Kudos if it helped you "

Mathematics is a thought process.

Kudos [?]: 51 [0], given: 1

Intern
Intern
avatar
Joined: 23 Jul 2012
Posts: 6

Kudos [?]: 3 [0], given: 2

Re: When the positive integer x is divided by 9, the remainder [#permalink]

Show Tags

New post 26 May 2014, 08:41
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6


dividend = quotient * divisior + R
so, x = q * 9 + 5
so, q * 9 = x - 5

also, 3x = 9 * q + R
so, q * 9 = 3x - R

Thus, 3x - R = x - 5
so, R = 2x + 5

Now x cannot be 0 or a negative number (as its given that it is positive). Thus, whatever the answer is, its greater than 5.
As per the answer choices, only 6 is greater than 5. Thus we have answer as 6 (choice E).

Kudos [?]: 3 [0], given: 2

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16713

Kudos [?]: 273 [0], given: 0

Premium Member
Re: When the positive integer x is divided by 9, the remainder [#permalink]

Show Tags

New post 25 Mar 2016, 03:43
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

Kudos [?]: 273 [0], given: 0

Senior Manager
Senior Manager
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 408

Kudos [?]: 23 [0], given: 283

Re: When the positive integer x is divided by 9, the remainder is 5. What [#permalink]

Show Tags

New post 16 Oct 2016, 12:37
E is correct. Here's why:

From the prompt we can create the following equation:

x=9y+5

Now, let's say y = 0 --> then x = 5 --> plug this into 3x --> 3x = 15

15/9 = 1 Remainder 6

Kudos [?]: 23 [0], given: 283

Director
Director
User avatar
P
Joined: 05 Mar 2015
Posts: 964

Kudos [?]: 287 [0], given: 41

Re: When the positive integer x is divided by 9, the remainder [#permalink]

Show Tags

New post 16 Oct 2016, 13:03
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6

Attachments

22.png
22.png [ 8.67 KiB | Viewed 3417 times ]

Kudos [?]: 287 [0], given: 41

Math Forum Moderator
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3003

Kudos [?]: 1087 [0], given: 325

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: When the positive integer x is divided by 9, the remainder [#permalink]

Show Tags

New post 16 Oct 2016, 13:44
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6


Least possible number of x is 5

So, 3x = 15

\(\frac{15}{9}\) = Remainder 6

Hence correct answer will be (E) 6

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1087 [0], given: 325

Expert Post
SVP
SVP
User avatar
G
Joined: 08 Jul 2010
Posts: 1834

Kudos [?]: 2276 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: When the positive integer x is divided by 9, the remainder [#permalink]

Show Tags

New post 10 Jul 2017, 23:28
alimad wrote:
When the positive integer x is divided by 9, the remainder is 5. What is the remainder when 3x is divided by 9?

A. 0
B. 1
C. 3
D. 4
E. 6


*Test like approach:*
choose a number that satisfies the given constraint I'm. Remainder 5 when divided by 9.
Such number, x = 5, 14, 23 etc.

Choose smallest and find 3x
I.e. 3x= 15
Divide by 9 and check remainder = 6

*Point to learn*
A number when divided by 9 leaves remainder 5 will be of the form = 9a+5

I.e. x= 9a+5

Now 3x = 3(9a+5)= 27a+15

When 3x is divided by 9 then 27a is always divisible hence remainder will be obtained by getting the remainder when 15 is divided by 9

Answer : Remainder =6

Answer option E
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2276 [0], given: 51

Re: When the positive integer x is divided by 9, the remainder   [#permalink] 10 Jul 2017, 23:28
Display posts from previous: Sort by

When the positive integer x is divided by 9, the remainder

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.